September 11, 2025 • 50 mins
Send us a text! (US messaging rates apply)
Have you ever felt like it's impossible to win an argument with someone, or even simply see eye to eye on anything? On today's episode, mathematician Eugenia Cheng joins Vanessa to challenge the black-and-white thinking that often defines our world - especially in math class.
3 Key Topics Discussed:
- Why seemingly silly questions like "is math real?" or "when does 1 + 1 not equal 2?" are both valid and valuable
- How Eugenia works to help people overcome math trauma the way she overcame ... sports trauma!
- How emphasizing context, creativity, and nuance - not just right or wrong answers - can help students develop more flexible and creative thinking
Show notes:
- Eugenia on The Late Show with Stephen Colbert
- Eugenia discussing viral "Is Math Real" TikTok on CBC Radio
About Eugenia Cheng: (Website, Twitter)
Dr Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist, composer and artist. Alongside her research and undergraduate teaching, her aim is to rid the world of “math phobia”. Her first popular math book, How to Bake Pi, was published by Profile (UK)/Basic Books (US) in 2015 to widespread acclaim including from the New York Times, National Geographic, Scientific American, and she was interviewed around the world including on the BBC, NPR and The Late Show with Stephen Colbert.
Connect with Math Therapy:
Shop the Math Therapy collection:
- paperback/ebook
- audiobook (US, Can, UK, Aus, Germany, or global)
- merch store
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Eugenia Cheng (00:02):
There are many situations where one plus one
can equal something else.
one plus one can equal zero.
For example, if you turn a pieceof paper over, and you turn it
over again, that's like havingturned it over zero times some
people say, oh, that doesn'tcount.
you can always say somethingdoesn't count.
But that's not what math does.
Math goes, this is interesting,let's study it.
The ultimate purpose of this isto stop closing off math.
(00:25):
Things are not as black andwhite And for some people that
horrifies them because that'sbeen their framework, that's
been their safety rails.
But for other people, it sparksthe curiosity that has
previously been squashed out andthat's why I want to bring it
back.
Vanessa Vakharia (00:42):
Hey guys, it's me, Vanessa, and we are back for
another episode of Math Therapy.
I have a question for you guys.
Have you ever felt like it'sjust impossible to win an
argument or like you just can'tconnect with someone you totally
disagree with, or, I don't know,maybe you have that friend,
family member or coworker whogets so stuck in their own way
of thinking that it feels likeyou can never find common
(01:04):
ground?
If that sounds familiar, you'regonna love today's episode.
Look, I am a Gemini, which meansI can always see both sides of
almost everything.
And honestly, it's a blessing,but it's also a curse because on
the one hand, it makes meempathetic and open-minded, but
on the other it leaves me torn,like, what's the right answer if
(01:24):
both sides always make sense.
And that's why I'm actually soexcited for today's guest.
Mathematician Eugenia Cheng isgoing to totally change the way
you think about right answers.
Her new book just came out lastweek, it's called Unequal, and
in it she argues that one plusone doesn't always equal two.
And I know that sounds wild, butI promise it's going to blow
(01:46):
your mind.
Eugenia is gonna help you seemath and the world in a whole
new way.
She's going to give youstrategies for embracing nuance,
for finding bridges in placesyou thought only walls existed.
And for teaching kids andourselves that math isn't about
memorizing right answers, it'sactually about thinking deeply
and seeing differently.
(02:07):
So if you've ever wished youcould connect more with someone
you disagree with, or if youwanna get better at finding
common ground in toughconversations, or if you wanna
learn how to bring more contextinto math class, this episode is
for you.
Let's get into it.
Eugenia.
Hello.
Welcome to the podcast.
Eugenia Cheng (02:25):
Thank you so much for having me.
I'm real excited.
Vanessa Vakharia (02:27):
I'm really, really excited.
So I've been a fan of yours foryears for a variety of reasons.
I will actually say the earliestone, which has nothing to do
with what we're gonna talkabout, but I remember there was
this TikTok that went viralbecause this girl asked what
math was and all these peoplewent on to troll her.
And then you sent the mostbeautiful response saying that
actually asking what math is isa very intelligent question and
(02:51):
not something we should bemaking fun of.
That was very cool.
Eugenia Cheng (02:55):
I got so many emotional responses to that from
people all around the world, andthat led to my previous book
actually, which was Is MathReal?
How Simple Questions Lead us toMathematics' Deepest Truths.
Vanessa Vakharia (03:09):
What did you tell this girl?
That she was like the inspo?
Eugenia Cheng (03:13):
I think that by the time it happened, she was so
over it.
I think she was just done withthe attention that this had got
her, and somebody tried tointerview her and ask her if she
knew about me and there was somekind of weird, she knew about me
because someone had made a videomaking fun of me and that was
that.
So I thought, you know what,maybe I'll just leave it.
Vanessa Vakharia (03:34):
Oh my God, that's so, but imagine, I love
how I was like, I don't wannatalk about this at all, but now
I'm like, wait a second.
Imagine this beautiful situationwhere this girl gets trolled for
being quote unquote dumb becauseshe asked what was considered a
dumb math question, but amathematician is like, this is
one of the most intelligentquestions, and now I'm gonna
write an entire book on it.
(03:56):
Like
Eugenia Cheng (03:56):
It was a whole series of questions that people
consider to be well, that peoplehave been told are stupid
questions.
But actually it's a really deepquestion.
Things like, why does one plusone equal two?
Which is a really deep question.
And so it unifies people who'vebeen put off math with research
(04:19):
mathematicians, because thoseare the two groups of people who
worry about that question.
And the people who don't worryabout that question are the ones
who are like, oh, math is easy.
I'm a math person.
Vanessa Vakharia (04:30):
Okay, well this actually kind of leads in
perfectly'cause we're gonna talkabout your new book, where I
believe one plus one equalingtwo is, is a hot topic.
Maybe.
Eugenia Cheng (04:39):
It's always a hot topic, and it's always
surprisingly divisive.
Vanessa Vakharia (04:45):
It's, it is very divisive and I can't wait
to discuss, but so that we allknow what we're talking about.
Your new book is called Unequal.
I mean, my first question is whynow?
Why was this the time to write abook about equality and fairness
and math?
Eugenia Cheng (05:00):
Well, it's just always a pressing question,
isn't it?
And I, unfortunately, this bookwas kind of catalyzed by an
absolutely terrible argument Ihad with someone that just went
worse and worse and worse.
And I'm not sure if I shouldreally say this because I'm
always saying, oh, math helps ushave better arguments.
And so I thought, I went intothis argument thinking, I'm not
(05:22):
going to, I'm not going to tryand, tell this person they're
wrong.
I'm going to find a point ofcommonality using math.
Uh, completely failed becausethis person was so far gone the
other way and was refusing toacknowledge that there is
anything ambiguous aboutequality and fairness.
And all I was trying to say was,well, we make decisions, don't
we, about what counts as equaland what, what fairness really
(05:45):
is in society?
And he was just like, no, wedon't.
Vanessa Vakharia (05:49):
Wait.
Eugenia Cheng (05:50):
don't get to decide what fairness means.
I get to decide what fairnessmeans.
And I just thought, oh no, thatdidn't go well at all.
Vanessa Vakharia (05:58):
Okay, hold on.
Can we, I need a little, can Iget a little more context?
Eugenia Cheng (06:02):
It was a long time ago actually, because books
take a long time to come intobeing, and it was about racism
and it was about what he wascalling affirmative action.
And I think there are differentthings that we can call it.
But he was basically saying thatwe shouldn't help anyone because
(06:23):
that's unfair.
Because nobody and his, it gotto the point where he was really
saying that, that nobody hasever been disadvantaged, so why
should we help anyone?
Vanessa Vakharia (06:34):
Ooh, that's a tough one to wade into.
Eugenia Cheng (06:37):
Yes.
And so I was, I thought I wasgoing to find some point of
agreement where we could agreeon at least somebody has been
disadvantaged in life and thatmaybe they deserve some help.
But it pushed him to the point,and I think that he didn't
really mean it, and that he justcouldn't bear to concede
anything to me.
So I didn't do very well becauseI, I, and I was really, I really
(06:57):
thought we could just agree onone person in the world who had
been disadvantaged by something.
Vanessa Vakharia (07:02):
Terry Fox.
Terry Fox,
Eugenia Cheng (07:05):
or, you know, someone who's, I don't know
whose parents served in a warand were killed and the baby was
born, we couldn't find anyone.
Vanessa Vakharia (07:13):
But what about being born like without limbs?
Eugenia Cheng (07:16):
Without limbs, without being able to anything,
he, he refused to concede thatanyone had any disadvantages.
And so we couldn't get anywhere.
And so then I thought.
I'll write a book about this.
Vanessa Vakharia (07:31):
it's funny you bring this up because just today
I was talking about with myfriend who's a therapist and we
were talking about this idea.
I feel like this is probablywhat this guy was doing even
though I was not there, like,I'm sure maybe you even know
what this phenomenon is called,but it's like when you believe
something, in order to preserveyour identity and value system,
you have to like double down onthat belief.
Otherwise it like threatens yourentire identity.
Eugenia Cheng (07:51):
Yes.
That, it's cognitive dissonance.
When the thing that you believeis being contradicted by some
other information and you can'tdeal with that dissonance, and
so you have to, in order toresolve the dissonance, you
either have to change what youthink, which is very hard if
you're attached to it or youjust have to squash out whatever
the other
Vanessa Vakharia (08:10):
The other thing is, and this is yeah, I,
that flat earthing documentary,have you ever seen that Flat
Earther documentary?
It was so fascinating becausethe guy kept getting evidence
that the earth was round.
And by the end, and I thoughtthis was very reflective of him,
he actually said, listen, likethe scientist was like, we've
like show all your experimentsare failing.
Like, and he goes, I cannotadmit the world is round because
(08:33):
I would lose all my friends.
My entire community's builtaround this, everything I do.
And he was basically like, Ican't, I can't entertain it
because my whole life would fallapart.
Eugenia Cheng (08:41):
Right, and I thought about this argument I
had with this guy for a reallylong time, way too long.
But this is what mathematiciansdo, right?
We think about the same thingfor a really long time and, and
I decided, my best guess is thathe feels that he has been
disadvantaged himself, butnobody's ever acknowledged it.
And because he's a white maleAmerican, he feels aggrieved
(09:04):
that he never gets to.
And so maybe if someone had justtaken him aside and went, I see
that you were disadvantaged inthese ways, here, have a hug or
something, now he probablydidn't want to hug, but
Vanessa Vakharia (09:17):
But I think you're onto something.
'cause that's actually kind ofhow I feel about math therapy
and when people like have such astaunch view of who can and
can't do math.
When you're simply like, Hey,listen, like, tell me about your
experience.
Like, oh man, that must havebeen hard.
Like people soften.
Eugenia Cheng (09:31):
Right, exactly.
Exactly.
What was it that caused thisperson to think this, it went,
goes back something, sosomething really deep.
Some experiences that they hadin very formative years and that
they can't give up on it nowbecause they've built their,
kind of personal narrative onthis.
And I understand that about mathprevious experiences, because I
had that about sport.
(09:53):
And in fact, a lot of what Iunderstand about other people's
math trauma comes from my sporttrauma, which I feel is quite
parallel and quite comparable.
Vanessa Vakharia (10:01):
Tell us.
Eugenia Cheng (10:02):
Well, when I was young, I did not play sport at
home with my parents becausethey were not sporty.
They were not into that.
They liked music and they likedreading and they liked math.
And so I did math at home withmy parents in the same way that
other people go into the parkand they, you know, hit a ball
around.
And so I couldn't throw, Icatch, I never ran, I couldn't
(10:24):
jump over things.
And so in all sports lessonsthrough my entire childhood, I
was so bad at it, so incrediblybad at it,'cause I'd never done
it before and everyone else wasahead.
And then, because I was good atacademic subjects, people liked
to make fun of me for when I wasbad at something.
And, and then the sportsteachers liked kind of
(10:47):
humiliating, not exactlyhumiliating, but they, but they
were so incredulous that anyonecould be this bad that they
often said things like, well youare obviously not trying because
there's no way you could betrying and still be this bad.
And so, of course, what did I dothen?
I stopped trying.
Because I was trying, I tried toget better at everything all the
(11:07):
time.
And I wanted to get better.
I didn't want to be terrible,and the last person chosen on a
team every time and everyonemakes fun of me.
And the kind of thing,especially in team sports, you
let the whole team down everysingle time.
And so I tried to get better,but once they said that, that I
didn't try anymore because ifthey were going to accuse me of
not trying, then I might as wellnot try.
But then I did what people dowith math as well, which is I
(11:30):
had to back up my own nottrying, by denigrating the
entire concept of sport.
Vanessa Vakharia (11:37):
So true.
This is such a, I'm, I'm, thisis, yeah.
Wow.
Eugenia Cheng (11:41):
And it took me years after leaving school to
realize that that was maybe notnecessary.
And I think that some of it,some of it I still believe in
because I still don't like thepart of sport that involves
trying to beat people.
And
Vanessa Vakharia (11:57):
Another parallel in my opinion.
Eugenia Cheng (11:58):
Right.
right.
And so I don't like the part ofmath that involves com
competitions in trying to beatpeople, and where people get
excited because they have beatbeaten somebody else.
I really, really, that makes mevery uncomfortable.
But I now am quite obsessed withplaying tennis, and so I have
got over it, and I only got overit in the last few years.
But honestly, when I, we foundsome free tennis courts in the
(12:21):
park near our house, and thefirst time my partner persuaded
me to go and play, I had a fullon panic attack, just like
people do with math, because Ithought, I'm gonna look like an
idiot.
Someone's gonna humiliate me,I'm gonna miss the ball.
We weren't even going to scoreor try and play a game, because
every time we try to, every timein my past when it's, there's
(12:41):
been a game with scores, I losejust always.
So what's the point?
I know I'm gonna lose.
There's no suspense.
There's no excitement.
I just lose.
And so I had this whole panicattack and I had to give myself
this giant pep talk saying, youknow, physical exercise is good
for us, especially as we getolder.
It's really important.
And anyone who makes fun of me,that's their problem.
(13:03):
At least I'm trying, at leastI'm trying to get better.
I'm making an effort.
I'm trying to be fit, you know,no one, if someone laughs at me,
then that shows that they're ahorrible person.
I, and then once I've got overthat and I've got, and I
realized that no one was goingto tell me I was bad, no one was
gonna humiliate me, that it isin fact good for me.
And I now appreciate that havingsome physical exercise is good
(13:24):
for me in the same way that I'vealways appreciated the
intellectual exercise is notonly good for me, but it's fun.
And so much so that, a yearlater, someone did make fun of
me, but I was okay because I'dgot over it.
Someone said the funniest thingto me, he came up to me and he
said he, he'd been watching meplay, and he said, I was
wondering if you'd like to playwith my daughter sometime.
she's 10 and she playscompetitively.
(13:46):
She plays competitively and sheplays with me, but, but I, I
think it'd be really good forher to play with someone who's
average or below
Vanessa Vakharia (13:53):
Oh my God.
Did you say yes?
I mean, I guess that could be acool opportunity.
Maybe she'd be an Olympian oneday.
Eugenia Cheng (14:02):
I don't, I didn't know.
I didn't know what to say andbecause I'm still conditioned to
be polite to people, I just kindof went.
Vanessa Vakharia (14:11):
Okay.
But this story, this is like alove story.
Like this is really givingrom-com because it's like you
have the like, oh my God, likeit sucked.
I was pushed out, dah, dah, dah.
And then you like come around,you finally try, you have the
breakdown, but then you get overit and you start seeing the
value in it.
And then again, that bully, the,the childhood bully comes back
(14:33):
in the form of a man asking youto play tennis with your
daughter.
And now you are healed.
It doesn't affect you.
But everything you've said is soparallel to math.
Even the whole idea of like, oh,if I was gonna score, if the
scoring happened, what was thepoint?
Right?
It's like, well, if grading'sgonna happen, what's the point?
And almost being like being ableto be like, well, I'm not doing
it to win the tennis match.
I'm doing it because physicalactivity is good and trying
(14:55):
something is good.
It's like
Eugenia Cheng (14:56):
Right, and it doesn't matter.
I don't need to compare myselfwith other people.
I just want to feel like I'mgetting better.
As long as I'm on a trajectorythat's getting better, it
doesn't matter what everyoneelse is doing because I'm not
trying to win Wimbledon orsomething.
Vanessa Vakharia (15:11):
Totally, but like, I guess like we're talking
about school I like, I'm like,yes, yes.
And then I'm like, well, it justkind of sucks because school is
kind of just designed that wayas like to,
Eugenia Cheng (15:19):
Yes.
Vanessa Vakharia (15:20):
you know, to sort of sort people.
So it's kind of hard to be
Eugenia Cheng (15:23):
Right.
And that was what my, uh,previous book of mine was about
X plus Y a MathematiciansManifesto for Rethinking Gender.
All about how one of the hugeproblems with how we present
math and who we keep in and whowe push out is because of how
competitive it is all the waythrough.
And so it appeals to people whohave a competitive nature, but
it also puts off people whodon't like the fact that they
(15:45):
got graded lower than someoneelse, or that they're humiliated
because, so they found it harderthan someone else.
Not to mention the fact thatoften the people who find it
harder.
Aren't worse at it.
They're just seeking a deeperunderstanding.
And that's what I always try tosay to, to people.
If you, if it takes you longer,if you feel like you don't
understand something, maybe it'sbecause you are seeking a deeper
(16:07):
understanding.
And the people who said they'veunderstood it, haven't
understood it more, they justweren't seeking as, as much
understanding.
Oh, an analogy just popped intomy head about, about about
eating.
So if you are full, it doesn'tmean that you ate more than
someone else.
Maybe you just had a smallerappetite.
Vanessa Vakharia (16:24):
That's good.
That's a good one.
Whereas like the person seekingthe deeper understanding,
they're not full yet.
They haven't gotten what theyneeded out of it.
Like that's it.
Okay, hold on.
So I wanna, I wanna say one morething before I get more into
your book.
But I actually have a questionabout what you were just talking
about, the competitive nature.
Like you saying that mathappeals to those with a
(16:45):
competitive nature.
And in your book,
Eugenia Cheng (16:48):
Well, math, math class.
Typical math education.
Yeah.
Vanessa Vakharia (16:52):
But here's my question.
Why is it that math educationappeals more to those with a
competitive nature as opposed toEnglish education, let's say.
Eugenia Cheng (17:04):
I think it's because it is presented it, it
is graded so quantitatively youcan really compare people with
other people.
And it doesn't have to be likethat.
It could be presented in a waythat is more like English, where
you, it's not just this personhas more points than somebody
else.
So if English essays were alljust, this is how right you
were, how right were you out ofa hundred then?
(17:28):
Then it would be much moreobvious that there was a scale
to compare people against.
But English, everyone kind ofknows that English, writing
English things isn't about howright you are.
And there are so many differentthings going on.
And so if we presented math.
In a way that was less aboutbeing right and wrong and more
about how much you haveexpressed this and taking a
situation in life and seeingwhat math we can find in it and
(17:51):
what we can, how we can use thatto illuminate our ways of
thinking.
Then it would be so much less athing where we could compare
everyone so directly and thenit, there wouldn't be so much
winning, losing, and humiliationinvolved.
I think.
Vanessa Vakharia (18:05):
Well, this is really making me think too,
that, you know, students likeknow everything.
They're like dogs.
Sorry, I'm not comparingstudents to dogs, just so
everyone's very clear on that.
Like they're very different.
But you know how people saylike, dogs are amazing, but
obviously I'm like, you know howdogs can like sense things,
Eugenia Cheng (18:23):
Mm-hmm.
Vanessa Vakharia (18:23):
can like sense energies in people before, like
even people can, I feel studentsare kind of like that.
They're like savvier than weever give them credit for.
So even if we're not publicly,you know, like we used to back
in the day, put their grades up.
Like my grades used to be up ona door.
Even if we're not doing that, Ithink you're right in the sense
that they know that they arebeing compared to other people
(18:44):
in this exact same way thatyou're talking about.
Things are being marked rightand wrong.
Some person next to'em got morethings right than they got
wrong, whatever, and that mustbe, it is for sure, such a key
part of math trauma formation isthat idea of like shame or
knowing you're being comparedto, it's like that causes so
much anxiety,
Eugenia Cheng (19:02):
Mm-hmm.
And, and it, but it, it's backedup.
It's kind of, played into by theidea that math is, has right and
wrong answers.
And so, the whole thing I'mtrying to say in my next book,
Unequal, it's the math of whenthings do and don't add up.
And it's, it's kind of subtlethat, because it's not that they
do or they don't, it's that theydo and they don't at the same
(19:23):
time.
And so things are equal andunequal at the same time So even
if we say, one plus one equalstwo.
There's something differentgoing on.
One of them is a one thing and aone thing, and the other one is
two.
It looks different.
The left and right of theequation are visibly different.
They're different.
And so there is always somethingthat's the same and different.
And we have decided what we'regoing to take into account.
(19:47):
And we make these decisions allthe time in math, but we usually
suppress them in math educationbecause we're trying to teach
people how to do it.
And so we say to them, this isequal.
We don't say, okay, here's howthey're not the same.
And so there was this incrediblyfrustrating memory I have when I
was an undergraduate, when I wasin a logic class and I didn't
(20:07):
understand, we, we were provingthat something or other was the
same as something or other else.
And um, and I didn't understandhow they were different.
And the tutor just kept sayingto me, well, that's the whole
point.
We are proving they're the same.
And I was like, yeah, but theremust be something different
about them.
Otherwise we wouldn't have toprove they're the same.
He's like, oh, but they're thesame.
Like so enraged.
Vanessa Vakharia (20:33):
Well that is, but hold on, you're kind of
blowing my mind.
'cause what you're saying is soobvious and so not obvious all
at once.
Like, I've never thought aboutthis.
Like, you're right.
Like why are you trying to provethey're equal if they're so
obviously equal?
There has to be some dispute.
So what's the dispute then?
Eugenia Cheng (20:51):
Right.
And that we hold those things inour brain at the same time,
which is an amazing thing to do,but we should realize we are
doing it.
And so there are all thesedifferent ways of thinking where
you can change your point ofview on what you are going to
accept as a difference and whatyou're going to be really picky
about.
And this is a really greattraining for our brain, if we
(21:12):
can bring it into ourconsciousness, because this is
what we should do in life withpeople as well.
Like, no, no, people aren't thesame as anyone else.
No one is the same.
And so if we're going to talkabout equality in life, which I
think we all should think aboutit, but, we shouldn't think
about equality because no one'sthe same.
What we are really thinkingabout is what differences we are
going to accept, and then wehave to take responsibility for
(21:32):
what we decide.
Vanessa Vakharia (21:34):
Okay, this is, this is wild because I get it
and then I don't get it, andthen I get it again, and then I
don't get it.
It's like at each point along,I'm assuming, tell me if I got
this wrong.
Along the decision makingprocess or at each, basically at
each specific juncture, you'rein that moment deciding what
differences actually matter andwhich don't.
Right?
Like, regardless of what we'retalking about, what point in
(21:55):
time, like, oh, I feel like I'vegot an analogy brewing.
Hold on, hold on.
Okay.
I feel like this is a, like Cokeand Pepsi are totally different,
but Right.
They're different.
Okay.
They're different things.
There's different tastes,whatever.
But like if I am at a bar thatonly serves a Pepsi product or a
Cola product, it's like the samething.
I'm just like, oh, I just wantlike a cola.
(22:16):
Like in that
Eugenia Cheng (22:17):
Yeah.
Yeah, exactly.
Great analogy.
Yeah.
Right.
But some people would be reallypicky and be like, no, I
absolutely do not want Pepsi inmy drink.
Vanessa Vakharia (22:27):
Yeah.
I, I would, I would only drink aCoke
Eugenia Cheng (22:29):
Mm.
Vanessa Vakharia (22:30):
Anyways.
That being said, unless it was adiet of Pepsi, it doesn't
matter.
Okay.
But, Okay.
I
Eugenia Cheng (22:34):
And there is no right and wrong answer
Vanessa Vakharia (22:35):
Well, that was my question.
because this is almost goingback to like that guy almost, I
don't wanna be that guy, but I'mlike, well, who, when do we, who
gets to, and I don't, I, I, Idon't think it's a who, but
like, how do we know when adifference is important or not?
Eugenia Cheng (22:51):
That's an amazing question.
And that's what I think isreally at the heart of math.
It's not about this is the rightanswer, this is the wrong
answer.
It's not about this person'sbetter, that person's better.
It's not about what's the answerto this thing.
It's about how are we going todecide what matters?
And math is not usuallypresented as being a system of
(23:13):
deciding how we think about
Vanessa Vakharia (23:16):
Like, it's not democratic.
Eugenia Cheng (23:18):
Well.
That's a whole different thing.
But math has a framework.
So all subjects have a frameworkfor how they're going to decide
things, and math has a frameworkfor deciding things, but each,
each field of math comes up witha different notion of what's
going to count as the same forthose purposes.
And there are reasons behind it,but in the end there aren't that
(23:40):
many, there aren't that manyreasons something would be a bad
choice.
So there are some reasons Imight go into them in the book.
So there are things like that,they're kind of technical.
So if something is gonna countas the same as something else,
then there are things like,there's reflexivity, which means
everything should count as thesame as itself and so then
there's symmetry, which is thatif a counts as the same as B,
(24:01):
then B should count as the sameas A.
Then there's transitivity, whichis about whether we can build up
long strings of these arguments.
So if A is the same as B and Bcounts the same as C should A
count as the same as C,probably.
But there are situations wherethat doesn't, that's not true
either.
Vanessa Vakharia (24:16):
Okay.
I have to tell you, this isbringing back a core memory of
me at 12 years old where I wrotethis poem and the poem was, oh
my God, I have not even thoughtabout this in so long, but maybe
this is gonna be the momentwhere I finally understand this.
I said, nothing is something,and everything is also
(24:39):
something.
Hold on.
I had I, I, it was somethinglike that.
It was like If nothing issomething and everything is also
something, then is everythingnothing.
And nothing is everything.
Like, do you know what I mean?
that's
Eugenia Cheng (24:50):
Mm-hmm.
Mm-hmm.
Yeah.
You were thinking abouttransitivity.
Vanessa Vakharia (24:54):
So in that case, is that true?
Is something nothing because'cause nothing is something
Eugenia Cheng (24:59):
Mm-hmm.
Vanessa Vakharia (25:00):
So is something nothing.
Eugenia Cheng (25:02):
Well, it, I don't think"is", is necessarily
symmetric
Vanessa Vakharia (25:07):
Oh,
Eugenia Cheng (25:09):
and because, and this is why in math, we use
language very carefully.
Whereas in normal life, we uselanguage a little less
carefully.
And that's one of the thingsthat can make math frustrating
because we use the same words,but we use them differently.
And so to make that more precisein math language, we might say
nothing is an example ofsomething.
Vanessa Vakharia (25:32):
Nothing is an example of something.
True.
But I guess now we're, it's notreally transitivity.
Eugenia Cheng (25:39):
Now it's cl, now it's symmetry and it's, it's
clearer.
It's clearer that it doesn'twork backwards because there are
way more things that aresomething than nothing.
So nothing is a thing.
There are way more things.
So not all something are anexample of nothing.
Vanessa Vakharia (25:54):
This is so cool.
Like, this is like such a,because we are talking about
math, but I've always believed,and I feel like this has always
been your vibe because you makemath so human and, and this book
kind of is, yes, it's math, butit's a way of understanding
nuance, right?
Especially in a world wherelike, it almost seems like we're
(26:15):
so focused on our differencesnow.
Like.
This feels like a way to almost,be able to see that we all have
at least one thing in commonwith someone.
Am I like taking it too far?
Eugenia Cheng (26:27):
No, that's, that's right.
And I think that it is stillimportant.
I'm not saying we shouldn't seeour differences at all, because
it's also important to see ourdifferences, especially when we
think about our pastexperiences.
So we've all had pastexperiences that are really
different, and that often playsa really crucial part in why we
are the way we are now.
Just as we were talking aboutwith the arguments we've had
(26:47):
with people and we think, wait,what in your past experience led
take this position?
And so I think it's alsoimportant to understand those
differences, but also to, to nottake those beyond where is
necessary.
So we can think about people'spast experiences and think about
how that affects how they behavenow and where they are now and
(27:08):
where they have got to.
But then we don't need to go,oh, well this means you can't
have this job
Vanessa Vakharia (27:12):
Mm-hmm.
Eugenia Cheng (27:13):
that, or the fact that the fact that you've cut
your hair short.
Does that matter for this job?
Well, it depends whether you aretrying to play somebody's body
double.
So I, I was talking about howfor a job, it shouldn't really
matter what you look like unlessyou are playing someone's body
double.
Vanessa Vakharia (27:29):
Right.
Can you tell me about one plusone equaling two?
What's, what's the hot topic?
What's the debate like?
Is there a world where theydon't equally each other?
Like where can we
Eugenia Cheng (27:38):
Yeah, there are many worlds where it doesn't
equal two, and mathematiciansall know this, but then people
who think of themselves as mathpeople sometimes get so angry
that we've changed the rules orwe've, we, that this isn't real
math or some kind math or this,yeah, exactly.
(27:58):
It's some kind of woke math thatlets more people in.
Oh no, we've let more people inthan we did before.
But there are many situationswhere one plus one can equal
something else.
So, one plus one can equal zero.
For example, if you turn a pieceof paper over, and you turn it
over again, that's like havingturned it over zero times
Vanessa Vakharia (28:16):
What?
Pause.
Hold on.
Let me just really observe this.
If you turn.
Eugenia Cheng (28:21):
a piece of paper over, and then turn it over
again.
It's like having turned it overzero times.
Vanessa Vakharia (28:28):
Okay.
Eugenia Cheng (28:30):
And so some people say, some people say, oh,
that doesn't count.
Vanessa Vakharia (28:33):
I was about to say that doesn't count!
Eugenia Cheng (28:38):
And the thing is, that's a valid answer, but it's
not the one mathematicians give.
Mathematicians go, well, that'san interesting scenario.
Let's model that with a world.
And so we get the Integers Modtwo, where every time you do
something twice, it goes back tozero.
And so you can always saysomething doesn't count.
But that's not what math does.
(28:58):
Math goes, this is interesting,let's study it.
Vanessa Vakharia (29:02):
So why am I, let me see why I'm having the
reaction that it doesn't count.
Because I think I'm like oneplus one.
That means we're adding twothings together.
Is me flipping a piece of paperover once and flipping it over
again.
It doesn't feel like addition tome.
Why is that?
Eugenia Cheng (29:20):
Because addition is usually presented in a very
restricted context.
Because it's often presented inthe context where it has to
equal two, because we're nottrying to let in the possibility
of other things.
But then there will be somechild in the class who's like,
I've turned my piece of paperover again, and now it's the
same way up.
Now what?
(29:40):
And so another of my favoriteones is when you press a button,
when you call an elevator, youpress the button and then
someone else comes along and youknow that thing where you've
already pressed it and it'silluminated and someone else
comes along and presses itagain.
Vanessa Vakharia (29:53):
Me, I'm the second person.
Eugenia Cheng (29:54):
You are the second person, right.
So, well, maybe we're having atheme here, so that does not
call two elevators.
Vanessa Vakharia (30:00):
Hold on.
You press the button.
Yeah, I got, I, I, yeah, but I'mnot, okay.
Yes, you're right.
You're right.
But I'm not seeing it as a, whyam I not seeing it as addition?
Eugenia Cheng (30:10):
I think because, you have been maybe trained to
think of only the naturalnumbers.
But mathematicians go, hmm,something's going on in this
situation, let's model thatsituation.
And so then there are placeswhere you can model one plus one
is two, and see what happens.
Vanessa Vakharia (30:27):
So here's my question.
The juicy question here is, sowhat do we do now?
What you're like, you know,we're in class the, the
teacher's teaching math, andthere's that kid that's like,
but I turned my paper overtwice, so one plus one does not
equal two.
But now we're in this classroomwhere the goal is they're
supposed to be getting two, youknow, in order to pass math
class or whatever, but they'renot wrong.
(30:50):
Now what happens?
Eugenia Cheng (30:51):
Well, so then you go that's a really great point,
that's a whole differentmathematical world.
Unfortunately, we don't havetime to study that world right
now because someone's decidedyou all have to pass this test.
But then maybe if we have someextra time at the end of the
week, then we'll investigatethat world.
Vanessa Vakharia (31:12):
It is really interesting because it's like we
we're in this kind of like veryinteresting place where, you
know, there's a lot of backlashagainst this idea of like, woke
math or like being like, we'reletting too many people in by
saying, all of a sudden there'sno right answers, everyone can
do whatever the fuck they want.
And it's like, that's not whatyou're saying here, but I almost
am curious what you would say tothose who are like, well, hold
(31:32):
on a second, you know, ifthere's no right answers in math
anymore and everything is thesame and it's different, like my
whole world is rocked.
Like how are they gonna passthis test?
How are I supposed, like what,what do you say to
Eugenia Cheng (31:42):
So I am not saying there are no right
answers.
Vanessa Vakharia (31:45):
Yeah.
Okay.
Let's clarify
Eugenia Cheng (31:46):
I'm saying that, I'm saying that math is a
framework for deciding what isgood information and that there
are many different possibleright answers in different
contexts.
That's the thing.
And so it's not that there's noright answers, it's that we
should be careful.
And so we might say, oh, that'stoo much for children.
And the thing is that if welimit in advance what we think
children can handle, then we arelimiting them.
(32:09):
And I don't want to limit them.
And children are usually capableof more than adults think
they're capable of.
Vanessa Vakharia (32:15):
Well, you know what else, this is making me
think.
I love how you just said that.
You said, the right answerdepends on the context,
basically, right?
Like whether one plus one equalstwo depends on the context.
And that kind of adds to thewhole idea of like, we should be
giving kids more context when weteach the math, right?
Like we often are just like,just do this thing.
And I'm not, I saying we as inlike traditionally,
(32:35):
historically, that's how mathhas been taught with very little
context.
And that's a complaint we hear alot, right?
Is like kids feel disengagedfrom it, disenchanted because
they don't like, there's nocontext to it.
So perhaps, you're kind ofadding more like oomph to the
reason why context is soimportant.
It's not only will they be moreinterested, but actually then
they have a deeper understandingof what they're learning.
(32:56):
And it leads to this whole ideaof nuance, which is one of the
most applicable skills in thereal world.
The ability to see that contextmatters.
Eugenia Cheng (33:04):
Yeah, exactly.
And this is the thing that ifyou, if you teach some rigid
thinking, some kids.
And they do really well at it,and they call themselves math
people and they will then defendit to the teeth, to the death
because they got all theirself-esteem from being good at
it.
But then, like you say, it's waymore applicable and transferable
to learn how to think well thanto learn some specific math
(33:27):
techniques.
And that if you learn somespecific math techniques that
help you pass a test, then allyou learn is how to pass that
test.
And I get it, and I'm notblaming teachers for this at
all, because teachers have theirhands really tied by all the
constraints that are put on themand how they are judged by what
their students do in thesetests.
But the whole system is theproblem.
(33:47):
And that that if we teacheveryone how to think, well,
then hopefully they can passtests and do more things as
well.
And so it's that much widerapplicability.
And too often applicability formath comes out to be things
like, oh, we shouldn't just doone plus one equals two.
We should go, if you go into astore and you buy eight
watermelons and then you, that'snot applicable at all.
(34:08):
That's just contriving some kindof thing that's gonna count as a
real world situation.
And like you said, students andchildren are very perceptive.
They can sniff that out frommiles away.
Vanessa Vakharia (34:19):
I always say like, I'm like, what's relevant
to kids doesn't mean like whatis on the planet we call Earth.
Like, oh, because you're addingan apple plus an apple.
Now it's relevant.
Like what's relevant to studentsis like, what's relevant to them
right now in their lives?
What's important to them rightnow?
And what's important right nowis exactly what you're talking
about, the idea of being curiousabout, Hey, I'm having all these
(34:42):
conversations with people, I'mhearing my parents talk about
things in the news.
Like this makes me wonder, like,is this really the same?
Is this really different?
Do these two differences betweenthese people matter?
Like that's relevant right now?
Eugenia Cheng (34:54):
But also whatever pops into their head is, is
what's relevant to them.
Because if you try and squashthat out, and the thing is, I
still have this problem when I'min a math talk or any kind of
talk, if something pops into myhead and isn't resolved, I can't
concentrate anymore because I'mtrying to resolve this thing in
my head.
And so I find it really hard toconcentrate in math talks
(35:16):
because if they're interesting,then something will pop into my
head and I try and resolve it.
And if they're not interesting,then I'm not interested.
So, and so if something popsinto, if something pops into
someone's, a child's head, andthey get told no, you're not
allowed to ask that question,and no, we can't do that now,
then they'll just lose interestbecause this thing is their
pressing question.
(35:36):
And so whether it is, why doesone plus one equal two, why
can't we divide by zero?
Or is infinity a number?
Or what happens if I cut thistriangle in half?
Is it two triangles or is ithalf a triangle and half a
triangle?
Now, whatever those questionsare is what is relevant to them
now.
Vanessa Vakharia (35:52):
It's so funny, like just listening to you talk.
I'm like, it's so wild that theidea of opening this up to like,
Hey, maybe one plus one doesn'talways equal two, and maybe we
should be looking at all thesedifferent angles to this
problem.
Instead of focusing on the rightanswer, that gets labeled as
like"dumbing math down".
Whereas what we're doing ismaking it like just, even just
(36:13):
hearing you talk about it, it'slike you're actually making it
so much richer and actually in asense, way more complex.
It's like the opposite ofdumbing down, right?
Like I'm just thinking about mesort of being like, but addition
is just compiling things, right?
And you're being so like niceand gentle and being like, oh
yes, perhaps you were taughtthat way, but, but I'm like, I'm
(36:33):
like, oh man, like I, I'm atrained high school math teacher
and I am having trouble beinglike, wait, how is flipping a,
I'm gonna really be thinkingabout how flipping a paper over
and, and flipping it back isactually addition.
Like, I'm all of a sudden inthis one hour together, my view
of addition is becoming so muchbroader and I'm really gonna
interrogate that.
(36:54):
Like, wow.
Eugenia Cheng (36:56):
Right, and again, there's no right answer.
The question is, does this wayof thinking help us?
Vanessa Vakharia (37:01):
Hmm.
Eugenia Cheng (37:02):
Does this open up some new avenue of thinking?
And that's what I always think.
It doesn't really, it's notreally a case of whether it's
right or wrong.
So some things are wrong.
There is definitely wronganswers in math.
If you contradict logic, thenyou are wrong.
But in terms of can we countthis as addition or not?
There are plenty of people whowill say, no, we shouldn't.
I'm like, well then you've, allyou've done then is you've
(37:23):
restricted your thinking, and Iprefer to expand my thinking.
Vanessa Vakharia (37:27):
Are there situations in which it does not
help to think this way?
Eugenia Cheng (37:32):
I, I'm going to guess yes, because there surely
is some example that we can comeup with.
I mean, I don't like makingsweeping statements, so if I
said this always helps us, thenI would feel very uncomfortable.
So yes.
So there are situations where wecould take it too far.
For example, if we think that$1and$1 doesn't make$2, then we
(37:53):
are gonna be in trouble with ourbank account.
And so we can't just make thingsup.
The other thing I like aboutthis approach is it gives
students some, uh, of their owncontribution into the
conversation.
So it's not telling them what todo, it's going, okay, can you
think of some other situations?
What do you think about thissituation?
What if you mix one color ofpaint with another color of
(38:14):
paint?
This was example that an artstudent of mine came up with
actually, and I loved it.
You don't get two.
If you mix
Vanessa Vakharia (38:21):
you don't get
Eugenia Cheng (38:22):
Yeah, you don't get two, you just get another
one.
Vanessa Vakharia (38:24):
You just get another one.
Eugenia Cheng (38:26):
The ultimate purpose of this is to stop
closing off math to people.
And, and what I would say, ifanyone is wondering about
specifics is that, if no onequestions why one plus one is
two, you don't have to go intoit.
But if someone does question it,and that's why it came up,
because it's one of the thingsthat people say, they say, why
does one plus one equal two?
And it's really hard.
(38:46):
And I think it's amazing.
We can think about it withoutreally thinking about it.
And sometimes there's a lot ofmath that you can do without
really thinking about it.
And then mathematicians sat downand went, wait, what even is
one, what is two?
We whole new field of math to dothis.
And then set theory was born andthen they had to do a whole load
of new definitions to go, whatis a number?
We didn't know?
Help.
Ah! And, and so that is where,that is why it is in fact very
(39:10):
deep.
And so if someone, the point forme is that if someone raised
this outta curiosity, it wouldbe to acknowledge that there is
a really good point in there andthat there are situations where
it doesn't equal two.
And my art students,'cause Iteach art students at the school
of the Art Institute now, almostall of them got put off math at
some point in the past.
And one of the things that putthem off was the fact that it
(39:31):
had rigid black and whiteanswers and they weren't allowed
to be creative.
And one of the first things I dois get them to just dream up
situations in which one plus onecan be something else.
And it's one of the first timesanyone has ever invited them to
dream in math class to dream upthings to create.
And that's what they want to do.
And sometimes they say, oh, wellI'm a creative person so I don't
like math.
(39:52):
And I go, wait.
That's just how math was taughtbefore.
And so I want to offerpossibilities for how you can be
creative in math class and tieit into things that really are
math.
Because all of those situations,it's not just semantics or woke
math or the girl math or dumbmath or dumbing it down.
They're all things, and I couldsay, you know, it's the integers
(40:12):
mod two or the integers modthree, or it's a, projection in,
in a monoid, or you know, they,they're all genuine things that
we study and we then we studywhat the behavior is and what
the consequences are.
And so it's just all to saythat, things are not as black
and white as they seem in math.
And for some people thathorrifies them because they're
(40:34):
clinging to those, that's their,that's been their framework,
that's been their safety rails.
But for other people, it sparksthe curiosity that has
previously been squashed out andthat's why I want to bring it
back.
Vanessa Vakharia (40:47):
It's, you know what is really making me think,
the thing that makes people themost uncomfortable is
uncertainty, right?
And ambiguity.
Because it's uncertain.
We want certainty.
So what's interesting is, whatyou're sort of talking about is
uncertainty adjacent, let's justsay, I've been thinking about
this a lot lately of just somany of the solutions to our
(41:08):
like quote unquote ailments,like whether health related,
where, whether it's mentalhealth, whether it's like
needing a new hair color, likewhatever it is, are targeted,
like advertising is targeted aslike, just get this thing and
you're gonna be sure that blah,blah, blah, blah.
Like it wants give you the surething.
And I think this really all tiesin because.
That's part of our nature is wewant security, we want
(41:29):
certainty.
We think certainty is gonna leadto security, et cetera, cetera.
So yes, this would make peopleuncomfortable.
But I think the other side ofthat is, I'm on a bit of a, a
tear here, but it's to circleback is the point is that
certainty isn't always better.
Right?
like,
Eugenia Cheng (41:45):
Right.
If it's wrong,
Vanessa Vakharia (41:46):
if it's wrong exactly.
Then not
Eugenia Cheng (41:48):
That is just wrong.
Right.
Vanessa Vakharia (41:50):
Or it's like, you know, again, like with the
food thing, I'm just thinking'cause like we're thinking of so
many food metaphors here.
I don't know why, like, itdoesn't mean that what I'm
eating isn't good, but itdoesn't mean there isn't
something I might like more, youknow what mean?
Like, and, and maybe I'm goingto be a bit uncomfortable and
try a few things that I don'treally like and then I'm gonna
find some food that I'm obsessedwith, like whatever it is.
But that is probably one of thelike spiritually and
(42:13):
philosophically and emotionallyand like cerebrally, like, in
order to really grow as people,what could be more beneficial
than learning to becomecomfortable with uncertainty at
an earlier age.
So you can try new things and beopen-minded.
Eugenia Cheng (42:27):
Right.
And it's not just uncertainty,it's also the context thing so
some things will be good in thiscontext and some things will be
good in this other context.
And it's like the fact whenpeople say, oh, this is good for
you.
Well, usually they did a studythat said it found it was good
for a certain percentage ofpeople on average overall.
Vanessa Vakharia (42:45):
Or if it's good, if you don't drink 10
glasses of it.
Eugenia Cheng (42:48):
well, exactly.
And so one example for me wasthe idea that, oh, physical
exercise to circle back to wherewe sort of started, physical
exercise is good for your mentalhealth.
Well, physical exercise wasn'tgood for my mental health when I
was just humiliated every time Idid it or I felt bad about
myself, or I had to go into agym where there were all these
muscle bros grunting anddropping their huge weights on
(43:10):
the floor and I didn't like thateither.
And so I had to find something.
But I liked.
And so it was much more helpfulfor me to go, okay, what
physical activity exists that Icould enjoy?
Rather oh, I should keep doingthis physical activity'cause
it's gonna be good for my mentalhealth.
And so realizing that there aredifferent contexts and then
there's also, at one point Irealized that if I was feeling
(43:32):
slightly bad, physical exercisewould make me feel worse.
If I was feeling slightly good,it would make me feel better.
And so it's these kind ofsubtleties that are much more
helpful for our personal lives,our own lives, as well as for,
it's not just about passingtests, it's about how are we
going to live as humans in acommunity?
How are we going to try to havebetter lives for ourselves and
(43:55):
the people that we care about?
Vanessa Vakharia (43:56):
Mm-hmm.
I love it.
I love this so much and yeah,I'm even like, now I'm like, are
ambiguity and uncertainty thesame thing?
I don't think so.
They're not, they're not quitethe same.
So like I'm kind of went on abig uncertainty tear, but I
think I'm more talking aboutbeing ambiguous, where there's
no one right answer, it iscontext dependent, which can
(44:20):
feel ambiguous when contextisn't part of the convo.
Eugenia Cheng (44:23):
Yes, exactly.
So sometimes it's not actuallyambiguous, it's just that we
didn't specify our contextclearly enough, and that's what
made it ambiguous.
And math is a really amazingdiscipline for clearing all
those things up so that we canbe much more precise about what
we mean, and hopefully we can bemuch more precise about what
other people mean, even if theydon't realize it themselves, and
(44:44):
then we can all reach a betterunderstanding of each other.
Vanessa Vakharia (44:48):
I cannot wait to read this book.
Okay, so we, we have to wrap upbut like I could talk to you for
10 years.
Um, this is just so fascinating.
And I mean, by the time thiscomes out, your book will have
just come out, but I wanteveryone to know that the
release date is September 2nd.
And Eugenia just found out thatthat is Keanu Reeves' birthday.
(45:11):
And how do you feel about that?
He is an angel among us.
Eugenia Cheng (45:15):
Yes.
Vanessa Vakharia (45:16):
Like, right, like
Eugenia Cheng (45:17):
Yes.
I mean, I've heard that he isjust such a nice person.
And Yeah.
And it wouldn't it be great ifeveryone was a nice person?
Vanessa Vakharia (45:25):
Well, I mean, it would be so great I think
that he would love this book,quite frankly.
Um, so it's coming out onSeptember 2nd, which is the
anniversary of my book that cameout last year on September 2nd.
So we both share Keanu Reeve'sbirthday book release in common.
So everyone go grab it.
It's gonna be out by the timethis comes out.
Um, if there was, if there was ateacher listening to this, and
they were like, oh, I love thisso much, what's one way I could
(45:47):
like bring this whole context,like equal, unequal, same but
different thing into classtomorrow.
Is there like a little thingsomeone could do?
Eugenia Cheng (45:55):
I think just pointing out what is unequal
about something.
If you are presenting anequation, whatever it is
pointing out, focusing on thefact that it's different and the
same at the same time, andcongratulating everyone if they
can hold both of those things intheir brain together.
Vanessa Vakharia (46:11):
I love that.
I really love that idea of beingable to hold both of those
things in our brains.
I feel we're really, um, part ofthe reason there's a whole like
war between creativity and mathis because we like, live on
binaries.
Like it has to be one thing orthe other.
Like, do you know what I mean?
Like, you're either acheerleader or you're good at
math.
Never seen a movie with both.
Like it's one or the other.
You know what I mean?
So being able to hold boththings in our mind, first of
(46:34):
all, allows us all to bring ourfull selves everywhere, right?
To not feel like we have to fitinto a mold.
Eugenia Cheng (46:39):
Yes.
Vanessa Vakharia (46:41):
I just love it.
Okay.
Are you ready for the final twoquestions?
Question number one, if you weregonna pick one thing to change
about the way math class istaught, what would it be?
Eugenia Cheng (46:51):
Uh, no grades
Vanessa Vakharia (46:54):
There it is.
No grades at all, ever.
Eugenia Cheng (46:57):
Ever.
Vanessa Vakharia (46:58):
We're gonna have to do a whole other episode
on this.
Okay?
No grades ever.
And question number two is ifsomebody listened to all of this
and they were like, no, I getwhat you're saying.
Like, awesome.
The thing is, I'm just not amath person.
How would you respond?
Eugenia Cheng (47:15):
I would quote the dedication of my previous book,
which is if you've been made tofeel that you are bad at math,
you didn't fail math, mathfailed you.
Vanessa Vakharia (47:24):
Oh my God, I love that.
I love it.
You're so cool.
Eugenia Cheng (47:31):
Oh, thanks.
This was so fun.
I do feel like we could justkeep talking for years.
Vanessa Vakharia (47:35):
We, I mean, the metaphors we could come up
with.
I can't even imagine.
We'd get, I think things wouldget weird, but I'd be down.
Um, okay.
Thank you so much.
I can't wait to read this book.
I can't wait for everyone toread it.
There's been so much amazingstuff in here.
It's really got me thinking, andI'm gonna go leave right now and
start thinking of all the waysthat one plus one does not equal
two.
I'm like looking around me.
(47:55):
I'm like, I don't even, it'shere.
It's among, it's among us.
Eugenia Cheng (47:59):
Yeah, right.
It walks among us.
Vanessa Vakharia (48:00):
It walks among us.
Thank you so much,
Eugenia Cheng (48:02):
Thank you so much.
That was great.
Vanessa Vakharia (48:05):
Bye.
Eugenia Cheng (48:06):
Bye.
Vanessa Vakharia (48:09):
Okay, I don't know about you guys, but my mind
is spinning.
One plus one not always equalingtwo is going to live in my brain
forever, and I, I still need tothink about it.
But more importantly, Eugeniareminded us that context and
nuance change everything, inmath, in conversations and in
how we see each other.
Okay, so now it's time for yourMath Therapy challenge this
(48:31):
week.
I want you to think of onerelationship or conversation
where you and someone else feelmiles apart.
Instead of asking who's right,ask what's the context and
where's our common ground?
And if you're a teacher, I wantyou to take this into the
classroom.
Think of one lesson this weekwhere you can invite your
students to notice nuance, wherethe answer isn't just about
(48:52):
being right or wrong, but aboutthe thinking and the context
behind it.
And don't keep this episode toyourself.
I want you to send it to thatfriend, that family member, or
that colleague who often getsstuck in black and white
thinking.
Honestly, it might change theway they think, and the way you
two talk.
I always wanna hear from you.
So if something in this episodeinspired you, you can now text
(49:15):
the podcast, it's a new feature,the link to text us is right in
the show description of yourpodcast app.
You can also DM me on Instagram@themathguru, or email me at
vanessa at themathguru dot ca.
And remember, Math Therapy isnow a weekly podcast, so make
sure you're subscribed so youdon't miss an episode.
A new one is coming your waynext week and the week after
(49:36):
that, and the week after that,and you get the picture.
Math Therapy is hosted by me,Vanessa Vakharia.
It's produced and edited byDavid Kochberg, and our theme
music is by our band GoodnightSunrise.
And guys, if you know someonewho needs Math Therapy, please
share this podcast rate orreview it on whatever podcast
app you use, because thosethings make a huge difference.
(49:58):
I'm so determined to change theculture surrounding math, and I
know you are too, and we allneed to help each other out.
So spread the word and untilnext time, peace, love, and pi.
There are many situations where one plus one
can equal something else.
one plus one can equal zero.
For example, if you turn a pieceof paper over, and you turn it
over again, that's like havingturned it over zero times some
people say, oh, that doesn'tcount.
you can always say somethingdoesn't count.
But that's not what math does.
Math goes, this is interesting,let's study it.
The ultimate purpose of this isto stop closing off math.
(00:25):
Things are not as black andwhite And for some people that
horrifies them because that'sbeen their framework, that's
been their safety rails.
But for other people, it sparksthe curiosity that has
previously been squashed out andthat's why I want to bring it
back.
Vanessa Vakharia (00:42):
Hey guys, it's me, Vanessa, and we are back for
another episode of Math Therapy.
I have a question for you guys.
Have you ever felt like it'sjust impossible to win an
argument or like you just can'tconnect with someone you totally
disagree with, or, I don't know,maybe you have that friend,
family member or coworker whogets so stuck in their own way
of thinking that it feels likeyou can never find common
(01:04):
ground?
If that sounds familiar, you'regonna love today's episode.
Look, I am a Gemini, which meansI can always see both sides of
almost everything.
And honestly, it's a blessing,but it's also a curse because on
the one hand, it makes meempathetic and open-minded, but
on the other it leaves me torn,like, what's the right answer if
(01:24):
both sides always make sense.
And that's why I'm actually soexcited for today's guest.
Mathematician Eugenia Cheng isgoing to totally change the way
you think about right answers.
Her new book just came out lastweek, it's called Unequal, and
in it she argues that one plusone doesn't always equal two.
And I know that sounds wild, butI promise it's going to blow
(01:46):
your mind.
Eugenia is gonna help you seemath and the world in a whole
new way.
She's going to give youstrategies for embracing nuance,
for finding bridges in placesyou thought only walls existed.
And for teaching kids andourselves that math isn't about
memorizing right answers, it'sactually about thinking deeply
and seeing differently.
(02:07):
So if you've ever wished youcould connect more with someone
you disagree with, or if youwanna get better at finding
common ground in toughconversations, or if you wanna
learn how to bring more contextinto math class, this episode is
for you.
Let's get into it.
Eugenia.
Hello.
Welcome to the podcast.
Eugenia Cheng (02:25):
Thank you so much for having me.
I'm real excited.
Vanessa Vakharia (02:27):
I'm really, really excited.
So I've been a fan of yours foryears for a variety of reasons.
I will actually say the earliestone, which has nothing to do
with what we're gonna talkabout, but I remember there was
this TikTok that went viralbecause this girl asked what
math was and all these peoplewent on to troll her.
And then you sent the mostbeautiful response saying that
actually asking what math is isa very intelligent question and
(02:51):
not something we should bemaking fun of.
That was very cool.
Eugenia Cheng (02:55):
I got so many emotional responses to that from
people all around the world, andthat led to my previous book
actually, which was Is MathReal?
How Simple Questions Lead us toMathematics' Deepest Truths.
Vanessa Vakharia (03:09):
What did you tell this girl?
That she was like the inspo?
Eugenia Cheng (03:13):
I think that by the time it happened, she was so
over it.
I think she was just done withthe attention that this had got
her, and somebody tried tointerview her and ask her if she
knew about me and there was somekind of weird, she knew about me
because someone had made a videomaking fun of me and that was
that.
So I thought, you know what,maybe I'll just leave it.
Vanessa Vakharia (03:34):
Oh my God, that's so, but imagine, I love
how I was like, I don't wannatalk about this at all, but now
I'm like, wait a second.
Imagine this beautiful situationwhere this girl gets trolled for
being quote unquote dumb becauseshe asked what was considered a
dumb math question, but amathematician is like, this is
one of the most intelligentquestions, and now I'm gonna
write an entire book on it.
(03:56):
Like
Eugenia Cheng (03:56):
It was a whole series of questions that people
consider to be well, that peoplehave been told are stupid
questions.
But actually it's a really deepquestion.
Things like, why does one plusone equal two?
Which is a really deep question.
And so it unifies people who'vebeen put off math with research
(04:19):
mathematicians, because thoseare the two groups of people who
worry about that question.
And the people who don't worryabout that question are the ones
who are like, oh, math is easy.
I'm a math person.
Vanessa Vakharia (04:30):
Okay, well this actually kind of leads in
perfectly'cause we're gonna talkabout your new book, where I
believe one plus one equalingtwo is, is a hot topic.
Maybe.
Eugenia Cheng (04:39):
It's always a hot topic, and it's always
surprisingly divisive.
Vanessa Vakharia (04:45):
It's, it is very divisive and I can't wait
to discuss, but so that we allknow what we're talking about.
Your new book is called Unequal.
I mean, my first question is whynow?
Why was this the time to write abook about equality and fairness
and math?
Eugenia Cheng (05:00):
Well, it's just always a pressing question,
isn't it?
And I, unfortunately, this bookwas kind of catalyzed by an
absolutely terrible argument Ihad with someone that just went
worse and worse and worse.
And I'm not sure if I shouldreally say this because I'm
always saying, oh, math helps ushave better arguments.
And so I thought, I went intothis argument thinking, I'm not
(05:22):
going to, I'm not going to tryand, tell this person they're
wrong.
I'm going to find a point ofcommonality using math.
Uh, completely failed becausethis person was so far gone the
other way and was refusing toacknowledge that there is
anything ambiguous aboutequality and fairness.
And all I was trying to say was,well, we make decisions, don't
we, about what counts as equaland what, what fairness really
(05:45):
is in society?
And he was just like, no, wedon't.
Vanessa Vakharia (05:49):
Wait.
Eugenia Cheng (05:50):
don't get to decide what fairness means.
I get to decide what fairnessmeans.
And I just thought, oh no, thatdidn't go well at all.
Vanessa Vakharia (05:58):
Okay, hold on.
Can we, I need a little, can Iget a little more context?
Eugenia Cheng (06:02):
It was a long time ago actually, because books
take a long time to come intobeing, and it was about racism
and it was about what he wascalling affirmative action.
And I think there are differentthings that we can call it.
But he was basically saying thatwe shouldn't help anyone because
(06:23):
that's unfair.
Because nobody and his, it gotto the point where he was really
saying that, that nobody hasever been disadvantaged, so why
should we help anyone?
Vanessa Vakharia (06:34):
Ooh, that's a tough one to wade into.
Eugenia Cheng (06:37):
Yes.
And so I was, I thought I wasgoing to find some point of
agreement where we could agreeon at least somebody has been
disadvantaged in life and thatmaybe they deserve some help.
But it pushed him to the point,and I think that he didn't
really mean it, and that he justcouldn't bear to concede
anything to me.
So I didn't do very well becauseI, I, and I was really, I really
(06:57):
thought we could just agree onone person in the world who had
been disadvantaged by something.
Vanessa Vakharia (07:02):
Terry Fox.
Terry Fox,
Eugenia Cheng (07:05):
or, you know, someone who's, I don't know
whose parents served in a warand were killed and the baby was
born, we couldn't find anyone.
Vanessa Vakharia (07:13):
But what about being born like without limbs?
Eugenia Cheng (07:16):
Without limbs, without being able to anything,
he, he refused to concede thatanyone had any disadvantages.
And so we couldn't get anywhere.
And so then I thought.
I'll write a book about this.
Vanessa Vakharia (07:31):
it's funny you bring this up because just today
I was talking about with myfriend who's a therapist and we
were talking about this idea.
I feel like this is probablywhat this guy was doing even
though I was not there, like,I'm sure maybe you even know
what this phenomenon is called,but it's like when you believe
something, in order to preserveyour identity and value system,
you have to like double down onthat belief.
Otherwise it like threatens yourentire identity.
Eugenia Cheng (07:51):
Yes.
That, it's cognitive dissonance.
When the thing that you believeis being contradicted by some
other information and you can'tdeal with that dissonance, and
so you have to, in order toresolve the dissonance, you
either have to change what youthink, which is very hard if
you're attached to it or youjust have to squash out whatever
the other
Vanessa Vakharia (08:10):
The other thing is, and this is yeah, I,
that flat earthing documentary,have you ever seen that Flat
Earther documentary?
It was so fascinating becausethe guy kept getting evidence
that the earth was round.
And by the end, and I thoughtthis was very reflective of him,
he actually said, listen, likethe scientist was like, we've
like show all your experimentsare failing.
Like, and he goes, I cannotadmit the world is round because
(08:33):
I would lose all my friends.
My entire community's builtaround this, everything I do.
And he was basically like, Ican't, I can't entertain it
because my whole life would fallapart.
Eugenia Cheng (08:41):
Right, and I thought about this argument I
had with this guy for a reallylong time, way too long.
But this is what mathematiciansdo, right?
We think about the same thingfor a really long time and, and
I decided, my best guess is thathe feels that he has been
disadvantaged himself, butnobody's ever acknowledged it.
And because he's a white maleAmerican, he feels aggrieved
(09:04):
that he never gets to.
And so maybe if someone had justtaken him aside and went, I see
that you were disadvantaged inthese ways, here, have a hug or
something, now he probablydidn't want to hug, but
Vanessa Vakharia (09:17):
But I think you're onto something.
'cause that's actually kind ofhow I feel about math therapy
and when people like have such astaunch view of who can and
can't do math.
When you're simply like, Hey,listen, like, tell me about your
experience.
Like, oh man, that must havebeen hard.
Like people soften.
Eugenia Cheng (09:31):
Right, exactly.
Exactly.
What was it that caused thisperson to think this, it went,
goes back something, sosomething really deep.
Some experiences that they hadin very formative years and that
they can't give up on it nowbecause they've built their,
kind of personal narrative onthis.
And I understand that about mathprevious experiences, because I
had that about sport.
(09:53):
And in fact, a lot of what Iunderstand about other people's
math trauma comes from my sporttrauma, which I feel is quite
parallel and quite comparable.
Vanessa Vakharia (10:01):
Tell us.
Eugenia Cheng (10:02):
Well, when I was young, I did not play sport at
home with my parents becausethey were not sporty.
They were not into that.
They liked music and they likedreading and they liked math.
And so I did math at home withmy parents in the same way that
other people go into the parkand they, you know, hit a ball
around.
And so I couldn't throw, Icatch, I never ran, I couldn't
(10:24):
jump over things.
And so in all sports lessonsthrough my entire childhood, I
was so bad at it, so incrediblybad at it,'cause I'd never done
it before and everyone else wasahead.
And then, because I was good atacademic subjects, people liked
to make fun of me for when I wasbad at something.
And, and then the sportsteachers liked kind of
(10:47):
humiliating, not exactlyhumiliating, but they, but they
were so incredulous that anyonecould be this bad that they
often said things like, well youare obviously not trying because
there's no way you could betrying and still be this bad.
And so, of course, what did I dothen?
I stopped trying.
Because I was trying, I tried toget better at everything all the
(11:07):
time.
And I wanted to get better.
I didn't want to be terrible,and the last person chosen on a
team every time and everyonemakes fun of me.
And the kind of thing,especially in team sports, you
let the whole team down everysingle time.
And so I tried to get better,but once they said that, that I
didn't try anymore because ifthey were going to accuse me of
not trying, then I might as wellnot try.
But then I did what people dowith math as well, which is I
(11:30):
had to back up my own nottrying, by denigrating the
entire concept of sport.
Vanessa Vakharia (11:37):
So true.
This is such a, I'm, I'm, thisis, yeah.
Wow.
Eugenia Cheng (11:41):
And it took me years after leaving school to
realize that that was maybe notnecessary.
And I think that some of it,some of it I still believe in
because I still don't like thepart of sport that involves
trying to beat people.
And
Vanessa Vakharia (11:57):
Another parallel in my opinion.
Eugenia Cheng (11:58):
Right.
right.
And so I don't like the part ofmath that involves com
competitions in trying to beatpeople, and where people get
excited because they have beatbeaten somebody else.
I really, really, that makes mevery uncomfortable.
But I now am quite obsessed withplaying tennis, and so I have
got over it, and I only got overit in the last few years.
But honestly, when I, we foundsome free tennis courts in the
(12:21):
park near our house, and thefirst time my partner persuaded
me to go and play, I had a fullon panic attack, just like
people do with math, because Ithought, I'm gonna look like an
idiot.
Someone's gonna humiliate me,I'm gonna miss the ball.
We weren't even going to scoreor try and play a game, because
every time we try to, every timein my past when it's, there's
(12:41):
been a game with scores, I losejust always.
So what's the point?
I know I'm gonna lose.
There's no suspense.
There's no excitement.
I just lose.
And so I had this whole panicattack and I had to give myself
this giant pep talk saying, youknow, physical exercise is good
for us, especially as we getolder.
It's really important.
And anyone who makes fun of me,that's their problem.
(13:03):
At least I'm trying, at leastI'm trying to get better.
I'm making an effort.
I'm trying to be fit, you know,no one, if someone laughs at me,
then that shows that they're ahorrible person.
I, and then once I've got overthat and I've got, and I
realized that no one was goingto tell me I was bad, no one was
gonna humiliate me, that it isin fact good for me.
And I now appreciate that havingsome physical exercise is good
(13:24):
for me in the same way that I'vealways appreciated the
intellectual exercise is notonly good for me, but it's fun.
And so much so that, a yearlater, someone did make fun of
me, but I was okay because I'dgot over it.
Someone said the funniest thingto me, he came up to me and he
said he, he'd been watching meplay, and he said, I was
wondering if you'd like to playwith my daughter sometime.
she's 10 and she playscompetitively.
(13:46):
She plays competitively and sheplays with me, but, but I, I
think it'd be really good forher to play with someone who's
average or below
Vanessa Vakharia (13:53):
Oh my God.
Did you say yes?
I mean, I guess that could be acool opportunity.
Maybe she'd be an Olympian oneday.
Eugenia Cheng (14:02):
I don't, I didn't know.
I didn't know what to say andbecause I'm still conditioned to
be polite to people, I just kindof went.
Vanessa Vakharia (14:11):
Okay.
But this story, this is like alove story.
Like this is really givingrom-com because it's like you
have the like, oh my God, likeit sucked.
I was pushed out, dah, dah, dah.
And then you like come around,you finally try, you have the
breakdown, but then you get overit and you start seeing the
value in it.
And then again, that bully, the,the childhood bully comes back
(14:33):
in the form of a man asking youto play tennis with your
daughter.
And now you are healed.
It doesn't affect you.
But everything you've said is soparallel to math.
Even the whole idea of like, oh,if I was gonna score, if the
scoring happened, what was thepoint?
Right?
It's like, well, if grading'sgonna happen, what's the point?
And almost being like being ableto be like, well, I'm not doing
it to win the tennis match.
I'm doing it because physicalactivity is good and trying
(14:55):
something is good.
It's like
Eugenia Cheng (14:56):
Right, and it doesn't matter.
I don't need to compare myselfwith other people.
I just want to feel like I'mgetting better.
As long as I'm on a trajectorythat's getting better, it
doesn't matter what everyoneelse is doing because I'm not
trying to win Wimbledon orsomething.
Vanessa Vakharia (15:11):
Totally, but like, I guess like we're talking
about school I like, I'm like,yes, yes.
And then I'm like, well, it justkind of sucks because school is
kind of just designed that wayas like to,
Eugenia Cheng (15:19):
Yes.
Vanessa Vakharia (15:20):
you know, to sort of sort people.
So it's kind of hard to be
Eugenia Cheng (15:23):
Right.
And that was what my, uh,previous book of mine was about
X plus Y a MathematiciansManifesto for Rethinking Gender.
All about how one of the hugeproblems with how we present
math and who we keep in and whowe push out is because of how
competitive it is all the waythrough.
And so it appeals to people whohave a competitive nature, but
it also puts off people whodon't like the fact that they
(15:45):
got graded lower than someoneelse, or that they're humiliated
because, so they found it harderthan someone else.
Not to mention the fact thatoften the people who find it
harder.
Aren't worse at it.
They're just seeking a deeperunderstanding.
And that's what I always try tosay to, to people.
If you, if it takes you longer,if you feel like you don't
understand something, maybe it'sbecause you are seeking a deeper
(16:07):
understanding.
And the people who said they'veunderstood it, haven't
understood it more, they justweren't seeking as, as much
understanding.
Oh, an analogy just popped intomy head about, about about
eating.
So if you are full, it doesn'tmean that you ate more than
someone else.
Maybe you just had a smallerappetite.
Vanessa Vakharia (16:24):
That's good.
That's a good one.
Whereas like the person seekingthe deeper understanding,
they're not full yet.
They haven't gotten what theyneeded out of it.
Like that's it.
Okay, hold on.
So I wanna, I wanna say one morething before I get more into
your book.
But I actually have a questionabout what you were just talking
about, the competitive nature.
Like you saying that mathappeals to those with a
(16:45):
competitive nature.
And in your book,
Eugenia Cheng (16:48):
Well, math, math class.
Typical math education.
Yeah.
Vanessa Vakharia (16:52):
But here's my question.
Why is it that math educationappeals more to those with a
competitive nature as opposed toEnglish education, let's say.
Eugenia Cheng (17:04):
I think it's because it is presented it, it
is graded so quantitatively youcan really compare people with
other people.
And it doesn't have to be likethat.
It could be presented in a waythat is more like English, where
you, it's not just this personhas more points than somebody
else.
So if English essays were alljust, this is how right you
were, how right were you out ofa hundred then?
(17:28):
Then it would be much moreobvious that there was a scale
to compare people against.
But English, everyone kind ofknows that English, writing
English things isn't about howright you are.
And there are so many differentthings going on.
And so if we presented math.
In a way that was less aboutbeing right and wrong and more
about how much you haveexpressed this and taking a
situation in life and seeingwhat math we can find in it and
(17:51):
what we can, how we can use thatto illuminate our ways of
thinking.
Then it would be so much less athing where we could compare
everyone so directly and thenit, there wouldn't be so much
winning, losing, and humiliationinvolved.
I think.
Vanessa Vakharia (18:05):
Well, this is really making me think too,
that, you know, students likeknow everything.
They're like dogs.
Sorry, I'm not comparingstudents to dogs, just so
everyone's very clear on that.
Like they're very different.
But you know how people saylike, dogs are amazing, but
obviously I'm like, you know howdogs can like sense things,
Eugenia Cheng (18:23):
Mm-hmm.
Vanessa Vakharia (18:23):
can like sense energies in people before, like
even people can, I feel studentsare kind of like that.
They're like savvier than weever give them credit for.
So even if we're not publicly,you know, like we used to back
in the day, put their grades up.
Like my grades used to be up ona door.
Even if we're not doing that, Ithink you're right in the sense
that they know that they arebeing compared to other people
(18:44):
in this exact same way thatyou're talking about.
Things are being marked rightand wrong.
Some person next to'em got morethings right than they got
wrong, whatever, and that mustbe, it is for sure, such a key
part of math trauma formation isthat idea of like shame or
knowing you're being comparedto, it's like that causes so
much anxiety,
Eugenia Cheng (19:02):
Mm-hmm.
And, and it, but it, it's backedup.
It's kind of, played into by theidea that math is, has right and
wrong answers.
And so, the whole thing I'mtrying to say in my next book,
Unequal, it's the math of whenthings do and don't add up.
And it's, it's kind of subtlethat, because it's not that they
do or they don't, it's that theydo and they don't at the same
(19:23):
time.
And so things are equal andunequal at the same time So even
if we say, one plus one equalstwo.
There's something differentgoing on.
One of them is a one thing and aone thing, and the other one is
two.
It looks different.
The left and right of theequation are visibly different.
They're different.
And so there is always somethingthat's the same and different.
And we have decided what we'regoing to take into account.
(19:47):
And we make these decisions allthe time in math, but we usually
suppress them in math educationbecause we're trying to teach
people how to do it.
And so we say to them, this isequal.
We don't say, okay, here's howthey're not the same.
And so there was this incrediblyfrustrating memory I have when I
was an undergraduate, when I wasin a logic class and I didn't
(20:07):
understand, we, we were provingthat something or other was the
same as something or other else.
And um, and I didn't understandhow they were different.
And the tutor just kept sayingto me, well, that's the whole
point.
We are proving they're the same.
And I was like, yeah, but theremust be something different
about them.
Otherwise we wouldn't have toprove they're the same.
He's like, oh, but they're thesame.
Like so enraged.
Vanessa Vakharia (20:33):
Well that is, but hold on, you're kind of
blowing my mind.
'cause what you're saying is soobvious and so not obvious all
at once.
Like, I've never thought aboutthis.
Like, you're right.
Like why are you trying to provethey're equal if they're so
obviously equal?
There has to be some dispute.
So what's the dispute then?
Eugenia Cheng (20:51):
Right.
And that we hold those things inour brain at the same time,
which is an amazing thing to do,but we should realize we are
doing it.
And so there are all thesedifferent ways of thinking where
you can change your point ofview on what you are going to
accept as a difference and whatyou're going to be really picky
about.
And this is a really greattraining for our brain, if we
(21:12):
can bring it into ourconsciousness, because this is
what we should do in life withpeople as well.
Like, no, no, people aren't thesame as anyone else.
No one is the same.
And so if we're going to talkabout equality in life, which I
think we all should think aboutit, but, we shouldn't think
about equality because no one'sthe same.
What we are really thinkingabout is what differences we are
going to accept, and then wehave to take responsibility for
(21:32):
what we decide.
Vanessa Vakharia (21:34):
Okay, this is, this is wild because I get it
and then I don't get it, andthen I get it again, and then I
don't get it.
It's like at each point along,I'm assuming, tell me if I got
this wrong.
Along the decision makingprocess or at each, basically at
each specific juncture, you'rein that moment deciding what
differences actually matter andwhich don't.
Right?
Like, regardless of what we'retalking about, what point in
(21:55):
time, like, oh, I feel like I'vegot an analogy brewing.
Hold on, hold on.
Okay.
I feel like this is a, like Cokeand Pepsi are totally different,
but Right.
They're different.
Okay.
They're different things.
There's different tastes,whatever.
But like if I am at a bar thatonly serves a Pepsi product or a
Cola product, it's like the samething.
I'm just like, oh, I just wantlike a cola.
(22:16):
Like in that
Eugenia Cheng (22:17):
Yeah.
Yeah, exactly.
Great analogy.
Yeah.
Right.
But some people would be reallypicky and be like, no, I
absolutely do not want Pepsi inmy drink.
Vanessa Vakharia (22:27):
Yeah.
I, I would, I would only drink aCoke
Eugenia Cheng (22:29):
Mm.
Vanessa Vakharia (22:30):
Anyways.
That being said, unless it was adiet of Pepsi, it doesn't
matter.
Okay.
But, Okay.
I
Eugenia Cheng (22:34):
And there is no right and wrong answer
Vanessa Vakharia (22:35):
Well, that was my question.
because this is almost goingback to like that guy almost, I
don't wanna be that guy, but I'mlike, well, who, when do we, who
gets to, and I don't, I, I, Idon't think it's a who, but
like, how do we know when adifference is important or not?
Eugenia Cheng (22:51):
That's an amazing question.
And that's what I think isreally at the heart of math.
It's not about this is the rightanswer, this is the wrong
answer.
It's not about this person'sbetter, that person's better.
It's not about what's the answerto this thing.
It's about how are we going todecide what matters?
And math is not usuallypresented as being a system of
(23:13):
deciding how we think about
Vanessa Vakharia (23:16):
Like, it's not democratic.
Eugenia Cheng (23:18):
Well.
That's a whole different thing.
But math has a framework.
So all subjects have a frameworkfor how they're going to decide
things, and math has a frameworkfor deciding things, but each,
each field of math comes up witha different notion of what's
going to count as the same forthose purposes.
And there are reasons behind it,but in the end there aren't that
(23:40):
many, there aren't that manyreasons something would be a bad
choice.
So there are some reasons Imight go into them in the book.
So there are things like that,they're kind of technical.
So if something is gonna countas the same as something else,
then there are things like,there's reflexivity, which means
everything should count as thesame as itself and so then
there's symmetry, which is thatif a counts as the same as B,
(24:01):
then B should count as the sameas A.
Then there's transitivity, whichis about whether we can build up
long strings of these arguments.
So if A is the same as B and Bcounts the same as C should A
count as the same as C,probably.
But there are situations wherethat doesn't, that's not true
either.
Vanessa Vakharia (24:16):
Okay.
I have to tell you, this isbringing back a core memory of
me at 12 years old where I wrotethis poem and the poem was, oh
my God, I have not even thoughtabout this in so long, but maybe
this is gonna be the momentwhere I finally understand this.
I said, nothing is something,and everything is also
(24:39):
something.
Hold on.
I had I, I, it was somethinglike that.
It was like If nothing issomething and everything is also
something, then is everythingnothing.
And nothing is everything.
Like, do you know what I mean?
that's
Eugenia Cheng (24:50):
Mm-hmm.
Mm-hmm.
Yeah.
You were thinking abouttransitivity.
Vanessa Vakharia (24:54):
So in that case, is that true?
Is something nothing because'cause nothing is something
Eugenia Cheng (24:59):
Mm-hmm.
Vanessa Vakharia (25:00):
So is something nothing.
Eugenia Cheng (25:02):
Well, it, I don't think"is", is necessarily
symmetric
Vanessa Vakharia (25:07):
Oh,
Eugenia Cheng (25:09):
and because, and this is why in math, we use
language very carefully.
Whereas in normal life, we uselanguage a little less
carefully.
And that's one of the thingsthat can make math frustrating
because we use the same words,but we use them differently.
And so to make that more precisein math language, we might say
nothing is an example ofsomething.
Vanessa Vakharia (25:32):
Nothing is an example of something.
True.
But I guess now we're, it's notreally transitivity.
Eugenia Cheng (25:39):
Now it's cl, now it's symmetry and it's, it's
clearer.
It's clearer that it doesn'twork backwards because there are
way more things that aresomething than nothing.
So nothing is a thing.
There are way more things.
So not all something are anexample of nothing.
Vanessa Vakharia (25:54):
This is so cool.
Like, this is like such a,because we are talking about
math, but I've always believed,and I feel like this has always
been your vibe because you makemath so human and, and this book
kind of is, yes, it's math, butit's a way of understanding
nuance, right?
Especially in a world wherelike, it almost seems like we're
(26:15):
so focused on our differencesnow.
Like.
This feels like a way to almost,be able to see that we all have
at least one thing in commonwith someone.
Am I like taking it too far?
Eugenia Cheng (26:27):
No, that's, that's right.
And I think that it is stillimportant.
I'm not saying we shouldn't seeour differences at all, because
it's also important to see ourdifferences, especially when we
think about our pastexperiences.
So we've all had pastexperiences that are really
different, and that often playsa really crucial part in why we
are the way we are now.
Just as we were talking aboutwith the arguments we've had
(26:47):
with people and we think, wait,what in your past experience led
take this position?
And so I think it's alsoimportant to understand those
differences, but also to, to nottake those beyond where is
necessary.
So we can think about people'spast experiences and think about
how that affects how they behavenow and where they are now and
(27:08):
where they have got to.
But then we don't need to go,oh, well this means you can't
have this job
Vanessa Vakharia (27:12):
Mm-hmm.
Eugenia Cheng (27:13):
that, or the fact that the fact that you've cut
your hair short.
Does that matter for this job?
Well, it depends whether you aretrying to play somebody's body
double.
So I, I was talking about howfor a job, it shouldn't really
matter what you look like unlessyou are playing someone's body
double.
Vanessa Vakharia (27:29):
Right.
Can you tell me about one plusone equaling two?
What's, what's the hot topic?
What's the debate like?
Is there a world where theydon't equally each other?
Like where can we
Eugenia Cheng (27:38):
Yeah, there are many worlds where it doesn't
equal two, and mathematiciansall know this, but then people
who think of themselves as mathpeople sometimes get so angry
that we've changed the rules orwe've, we, that this isn't real
math or some kind math or this,yeah, exactly.
(27:58):
It's some kind of woke math thatlets more people in.
Oh no, we've let more people inthan we did before.
But there are many situationswhere one plus one can equal
something else.
So, one plus one can equal zero.
For example, if you turn a pieceof paper over, and you turn it
over again, that's like havingturned it over zero times
Vanessa Vakharia (28:16):
What?
Pause.
Hold on.
Let me just really observe this.
If you turn.
Eugenia Cheng (28:21):
a piece of paper over, and then turn it over
again.
It's like having turned it overzero times.
Vanessa Vakharia (28:28):
Okay.
Eugenia Cheng (28:30):
And so some people say, some people say, oh,
that doesn't count.
Vanessa Vakharia (28:33):
I was about to say that doesn't count!
Eugenia Cheng (28:38):
And the thing is, that's a valid answer, but it's
not the one mathematicians give.
Mathematicians go, well, that'san interesting scenario.
Let's model that with a world.
And so we get the Integers Modtwo, where every time you do
something twice, it goes back tozero.
And so you can always saysomething doesn't count.
But that's not what math does.
(28:58):
Math goes, this is interesting,let's study it.
Vanessa Vakharia (29:02):
So why am I, let me see why I'm having the
reaction that it doesn't count.
Because I think I'm like oneplus one.
That means we're adding twothings together.
Is me flipping a piece of paperover once and flipping it over
again.
It doesn't feel like addition tome.
Why is that?
Eugenia Cheng (29:20):
Because addition is usually presented in a very
restricted context.
Because it's often presented inthe context where it has to
equal two, because we're nottrying to let in the possibility
of other things.
But then there will be somechild in the class who's like,
I've turned my piece of paperover again, and now it's the
same way up.
Now what?
(29:40):
And so another of my favoriteones is when you press a button,
when you call an elevator, youpress the button and then
someone else comes along and youknow that thing where you've
already pressed it and it'silluminated and someone else
comes along and presses itagain.
Vanessa Vakharia (29:53):
Me, I'm the second person.
Eugenia Cheng (29:54):
You are the second person, right.
So, well, maybe we're having atheme here, so that does not
call two elevators.
Vanessa Vakharia (30:00):
Hold on.
You press the button.
Yeah, I got, I, I, yeah, but I'mnot, okay.
Yes, you're right.
You're right.
But I'm not seeing it as a, whyam I not seeing it as addition?
Eugenia Cheng (30:10):
I think because, you have been maybe trained to
think of only the naturalnumbers.
But mathematicians go, hmm,something's going on in this
situation, let's model thatsituation.
And so then there are placeswhere you can model one plus one
is two, and see what happens.
Vanessa Vakharia (30:27):
So here's my question.
The juicy question here is, sowhat do we do now?
What you're like, you know,we're in class the, the
teacher's teaching math, andthere's that kid that's like,
but I turned my paper overtwice, so one plus one does not
equal two.
But now we're in this classroomwhere the goal is they're
supposed to be getting two, youknow, in order to pass math
class or whatever, but they'renot wrong.
(30:50):
Now what happens?
Eugenia Cheng (30:51):
Well, so then you go that's a really great point,
that's a whole differentmathematical world.
Unfortunately, we don't havetime to study that world right
now because someone's decidedyou all have to pass this test.
But then maybe if we have someextra time at the end of the
week, then we'll investigatethat world.
Vanessa Vakharia (31:12):
It is really interesting because it's like we
we're in this kind of like veryinteresting place where, you
know, there's a lot of backlashagainst this idea of like, woke
math or like being like, we'reletting too many people in by
saying, all of a sudden there'sno right answers, everyone can
do whatever the fuck they want.
And it's like, that's not whatyou're saying here, but I almost
am curious what you would say tothose who are like, well, hold
(31:32):
on a second, you know, ifthere's no right answers in math
anymore and everything is thesame and it's different, like my
whole world is rocked.
Like how are they gonna passthis test?
How are I supposed, like what,what do you say to
Eugenia Cheng (31:42):
So I am not saying there are no right
answers.
Vanessa Vakharia (31:45):
Yeah.
Okay.
Let's clarify
Eugenia Cheng (31:46):
I'm saying that, I'm saying that math is a
framework for deciding what isgood information and that there
are many different possibleright answers in different
contexts.
That's the thing.
And so it's not that there's noright answers, it's that we
should be careful.
And so we might say, oh, that'stoo much for children.
And the thing is that if welimit in advance what we think
children can handle, then we arelimiting them.
(32:09):
And I don't want to limit them.
And children are usually capableof more than adults think
they're capable of.
Vanessa Vakharia (32:15):
Well, you know what else, this is making me
think.
I love how you just said that.
You said, the right answerdepends on the context,
basically, right?
Like whether one plus one equalstwo depends on the context.
And that kind of adds to thewhole idea of like, we should be
giving kids more context when weteach the math, right?
Like we often are just like,just do this thing.
And I'm not, I saying we as inlike traditionally,
(32:35):
historically, that's how mathhas been taught with very little
context.
And that's a complaint we hear alot, right?
Is like kids feel disengagedfrom it, disenchanted because
they don't like, there's nocontext to it.
So perhaps, you're kind ofadding more like oomph to the
reason why context is soimportant.
It's not only will they be moreinterested, but actually then
they have a deeper understandingof what they're learning.
(32:56):
And it leads to this whole ideaof nuance, which is one of the
most applicable skills in thereal world.
The ability to see that contextmatters.
Eugenia Cheng (33:04):
Yeah, exactly.
And this is the thing that ifyou, if you teach some rigid
thinking, some kids.
And they do really well at it,and they call themselves math
people and they will then defendit to the teeth, to the death
because they got all theirself-esteem from being good at
it.
But then, like you say, it's waymore applicable and transferable
to learn how to think well thanto learn some specific math
(33:27):
techniques.
And that if you learn somespecific math techniques that
help you pass a test, then allyou learn is how to pass that
test.
And I get it, and I'm notblaming teachers for this at
all, because teachers have theirhands really tied by all the
constraints that are put on themand how they are judged by what
their students do in thesetests.
But the whole system is theproblem.
(33:47):
And that that if we teacheveryone how to think, well,
then hopefully they can passtests and do more things as
well.
And so it's that much widerapplicability.
And too often applicability formath comes out to be things
like, oh, we shouldn't just doone plus one equals two.
We should go, if you go into astore and you buy eight
watermelons and then you, that'snot applicable at all.
(34:08):
That's just contriving some kindof thing that's gonna count as a
real world situation.
And like you said, students andchildren are very perceptive.
They can sniff that out frommiles away.
Vanessa Vakharia (34:19):
I always say like, I'm like, what's relevant
to kids doesn't mean like whatis on the planet we call Earth.
Like, oh, because you're addingan apple plus an apple.
Now it's relevant.
Like what's relevant to studentsis like, what's relevant to them
right now in their lives?
What's important to them rightnow?
And what's important right nowis exactly what you're talking
about, the idea of being curiousabout, Hey, I'm having all these
(34:42):
conversations with people, I'mhearing my parents talk about
things in the news.
Like this makes me wonder, like,is this really the same?
Is this really different?
Do these two differences betweenthese people matter?
Like that's relevant right now?
Eugenia Cheng (34:54):
But also whatever pops into their head is, is
what's relevant to them.
Because if you try and squashthat out, and the thing is, I
still have this problem when I'min a math talk or any kind of
talk, if something pops into myhead and isn't resolved, I can't
concentrate anymore because I'mtrying to resolve this thing in
my head.
And so I find it really hard toconcentrate in math talks
(35:16):
because if they're interesting,then something will pop into my
head and I try and resolve it.
And if they're not interesting,then I'm not interested.
So, and so if something popsinto, if something pops into
someone's, a child's head, andthey get told no, you're not
allowed to ask that question,and no, we can't do that now,
then they'll just lose interestbecause this thing is their
pressing question.
(35:36):
And so whether it is, why doesone plus one equal two, why
can't we divide by zero?
Or is infinity a number?
Or what happens if I cut thistriangle in half?
Is it two triangles or is ithalf a triangle and half a
triangle?
Now, whatever those questionsare is what is relevant to them
now.
Vanessa Vakharia (35:52):
It's so funny, like just listening to you talk.
I'm like, it's so wild that theidea of opening this up to like,
Hey, maybe one plus one doesn'talways equal two, and maybe we
should be looking at all thesedifferent angles to this
problem.
Instead of focusing on the rightanswer, that gets labeled as
like"dumbing math down".
Whereas what we're doing ismaking it like just, even just
(36:13):
hearing you talk about it, it'slike you're actually making it
so much richer and actually in asense, way more complex.
It's like the opposite ofdumbing down, right?
Like I'm just thinking about mesort of being like, but addition
is just compiling things, right?
And you're being so like niceand gentle and being like, oh
yes, perhaps you were taughtthat way, but, but I'm like, I'm
(36:33):
like, oh man, like I, I'm atrained high school math teacher
and I am having trouble beinglike, wait, how is flipping a,
I'm gonna really be thinkingabout how flipping a paper over
and, and flipping it back isactually addition.
Like, I'm all of a sudden inthis one hour together, my view
of addition is becoming so muchbroader and I'm really gonna
interrogate that.
(36:54):
Like, wow.
Eugenia Cheng (36:56):
Right, and again, there's no right answer.
The question is, does this wayof thinking help us?
Vanessa Vakharia (37:01):
Hmm.
Eugenia Cheng (37:02):
Does this open up some new avenue of thinking?
And that's what I always think.
It doesn't really, it's notreally a case of whether it's
right or wrong.
So some things are wrong.
There is definitely wronganswers in math.
If you contradict logic, thenyou are wrong.
But in terms of can we countthis as addition or not?
There are plenty of people whowill say, no, we shouldn't.
I'm like, well then you've, allyou've done then is you've
(37:23):
restricted your thinking, and Iprefer to expand my thinking.
Vanessa Vakharia (37:27):
Are there situations in which it does not
help to think this way?
Eugenia Cheng (37:32):
I, I'm going to guess yes, because there surely
is some example that we can comeup with.
I mean, I don't like makingsweeping statements, so if I
said this always helps us, thenI would feel very uncomfortable.
So yes.
So there are situations where wecould take it too far.
For example, if we think that$1and$1 doesn't make$2, then we
(37:53):
are gonna be in trouble with ourbank account.
And so we can't just make thingsup.
The other thing I like aboutthis approach is it gives
students some, uh, of their owncontribution into the
conversation.
So it's not telling them what todo, it's going, okay, can you
think of some other situations?
What do you think about thissituation?
What if you mix one color ofpaint with another color of
(38:14):
paint?
This was example that an artstudent of mine came up with
actually, and I loved it.
You don't get two.
If you mix
Vanessa Vakharia (38:21):
you don't get
Eugenia Cheng (38:22):
Yeah, you don't get two, you just get another
one.
Vanessa Vakharia (38:24):
You just get another one.
Eugenia Cheng (38:26):
The ultimate purpose of this is to stop
closing off math to people.
And, and what I would say, ifanyone is wondering about
specifics is that, if no onequestions why one plus one is
two, you don't have to go intoit.
But if someone does question it,and that's why it came up,
because it's one of the thingsthat people say, they say, why
does one plus one equal two?
And it's really hard.
(38:46):
And I think it's amazing.
We can think about it withoutreally thinking about it.
And sometimes there's a lot ofmath that you can do without
really thinking about it.
And then mathematicians sat downand went, wait, what even is
one, what is two?
We whole new field of math to dothis.
And then set theory was born andthen they had to do a whole load
of new definitions to go, whatis a number?
We didn't know?
Help.
Ah! And, and so that is where,that is why it is in fact very
(39:10):
deep.
And so if someone, the point forme is that if someone raised
this outta curiosity, it wouldbe to acknowledge that there is
a really good point in there andthat there are situations where
it doesn't equal two.
And my art students,'cause Iteach art students at the school
of the Art Institute now, almostall of them got put off math at
some point in the past.
And one of the things that putthem off was the fact that it
(39:31):
had rigid black and whiteanswers and they weren't allowed
to be creative.
And one of the first things I dois get them to just dream up
situations in which one plus onecan be something else.
And it's one of the first timesanyone has ever invited them to
dream in math class to dream upthings to create.
And that's what they want to do.
And sometimes they say, oh, wellI'm a creative person so I don't
like math.
(39:52):
And I go, wait.
That's just how math was taughtbefore.
And so I want to offerpossibilities for how you can be
creative in math class and tieit into things that really are
math.
Because all of those situations,it's not just semantics or woke
math or the girl math or dumbmath or dumbing it down.
They're all things, and I couldsay, you know, it's the integers
(40:12):
mod two or the integers modthree, or it's a, projection in,
in a monoid, or you know, they,they're all genuine things that
we study and we then we studywhat the behavior is and what
the consequences are.
And so it's just all to saythat, things are not as black
and white as they seem in math.
And for some people thathorrifies them because they're
(40:34):
clinging to those, that's their,that's been their framework,
that's been their safety rails.
But for other people, it sparksthe curiosity that has
previously been squashed out andthat's why I want to bring it
back.
Vanessa Vakharia (40:47):
It's, you know what is really making me think,
the thing that makes people themost uncomfortable is
uncertainty, right?
And ambiguity.
Because it's uncertain.
We want certainty.
So what's interesting is, whatyou're sort of talking about is
uncertainty adjacent, let's justsay, I've been thinking about
this a lot lately of just somany of the solutions to our
(41:08):
like quote unquote ailments,like whether health related,
where, whether it's mentalhealth, whether it's like
needing a new hair color, likewhatever it is, are targeted,
like advertising is targeted aslike, just get this thing and
you're gonna be sure that blah,blah, blah, blah.
Like it wants give you the surething.
And I think this really all tiesin because.
That's part of our nature is wewant security, we want
(41:29):
certainty.
We think certainty is gonna leadto security, et cetera, cetera.
So yes, this would make peopleuncomfortable.
But I think the other side ofthat is, I'm on a bit of a, a
tear here, but it's to circleback is the point is that
certainty isn't always better.
Right?
like,
Eugenia Cheng (41:45):
Right.
If it's wrong,
Vanessa Vakharia (41:46):
if it's wrong exactly.
Then not
Eugenia Cheng (41:48):
That is just wrong.
Right.
Vanessa Vakharia (41:50):
Or it's like, you know, again, like with the
food thing, I'm just thinking'cause like we're thinking of so
many food metaphors here.
I don't know why, like, itdoesn't mean that what I'm
eating isn't good, but itdoesn't mean there isn't
something I might like more, youknow what mean?
Like, and, and maybe I'm goingto be a bit uncomfortable and
try a few things that I don'treally like and then I'm gonna
find some food that I'm obsessedwith, like whatever it is.
But that is probably one of thelike spiritually and
(42:13):
philosophically and emotionallyand like cerebrally, like, in
order to really grow as people,what could be more beneficial
than learning to becomecomfortable with uncertainty at
an earlier age.
So you can try new things and beopen-minded.
Eugenia Cheng (42:27):
Right.
And it's not just uncertainty,it's also the context thing so
some things will be good in thiscontext and some things will be
good in this other context.
And it's like the fact whenpeople say, oh, this is good for
you.
Well, usually they did a studythat said it found it was good
for a certain percentage ofpeople on average overall.
Vanessa Vakharia (42:45):
Or if it's good, if you don't drink 10
glasses of it.
Eugenia Cheng (42:48):
well, exactly.
And so one example for me wasthe idea that, oh, physical
exercise to circle back to wherewe sort of started, physical
exercise is good for your mentalhealth.
Well, physical exercise wasn'tgood for my mental health when I
was just humiliated every time Idid it or I felt bad about
myself, or I had to go into agym where there were all these
muscle bros grunting anddropping their huge weights on
(43:10):
the floor and I didn't like thateither.
And so I had to find something.
But I liked.
And so it was much more helpfulfor me to go, okay, what
physical activity exists that Icould enjoy?
Rather oh, I should keep doingthis physical activity'cause
it's gonna be good for my mentalhealth.
And so realizing that there aredifferent contexts and then
there's also, at one point Irealized that if I was feeling
(43:32):
slightly bad, physical exercisewould make me feel worse.
If I was feeling slightly good,it would make me feel better.
And so it's these kind ofsubtleties that are much more
helpful for our personal lives,our own lives, as well as for,
it's not just about passingtests, it's about how are we
going to live as humans in acommunity?
How are we going to try to havebetter lives for ourselves and
(43:55):
the people that we care about?
Vanessa Vakharia (43:56):
Mm-hmm.
I love it.
I love this so much and yeah,I'm even like, now I'm like, are
ambiguity and uncertainty thesame thing?
I don't think so.
They're not, they're not quitethe same.
So like I'm kind of went on abig uncertainty tear, but I
think I'm more talking aboutbeing ambiguous, where there's
no one right answer, it iscontext dependent, which can
(44:20):
feel ambiguous when contextisn't part of the convo.
Eugenia Cheng (44:23):
Yes, exactly.
So sometimes it's not actuallyambiguous, it's just that we
didn't specify our contextclearly enough, and that's what
made it ambiguous.
And math is a really amazingdiscipline for clearing all
those things up so that we canbe much more precise about what
we mean, and hopefully we can bemuch more precise about what
other people mean, even if theydon't realize it themselves, and
(44:44):
then we can all reach a betterunderstanding of each other.
Vanessa Vakharia (44:48):
I cannot wait to read this book.
Okay, so we, we have to wrap upbut like I could talk to you for
10 years.
Um, this is just so fascinating.
And I mean, by the time thiscomes out, your book will have
just come out, but I wanteveryone to know that the
release date is September 2nd.
And Eugenia just found out thatthat is Keanu Reeves' birthday.
(45:11):
And how do you feel about that?
He is an angel among us.
Eugenia Cheng (45:15):
Yes.
Vanessa Vakharia (45:16):
Like, right, like
Eugenia Cheng (45:17):
Yes.
I mean, I've heard that he isjust such a nice person.
And Yeah.
And it wouldn't it be great ifeveryone was a nice person?
Vanessa Vakharia (45:25):
Well, I mean, it would be so great I think
that he would love this book,quite frankly.
Um, so it's coming out onSeptember 2nd, which is the
anniversary of my book that cameout last year on September 2nd.
So we both share Keanu Reeve'sbirthday book release in common.
So everyone go grab it.
It's gonna be out by the timethis comes out.
Um, if there was, if there was ateacher listening to this, and
they were like, oh, I love thisso much, what's one way I could
(45:47):
like bring this whole context,like equal, unequal, same but
different thing into classtomorrow.
Is there like a little thingsomeone could do?
Eugenia Cheng (45:55):
I think just pointing out what is unequal
about something.
If you are presenting anequation, whatever it is
pointing out, focusing on thefact that it's different and the
same at the same time, andcongratulating everyone if they
can hold both of those things intheir brain together.
Vanessa Vakharia (46:11):
I love that.
I really love that idea of beingable to hold both of those
things in our brains.
I feel we're really, um, part ofthe reason there's a whole like
war between creativity and mathis because we like, live on
binaries.
Like it has to be one thing orthe other.
Like, do you know what I mean?
Like, you're either acheerleader or you're good at
math.
Never seen a movie with both.
Like it's one or the other.
You know what I mean?
So being able to hold boththings in our mind, first of
(46:34):
all, allows us all to bring ourfull selves everywhere, right?
To not feel like we have to fitinto a mold.
Eugenia Cheng (46:39):
Yes.
Vanessa Vakharia (46:41):
I just love it.
Okay.
Are you ready for the final twoquestions?
Question number one, if you weregonna pick one thing to change
about the way math class istaught, what would it be?
Eugenia Cheng (46:51):
Uh, no grades
Vanessa Vakharia (46:54):
There it is.
No grades at all, ever.
Eugenia Cheng (46:57):
Ever.
Vanessa Vakharia (46:58):
We're gonna have to do a whole other episode
on this.
Okay?
No grades ever.
And question number two is ifsomebody listened to all of this
and they were like, no, I getwhat you're saying.
Like, awesome.
The thing is, I'm just not amath person.
How would you respond?
Eugenia Cheng (47:15):
I would quote the dedication of my previous book,
which is if you've been made tofeel that you are bad at math,
you didn't fail math, mathfailed you.
Vanessa Vakharia (47:24):
Oh my God, I love that.
I love it.
You're so cool.
Eugenia Cheng (47:31):
Oh, thanks.
This was so fun.
I do feel like we could justkeep talking for years.
Vanessa Vakharia (47:35):
We, I mean, the metaphors we could come up
with.
I can't even imagine.
We'd get, I think things wouldget weird, but I'd be down.
Um, okay.
Thank you so much.
I can't wait to read this book.
I can't wait for everyone toread it.
There's been so much amazingstuff in here.
It's really got me thinking, andI'm gonna go leave right now and
start thinking of all the waysthat one plus one does not equal
two.
I'm like looking around me.
(47:55):
I'm like, I don't even, it'shere.
It's among, it's among us.
Eugenia Cheng (47:59):
Yeah, right.
It walks among us.
Vanessa Vakharia (48:00):
It walks among us.
Thank you so much,
Eugenia Cheng (48:02):
Thank you so much.
That was great.
Vanessa Vakharia (48:05):
Bye.
Eugenia Cheng (48:06):
Bye.
Vanessa Vakharia (48:09):
Okay, I don't know about you guys, but my mind
is spinning.
One plus one not always equalingtwo is going to live in my brain
forever, and I, I still need tothink about it.
But more importantly, Eugeniareminded us that context and
nuance change everything, inmath, in conversations and in
how we see each other.
Okay, so now it's time for yourMath Therapy challenge this
(48:31):
week.
I want you to think of onerelationship or conversation
where you and someone else feelmiles apart.
Instead of asking who's right,ask what's the context and
where's our common ground?
And if you're a teacher, I wantyou to take this into the
classroom.
Think of one lesson this weekwhere you can invite your
students to notice nuance, wherethe answer isn't just about
(48:52):
being right or wrong, but aboutthe thinking and the context
behind it.
And don't keep this episode toyourself.
I want you to send it to thatfriend, that family member, or
that colleague who often getsstuck in black and white
thinking.
Honestly, it might change theway they think, and the way you
two talk.
I always wanna hear from you.
So if something in this episodeinspired you, you can now text
(49:15):
the podcast, it's a new feature,the link to text us is right in
the show description of yourpodcast app.
You can also DM me on Instagram@themathguru, or email me at
vanessa at themathguru dot ca.
And remember, Math Therapy isnow a weekly podcast, so make
sure you're subscribed so youdon't miss an episode.
A new one is coming your waynext week and the week after
(49:36):
that, and the week after that,and you get the picture.
Math Therapy is hosted by me,Vanessa Vakharia.
It's produced and edited byDavid Kochberg, and our theme
music is by our band GoodnightSunrise.
And guys, if you know someonewho needs Math Therapy, please
share this podcast rate orreview it on whatever podcast
app you use, because thosethings make a huge difference.
(49:58):
I'm so determined to change theculture surrounding math, and I
know you are too, and we allneed to help each other out.
So spread the word and untilnext time, peace, love, and pi.
Popular Podcasts
On Purpose with Jay Shetty
I’m Jay Shetty host of On Purpose the worlds #1 Mental Health podcast and I’m so grateful you found us. I started this podcast 5 years ago to invite you into conversations and workshops that are designed to help make you happier, healthier and more healed. I believe that when you (yes you) feel seen, heard and understood you’re able to deal with relationship struggles, work challenges and life’s ups and downs with more ease and grace. I interview experts, celebrities, thought leaders and athletes so that we can grow our mindset, build better habits and uncover a side of them we’ve never seen before. New episodes every Monday and Friday. Your support means the world to me and I don’t take it for granted — click the follow button and leave a review to help us spread the love with On Purpose. I can’t wait for you to listen to your first or 500th episode!
Crime Junkie
Does hearing about a true crime case always leave you scouring the internet for the truth behind the story? Dive into your next mystery with Crime Junkie. Every Monday, join your host Ashley Flowers as she unravels all the details of infamous and underreported true crime cases with her best friend Brit Prawat. From cold cases to missing persons and heroes in our community who seek justice, Crime Junkie is your destination for theories and stories you won’t hear anywhere else. Whether you're a seasoned true crime enthusiast or new to the genre, you'll find yourself on the edge of your seat awaiting a new episode every Monday. If you can never get enough true crime... Congratulations, you’ve found your people. Follow to join a community of Crime Junkies! Crime Junkie is presented by audiochuck Media Company.
Cardiac Cowboys
The heart was always off-limits to surgeons. Cutting into it spelled instant death for the patient. That is, until a ragtag group of doctors scattered across the Midwest and Texas decided to throw out the rule book. Working in makeshift laboratories and home garages, using medical devices made from scavenged machine parts and beer tubes, these men and women invented the field of open heart surgery. Odds are, someone you know is alive because of them. So why has history left them behind? Presented by Chris Pine, CARDIAC COWBOYS tells the gripping true story behind the birth of heart surgery, and the young, Greatest Generation doctors who made it happen. For years, they competed and feuded, racing to be the first, the best, and the most prolific. Some appeared on the cover of Time Magazine, operated on kings and advised presidents. Others ended up disgraced, penniless, and convicted of felonies. Together, they ignited a revolution in medicine, and changed the world.