April 11, 2024 • 37 mins
When you picture a mathematician, what comes to mind? Now … what about a “mathematical explorer”? Well, that’s what Francis Su calls himself, and when Vanessa picked up his book Mathematics for Human Flourishing, she couldn’t put it down. On today's episode they explore how mathematical discovery can unleash the wonder and curiosity innate within us all. They also discuss some deep questions, like why do people have different emotional reactions to math compared to other fields? How can humans cultivate the virtues we'll need to keep AI in check? And why is change so hard, both in educational reform but also in our own lives?
About Francis (Website, Twitter)
Francis Su is an award-winning professor and author who writes about the dignity of human beings and the wonder of mathematical teaching. The Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a former president of the Mathematical Association of America, his work has been featured in Quanta Magazine, Wired, and the New York Times.
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Francis Su (00:02):
It's kind of like learning your musical scales, if
you want to play a concerto.
You don't learn music to startlearning to play scales.
People put the emphasis onthinking about math as learning
scales, versus listening to asymphony.
I just want people to experiencethe symphony, even if they don't
end up becoming professionalmusicians.
Vanessa Vakharia (00:23):
Hi, I'm Vanessa Vakharia, aka The Math
Guru, and you're listening toMath Therapy, a podcast that
explores the root causes of mathtrauma, and the empowering ways
we can heal from it.
Whether you think you're a mathperson or not, you're about to
find out that math people don'tactually exist.
But the scars that math classleft on many of us definitely
do.
Oh, and don't worry, nocalculators or actual math were
(00:46):
involved in the making of thispodcast.
Okay, let me ask you guys this.
What comes to mind when you hearthe words mathematics for human
flourishing?
Like really think about it.
"Mathematics for HumanFlourishing".
What a beautiful sentiment.
And it is also the title of anincredible book by Dr.
Francis Su and the reason I hadto have him on the podcast.
(01:08):
I devoured that book cover tocover and was so deeply moved by
the way he views mathematics,and the awe he believes it could
inspire in our students.
And I just, I can't wait for youguys to hear him explain how
finding the beauty and wonder inmath can make it possible for
all of us to truly flourish ashumans.
Francis, welcome to the podcast!I'm so excited to have you.
(01:30):
There's a lot I want to talk toyou about.
Truthfully, I have you on thepodcast as like a fan, like I
read your book and I was like,I'm a huge fan.
But, as I was like, Oh, I'mhaving him on the podcast, I
should like just do a littlemore research, I started kind of
like looking into you and, Ifound the reflection questions
you had written for your bookand that actually opened up like
(01:52):
a whole new thing in me.
And so, I actually have so manyquestions just about the first
thing I saw on your website,which was that you call yourself
a mathematical explorer.
Francis Su (02:04):
Yeah.
Well, I mean, I guess one ofthe, the ways that I think about
math, I think is a veryimportant aspect of math is the
exploratory nature of math,which a lot of people don't see.
And, I could call myself amathematician, but for some
people, when they hear thatterm, they think professional
mathematician who does research,for instance, like, one set of
(02:24):
people like college professorsthink mathematician is just
someone who does mathematicalresearch, but maybe other people
who are familiar with what amathematician does, who knows
what they think about when theythink about a mathematician?
And so I prefer to use the termmathematical explorer, because I
think that maybe is a littlemore accessible.
(02:45):
People don't have preconceivednotions about what it means to
be a mathematician.
Vanessa Vakharia (02:50):
Well, yeah, I would say that if you tell
anyone you're a mathematician,like, no one other than a
mathematician is going to thinkanything good.
Francis Su (02:58):
Yes, yes.
Vanessa Vakharia (02:59):
Like, that's not, that's not a good vibe.
Also, do you know, um, DeborahPeart at all, and like the work
she does around the term"mather"?
Francis Su (03:06):
Yes.
Vanessa Vakharia (03:07):
So it's like making me think about that.
Francis Su (03:09):
Yes, yeah, I mean I appreciate all these reframings
that help people get out of theusual mode when they think about
a particular word.
Vanessa Vakharia (03:18):
So like, why do you think that the word
mathematician has such a badreputation?
Francis Su (03:24):
That's a great question.
I think when people think ofmathematician, they think of, a
reclusive hermit who works on,you know, difficult problem for
many years and avoids people.
And, you know, to some extentthat narrative is, is sometimes
fed by media, right.
Or fed by stereotypes thatpeople have around who can be a
(03:44):
mathematician, and uh, what theydo.
And of course you hear thesestories about, you know, these
very, very hard centuries oldproblems that someone's been
working on, in silence untilthey suddenly solve it, right?
Like, that's one narrative thatoften gets press, but it's maybe
not the most common narrative orthe way that we do math.
Vanessa Vakharia (04:06):
Well, yeah, my whole master's thesis, it, well,
it's called Imagining a WorldWhere Paris Hilton Loves Math,
and it was entirely about mediarepresentations of
mathematicians, especially forwomen, and how it like, turns
them off the subject entirely,because who would be like, ooh,
you know what I want to do?
I want to be a recluse and,like, never have a romantic
relationship and have nofriends, but, like, all do math.
(04:28):
You know,
Francis Su (04:28):
Right.
That's right.
Vanessa Vakharia (04:29):
But it's, it's crazy because I wrote it in
2010, and you would think somuch has changed, but like
still, you're hard pressed tofind, a representation of a
mathematician that doesn't fitinto one of these tropes.
Francis Su (04:42):
Yes,
Vanessa Vakharia (04:43):
Like, think about the Queen's Gambit.
Did you watch that?
Francis Su (04:46):
Yes.
I love that.
I love that series.
Vanessa Vakharia (04:49):
Okay, but what did you think of, what was her
name?
The main character?
Francis Su (04:54):
I, yeah, I don't remember her name.
Vanessa Vakharia (04:55):
Well, whatever, but what did you think
of her?
Francis Su (04:57):
Well, I mean, there are some ways in which her
character broke stereotypes,right?
This is maybe for the listeners.
The main character is a girl whoplays chess and does a lot of
mathematical thinking, but shehas a very difficult life and,
the series tries to unpack alittle bit about her journey
into chess.
And it's been a little whilesince I watched it, so maybe you
(05:19):
should start with what youthought was recycling old
tropes.
Vanessa Vakharia (05:23):
I just think it's interesting.
Cause when I watched it, I waslike, yes, a woman who plays
chess..
And then I started looking at itas like, the full picture.
And I was like, but hold on asecond.
What did she have to do to be agreat mathematical thinker?
Oh, she had all of theseproblems.
She had to do all of thesedrugs.
They kind of made it seem likeshe had like severe mental
health issues.
Francis Su (05:43):
Yes.
Yes.
Vanessa Vakharia (05:44):
Right?
So I was like, wait, this isjust the same trope now of being
like, the only way you can begood at math is if there's
something like wrong with you inevery
Francis Su (05:51):
Yes.
No, that's very true.
That's very true.
Yeah, I mean that's similar toGood Will Hunting, right?
Like, Good Will Hunting is, itfollows that.
Vanessa Vakharia (05:59):
A Beautiful Mind.
Francis Su (06:00):
Yes, Beautiful Mind, um, to some extent Jeff
Goldblum, uh, in, uh, uh,Jurassic Park, is this sort of
crazy mathematician who is alittle, you know, he's a little
weird in some sense and, yeah,all these things sort of feed
into that, that stereotype.
But there are ways which Iappreciated Queen's Gambit, they
do a pretty good job of, helpingpeople see what it means to
(06:25):
visualize math or visualizechess, like doing chess on the
ceiling.
I, I love some of those scenes.
Vanessa Vakharia (06:31):
I loved that.
Well, and like, so I run a mathtutoring center.
We tutor math, and literally,I'm not kidding, after that came
out, I had at least 10 femalestudents being like, do you guys
tutor chess?
Like it worked in a way, right?
Like it, it got women, like aton of my teenage students, like
getting into chess.
So, okay.
Well, anyway, so MathematicalExplorer it is, and that's what
(06:51):
we're using from now on becauseit sounds way cooler and way
more fun.
And I think really touches onthat exploratory nature of what
mathematics could be.
This thing filled with likecuriosity.
And what you talk about ismathematics for human
flourishing.
That's the title of your bookand that's what it's about.
And I guess my first question islike, what is human flourishing
(07:14):
to you?
Francis Su (07:15):
Yeah, the way I like to think about human flourishing
is it's both a state of beingand doing and so the being
aspect is it's beyond happiness.
It's a beyond joy.
In fact, you could be goingthrough very difficult
circumstances and still beflourishing in those
circumstances.
(07:36):
It's a state of living andacting in accordance with,
living to your fullestpotential, maybe it's one way of
putting it.
And acting in accordance withyour values.
It's a holistic state of being.
I mean, one way of thinkingabout it is, is the way the
ancient Greeks thought abouthuman flourishing, right?
(07:58):
It's the ultimate good in lifein some sense, right?
It's the highest good is one inwhich you are, maybe in, in
modern parlance, it's, you're ina state of flow and that's the
way some people in thepsychology literature talk about
being in flow, right?
You are so, absorbed orengrossed in, in this case, it
could be maybe a, solving aproblem, but, generally
(08:19):
speaking, outside themathematical context, it's um,
I, I hate to use this term"living your best life" because
that also sounds like it hassomething to do with
Vanessa Vakharia (08:29):
So YOLO.
Francis Su (08:29):
circumstances.
Vanessa Vakharia (08:30):
It means YOLO.
Francis Su (08:31):
Yes,
Vanessa Vakharia (08:32):
You could have titled your book, Mathematics
for YOLO.
Okay, cool.
Francis Su (08:36):
But let me give you an example.
I mean, like, for instance, whenmy, um, my mother was dying,
that's, that, that's a difficultsituation, right?
But, you know, sometimes whenyou have difficult situations
you're living through, you canstill, you know, that, that
started lots of conversations,hard conversations, good
conversations, richconversations.
(08:58):
And somehow you're like, oh,really in the moment, you are
really loving someone through adifficult time, that could also
be a state of human flourishing.
Vanessa Vakharia (09:10):
It's so crazy because, first of all, you said
it so beautifully.
And I, I feel like we're, I usedifferent words, but to me, this
sounds like you're talking aboutliving in alignment, really,
with like your values, whateverthat is.
And it feels really spiritual tome in the sense that it, like,
has nothing to do with thematerial world, it's something
so internal, but, so you're on apodcast called Math Therapy, and
(09:32):
my whole, thing really is theidea that, like, yes, it's very
cool to learn math andmathematical thinking and all of
that, but to me, the skillsstudents have the capacity to
learn in math class are onesthat I really believe can lead
them to a lifetime of joy.
In, I always say, helpingstudents break myth around math
ability that have been like puton them can help lead them to a
(09:54):
place where they truly believethey're capable of anything.
I can think of no greater, morenoble cause than to help young
people discover how to do that.
Francis Su (10:03):
Yes.
Right.
Right.
Yeah.
I mean, living life is hard.
Vanessa Vakharia (10:07):
It's hard.
Francis Su (10:08):
It's hard, and how do we, how do we move through
the world?
You know, I think mathematicscertainly helps people, to see
the world more clearly and movethrough it in ways that if you
don't have that experience, evenhaving the experience of beauty
in seeing mathematics, that's toour detriment, right?
That's, there's something we'remissing by, not experiencing
(10:32):
some of those things.
Vanessa Vakharia (10:33):
So how do you tie those ideas of human
flourishing, this beautifulincredible thing that it'd be so
great for every human to be ableto like actualize, and doing
that through mathematics?
Like tie those together for me.
Francis Su (10:48):
Yeah.
Uh, well, I guess the way that Itry to do that in the book is to
connect with everybody'sexperience of, of having deep
human desires, right?
Like we all have a deep desirefor community, to be in
connection with other people.
We all have a deep desire formeaning.
nobody wants to live a life thatsomehow feels meaningless.
(11:09):
So we automatically makeconnections, between events and
people and ideas.
And the same thing happens inmath, right?
You, you make connectionsbetween something you're just
learning and something thatyou've seen in another context.
We all have a deep desire forfreedom and being able to have
agency to make choices in whatwe do.
(11:30):
Um, we all have a, a deep desirefor beauty to experience, that
feeling of transcendence, whichpeople experience in other
contexts, but only people who domath professionally begin to see
the sort of transcendent side oflike, oh, whoa, you know, this
idea is connected to this oneand it's so beautiful.
(11:51):
Right?
And, you know, this is part ofwhy, you know, you see, in a
beautiful mind, you've got thislike, um, characters who
experienced that beauty.
And then, of course, everyonelooks at that and says, oh,
they're crazy, you know, ratherthan, oh, I want some of that,
right?
I want to be able to see theconnectedness of ideas and feel
like I have a window intosomething that I otherwise
(12:14):
wouldn't see.
Vanessa Vakharia (12:15):
Yeah, I think part of that reason is because
that character never is able tolike get a girlfriend.
You know, like, so you're like,yeah, I'd like to feel like
that, but not at the expense oflike my social life.
But that being said, but, butwhat's so interesting about what
you said is you're talking aboutmath in this incredibly like
liberating way, but how is itthat you are talking about it
(12:38):
this way yet, I would say thatmost people I know would think
of math as like one of the mostrestrictive things.
One of the things that wouldabsolutely not lead to freedom.
Francis Su (12:48):
Yes.
Yes.
and that's, that's because mathhas this other side, right?
The side of, um,
Vanessa Vakharia (12:54):
The dark side.
Francis Su (12:56):
Ha, well it doesn't have to be dark, but it's often
taught that way.
Like, you know, some of these,basic understandings, that you
need in order to experience someof that beauty and joy, is some
basic, you know, basic numberfacts, right?
And, you know, I think thosethings are, are important, but
it's sometimes often taughtlike, Hey, just try to be a
better human calculator.
(13:17):
And, you know, what I like tosay is the world doesn't need
better human calculators.
Yes.
It's important that we know ourbasic facts and that having a
fluency, there's that technicalside, but people often confuse
that, fluency with.
the deeper joy or the deeperpossibilities inherent in
learning math.
And you know, there, there areways in which that's, you know,
(13:39):
that, that takes practice andit's, it's kind of like learning
your musical scales, right?
If you want to play a concerto,right?
But, you don't learn music tostart learning to play scales.
Right?
Like people put the, you know,maybe switch the emphasis on
thinking about math as learningscales, versus listening to a
symphony.
(13:59):
And I just want people toexperience the symphony, even if
they don't end up becomingprofessional musicians,
Vanessa Vakharia (14:08):
And even if they can't like write the
symphony themselves, like theycan still listen to it.
Francis Su (14:13):
Yes, and enjoy, experience that.
If you think about what we do inmath, often we teach people to
learn scales before theyactually experience the
symphony.
And some people think, well,gosh, you know, kids can't
experience a symphony until theylearn the scales.
And I'm like, no, no, you cangive them glimpses of what's
possible.
Vanessa Vakharia (14:32):
But they've heard music.
That's the other, Okay.
But now I'm obsessed with thisidea because I'm like, okay,
hold on.
So I'm like, well, of course,again, I'm in a band.
So like tons of people go toconcerts and they're not I can't
get into this because I don'tknow how to play the guitar.
Francis Su (14:47):
Right.
Vanessa Vakharia (14:48):
But why is it different for math?
is it because there's so muchguilt and shame around not being
able to like understand everybit of it?
Whereas like, there's no guiltand shame around not being able
to perform an instrument.
Francis Su (15:00):
Yeah, I think that there, there's some aspect of
that, right?
Like there's this idea that, Oh,I can't teach kids, I can't show
kids the beautiful side of math,until they learn their times
tables.
Vanessa Vakharia (15:12):
Hmm.
Mm
Francis Su (15:13):
And so, of course, part of that, the thing that I
say is that that's theexploratory side that the
playful side of mathematics isoften what gets people
interested and helps them seethat, oh, actually, math is
actually fun.
Right?
And they begin to enjoy thoseaspects of mathematical
thinking.
You know, think about what'sgoing on in the world today,
(15:33):
right?
Like where we have calculators,computers that can do a lot of
the routine stuff for us, right?
It's valuable, it's importantfor kids to know how to multiply
7 times 5 quickly, so you're notalways reaching for a
calculator.
Yes.
But, as an example, do we reallyneed to teach long division?
You know, there's, there's alittle bit of a debate, right?
(15:55):
Like, what would I like kids tolearn, that I think is way more
valuable, is having a certainnumber sense, right?
Being able to say that, oh, if Imultiply, 39 times 4, I should
get something that's about 160.
Because that's almost 40 times4, right?
That, that's a skill that'suseful in today's modern world.
(16:15):
We can let calculators andcomputers and AI do the, the
routine stuff, but what we needare people with virtues who are
able to say, ah, I thinksomething went wrong with that
computer, right?
Like I think the answer, ormaybe somebody entered the
numbers wrong, but I know that,you know, 39 times 4 isn't gonna
(16:37):
give me 2000, right?
Like so
Vanessa Vakharia (16:38):
Right.
Francis Su (16:39):
That, that's what we need.
We need people who are able todo the checks and say ah
something went wrong somewhere.
Vanessa Vakharia (16:44):
But I love that you just said people with
virtues.
What a way to put it.
Francis Su (16:49):
Yeah.
And of course, that's theargument.
the big argument I'm making inthe book is that math is more
than just a bunch of skills likelearning how to multiply numbers
and factor a quadratic.
Like skills are things thatcalculators and computers can do
because they can be automated,but virtues are always going to
be in demand, right?
If you have a job that dependson having skills, that job's in
(17:11):
jeopardy, right?
Vanessa Vakharia (17:12):
Right.
Right.
Yeah.
Francis Su (17:15):
But if you have people who actually have the
capacity to think, to reason, tovisualize, to abstract, to
define, to quantify, those,virtues are always going to be
in demand.
Those are the things that agreat math education builds, and
unfortunately, people don't getthat impression when they leave
a math class Maybe we don't do agood enough sales job as
(17:38):
teachers.
Vanessa Vakharia (17:38):
We do not.
No, I've never, no.
Francis Su (17:43):
Yeah, and when people say, well, why do I need
to know this stuff?
The reason is often because theythink math is just skills, like,
why do I need to know how tofactor a quadratic?
Well, people who go off in STEMand subjects, um, but most
people never need to factor aquadratic in their daily lives.
But will they actually need tobe able to think, and to reason,
Vanessa Vakharia (18:04):
Yes.
Francis Su (18:05):
and to understand?
Yes!
Vanessa Vakharia (18:07):
And that's what I always say too.
I'm like, it's like the mathadjacent skills you're building.
Obviously we would love to go inand change the curriculum and
the content and all, but likethe only thing I think you could
do to convince a, like a childor a teenager or whatever that
it was important is to be like,you're going to be building
skills that will be important inthe areas of your life that
matter.
Like, you know what I mean?
Like factoring a quadratic.
Okay.
First of all, I actually lovefactoring quadratics.
(18:29):
Regardless of whether it'suseful.
Okay.
That's one of my favoritethings, but I'm always like, no,
it's like the thinking, it's thelike ability to like problem
solve and to work through it.
Like all of that stuff.
But like, okay, but hold on, wehave to back up.
Cause you said something thatI'm like, still like shell
shocked over.
kind of.
I'm still thinking about themusic thing, Think about it from
the students.
Okay, let's not even use theword student.
(18:51):
Think about it from thelearner's perspective, okay?
I'm a learner of life.
I'm just a person.
I go to a rock concert.
I listen to a band.
I love the band, I leave.
In no way am I like walking intothe concert being like fuck like
I might not understand this andlike I don't know how to do it,
and like I'm, right?
And then so like same person, Iwalk into a math class and my
(19:13):
teacher shows me this likereally cool math thing, like I
don't know whatever it is cool,it's like cool stuff, it's not
like, but I'm like, I would feellike I, I'd be so blocked.
By a previous math trauma orlike by whatever, I don't know
that I'd be able to do whatyou're wanting, I don't think we
can just show kids cool stuffwithout doing all this like prep
(19:34):
work emotionally.
Well, what do you think though?
Do you think I'm like, no, maybeI'm wrong.
Francis Su (19:39):
Yeah.
Vanessa Vakharia (19:41):
People don't have like, music trauma.
Francis Su (19:44):
Yeah.
Why, and why is that?
Vanessa Vakharia (19:47):
Tell me you're the guest.
You're
Francis Su (19:49):
Yes.
Yes.
Well, I mean, I'm just thinkingout loud here, which is what I
think math helps us to do often.
But, you know, if I think aboutmusic, people have early
introduction to music, so it'snot unfamiliar.
Vanessa Vakharia (20:04):
Lullabies, even.
Francis Su (20:05):
Lullabies.
People sing.
you know, I have a three yearold and I.
I'm basically, doing littlemathematical things just to get
him ready, right?
Like, back when we were, I waschanging his diaper, I would say
what's one plus one.
And he'd say two.
And that's, of course, that'sall memory, right?
He's not doing anyunderstanding.
(20:25):
But I have to say, so now he'sthree, three and a half.
just the other day, for thefirst time I saw him thinking
about this, right?
So we do, you know, one plus oneis two, two plus two is four.
And he knows these things byheart now, but then I, you know,
recently I started doing this,one plus one is, Oh, count them
two, right?
And so, this was maybe a monthago or so he, I said, what's one
(20:50):
plus one.
And he did this.
And he thought of,
Vanessa Vakharia (20:54):
Okay, wait.
Everyone needs to know whatyou're doing.
This is a podcast.
Francis Su (20:57):
yes, oh I'm sorry, yes, yes.
I'm holding up fingers, and thenputting them together, right?
So two plus two, I'd hold up twoon one hand, two on the other
hand, and then I put themtogether, and then we, you know,
then we start counting them,right?
And so the funny thing is he'svery good at just reciting, but
the other day he actually pausedand that's how I knew he was
(21:19):
thinking.
And I saw his eyes move andthink, right.
And so I put up, you know, oneplus one and he's like looking
and then thinking, and then hesays two.
And I say, two plus two.
And then he pauses in a way henever did that before and then
he goes four and then just totest him I mean, we don't recite
this one.
I said what's one plus two?
Vanessa Vakharia (21:39):
Oh my god.
Francis Su (21:41):
We've never practiced that one before and I
could see the gears turning andhe said three!
Vanessa Vakharia (21:46):
No, he didn't! Mazel.
Oh my god.
That's incredible.
Francis Su (21:51):
But see that, he's not afraid to engage that way
because we did all this prepwork, but it wasn't like, he
would get the answer wrong lots,like, sometimes he wouldn't
remember 2 plus 2 is 4.
He'd say 5 or whatever, and Idon't shame him, right?
I don't say, you're wrong, it's4, and now you don't get your
supper.
You know, like, um, it's sofunny how kids learn through
(22:16):
revision and I don't make themfeel bad that they don't get it
the first time.
But then of course when hebegins to see it, has a insight,
I'm like, whoa, that's cool.
That's great So so maybe I meanthat like with music is like
that, too.
People have an introduction inmusic and I guess maybe they
don't necessarily learn how toplay music until much later
Vanessa Vakharia (22:39):
Or ever though.
Like they could never learn itand they wouldn't learn, they
wouldn't feel dumb about beinglike, oh man, I can't play what
the band is playing, like,
Francis Su (22:49):
Yes.
Vanessa Vakharia (22:50):
Because I'm also thinking, like, I literally
just thought of this questionnow with you.
So, speaking of learning throughrevision, like, that's literally
what we're doing.
And we're not like, no, like,take back your previous answer.
So, first of all, that's adirect application of what
you're talking about in termsof, like, translatable
mathematical skill.
But I'm also thinking out loud,is it because there are no
stakes attached to music the waythey are with math?
Francis Su (23:11):
Yeah, or less.
Less so.
Vanessa Vakharia (23:13):
No one's going to call you dumb if you don't
know how to play music.
Francis Su (23:16):
That's right.
And, one could argue, I'm notsure I'm gonna stand by this,
but I'll just say it.
Like, one could argue that mathis such a necessary skill to
have in a way that music isn't,but you know, the thing is,
like, I, that's, that's part ofthe whole flourishing aspect.
Like, I would say, if you liveda life where you never
(23:36):
experienced music, that would bea real shame, right?
That like maybe, you know,something like music is, you
don't need that to live, butmusic is part of what makes life
worth living, right?
Like it's part of why you live.
Vanessa Vakharia (23:55):
That's, whoa.
That's fucking deep and I know,I see what you're saying of
being like, I don't know if I'mgonna say, like I know what
you're saying.
I'm like, I don't know but thenI'm kind of like well, hold on,
what does it mean to even needsomething to live?
Francis Su (24:07):
Yeah.
I mean, you could go throughyour whole life and not listen
to much music and, but I wouldsay that there's, you've lost
something if you haven'tactually, haven't actually
experienced music.
You know, right.
And the other thing, of course,is that there's lots of
different ways to experiencemusic, lots of different kinds
(24:28):
of music.
And to get to your point, we'revery limited in what we think of
as math.
We think of math is just thosecalculator skills.
And it's actually much larger,like math includes, of course, I
like to call them virtues, beingable to visualize, right?
Being able to define, toquantify, to abstract, like
(24:50):
these are all different ways ofbeing mathematical and we don't
often talk about that or discussthat or assess that.
But that's why I love theQueen's Gambit, right?
Like you, you saw this girlpracticing her chess skills by
visualization and, you know,laying awake at night and
looking up at the ceiling,right?
(25:11):
I can't tell you the number oftimes that I, I do that as a
mathematician thinking about ahard problem.
I try to visualize it in someway that's completely different
than the way I was thinkingabout it before.
Vanessa Vakharia (25:20):
Oh, and I love, and also doesn't that
speak to the way we would lovepeople to think about ideas that
they're so polarized against?
Looking at it, reframing it in adifferent way from a different
perspective and a differentcontext.
Francis Su (25:33):
Yes, that's how you have empathy for other people,
even if you don't agree withthem, like, it would be great if
every person could argue to givethe best argument for why their
ideological opponent has aparticular point of view, right?
Like,
Vanessa Vakharia (25:51):
Wait, I love that.
Like, you have to find one thingin the other person's argument
that, like, speaks to you insome way that's, like
meaningful.
Francis Su (26:00):
Yeah, yeah.
I mean
Vanessa Vakharia (26:01):
You should tell this to Chris.
This is great for his debatestuff.
Francis Su (26:06):
uh, yeah, yeah.
Sorry.
Who?
Chris?
Chris who?
Vanessa Vakharia (26:09):
Chris Luzniak, who thinks you're very nice, who
I just interviewed.
Francis Su (26:12):
Oh, I see.
Yes, and of course that's what Ilike about Chris Luzniak's work
is, which, uh, for the listenerwho doesn't know is, um, he
frames math around thinkingabout debates.
And how engaging it is to havedebates.
So you're not, debating whethertwo plus two equals four, but
you're debating what's the beststrategy to get to this or that
(26:33):
answer.
And that, that is really moreabout what math is about.
So he's actually like, gettingat an aspect of math that, hits
at the community aspect, right?
Being able to have interestingconversations about how you
might try to solve a problem.
Vanessa Vakharia (26:47):
Hmm.
Mm hmm.
Francis Su (26:48):
That's really more about, as a professional
mathematician, that's more likewhat my life is like is I have
I'm having debates, little mini,discussions with my
collaborators and how we'regoing to approach this or that
problem.
That's way more interesting andengaging than.
having debates over facts, whichI hope we don't have debates
over.
Vanessa Vakharia (27:09):
Well, yeah, exactly.
And also it's like that, but Ithink that's what people think.
They think that's the only wayto talk about math.
Okay.
I'm, I'm actually looking at my,list of questions and I haven't
asked you one thing I wanted toask.
And I kind of love that becausethis is the best, but I do,
there's one thing, I mean,there's one final question I'm
going to ask you.
Um.
But also how funny is that?
I was like, Oh, I didn't askactually one of these questions,
(27:30):
but this has been the best convoanyhow.
Here's my question.
Do you know Gabor Mate?
I'm listening to his book onAudible.
It's just about, it's abouttrauma, and I'm writing a book
on math trauma and math therapy,and the way he frames it made me
want to ask you about it.
He talks about trauma as awound.
He's like, you know, when wetalk about trauma, we make it
(27:51):
this whole big thing, but it'snot like trauma is basically
like any wound you have, aninternal wound.
And with a wound, it eitherscars over, so it becomes rigid
and immovable and you can't growover it, or it doesn't scar
over, so anytime anyone touchesthat wound, it hurts again.
So like, I think about mathtrauma that way.
(28:12):
You know, you have an experiencewith math that it just leaves a
little bit of a wound.
Either you, you can't, uh, dowhat we were saying, you can't
go to a math rock concert andtake in the math because you
just don't feel like you cangrow, or it hurts and you feel,
you know, whatever.
So, do you feel the way that weare currently teaching math,
which I would say is obviouslynot in any way towards the end
(28:32):
goal of human flourishing inmost classrooms, do you think
there's something about teachingmath in the way we are that
leads to that wound or leads tothat wound being re touched or
re triggered?
Francis Su (28:46):
Mm Yeah, I mean, I, I do.
I think that there's a hugeemphasis.
And again, I understand why,where it comes from, but there's
a huge emphasis in the earlygrades on speed as a measure of
ability.
When, you know, if you even lookat in college or advanced
levels, speed isn't even athing, right?
(29:06):
But I understand, I understandwhy we do it.
It's because we want kids to befluent in their math facts.
And that's, that's valuable.
But maybe we should rethink,just to start in one place,
maybe we should rethink how weuse speed and why we, can we
design activities, strategiesfor getting kids to learn their
(29:28):
math facts without shame andwithout speed being a factor.
If you just do that, and I thinkthere are many ways that you
could do that, I think thatwould go a long way to, helping
kids not experience that wound.
That's not the only thing,there's lots of different ways
that we could change.
I think we've got to change alot of how we assess math,
right?
We got to give studentsexperiences where they reflect
(29:51):
on some of the joyful aspects ofmath, right?
Actually, I, what I like to doin my class is actually have
students write and doreflections.
So, part of, part of that is, istrying to heal some math trauma,
and, um, part of that is justgetting them to realize that,
that I think, as a teacher, thatthere are these other things
that are equally important,right?
(30:13):
I do want my students to, tolearn the skills that they're
supposed to learn in this orthat class, but I want them to
also have, times when they, theyactually reflect.
You know, like, what's, what'sthe most beautiful idea that
you've seen so far in thisclass?
And why is it beautiful to you?
These kinds of things should bepart of our assessments.
Vanessa Vakharia (30:32):
Okay, We're on to the final questions.
But okay, I'm asking one moreand then we're honestly final
questions, which are like, bang,bang, like quick.
But like, here's the thing.
Francis Su (30:40):
Speed, oh no,
Vanessa Vakharia (30:41):
No, I, speed, speed.
You're being tested.
The rubric is only speed.
No, if we're all, kind of like,math needs to change.
Math needs to change.
Why isn't it?
Francis Su (30:50):
Yes, um, it's complicated.
It's complicated.
Vanessa Vakharia (30:55):
Okay.
Okay.
Francis Su (30:56):
I don't know.
I don't know if there's any easyanswers that question.
Part of it is we teach what weknow and how It's easier to be
in our comfort zone than to notbe in our comfort zone.
Part of it is that we needstructures around us as teachers
that encourage us to beexperimental and, uh, and don't
discourage us, right?
(31:16):
Like all of us want to, there'sno teacher who doesn't want to
improve their craft, but I knowif I have limited time and I
don't get rewarded for tryingthings that are risky, that I'm
just going to default to whatI've done before.
Vanessa Vakharia (31:31):
Yeah.
Francis Su (31:32):
And, that's not, the fault of the teacher if you
don't have people around you andstructures around you that
encourage you to try somethingdifferent.
Vanessa Vakharia (31:41):
Beautifully put.
Clapping at that one.
David probably hates this in themic.
Final two questions.
Number one.
What is the one thing you'd liketo see change about the way math
is taught in schools?
One thing.
Francis Su (31:53):
Uh, assessments.
Let's change what we value andhelp students see that too.
Because students only see whatthey're tested on.
Vanessa Vakharia (32:02):
A million percent, yes, we are so aligned
right now, an hour in and we areon the same page.
Finally, second question, whatwould you say to someone who is
like, very cool that you saidall this, Francis, but like, I'm
just not a math person.
Francis Su (32:17):
Oh, um, again, that's complicated.
But I usually start with theirexperiences and help them see
what they're already doing ismathematical, right?
Um, people think of math aslike, okay, can you compute this
or that?
Right?
But, you know, if an artist isvery visual, then I'd say, hey,
(32:39):
help them see that visualizationis a huge part of what it means
to do math as well.
And, they've honed this throughyears of experience doing
visualization, that they'reactually doing something
mathematical.
Vanessa Vakharia (32:52):
Just beautiful.
Is there anything I haven'tasked you that you feel you'd
like to say to our listeners?
Francis Su (32:59):
Um, I, I hope that every person is able to see that
math can be a part of theirlives in a rich and fruitful
way, even if it's not somethingthey regularly do or regularly
enjoy.
Vanessa Vakharia (33:13):
That's very lovely.
And I think you have to readFrancis's book, even if you
like, hate math.
No, seriously, like, even if youhate math, I would just read it.
Because it's like, I, I wasreading, like, I failed grade 11
math twice.
Like I, I've gone from one sideto the other and I was reading
it, jaw agaping, like, Oh myGod, exactly.
Like, so like, even if you'relistening to this and you're
(33:35):
like, ugh, I feel your book ismath therapy.
So I would read your book,Mathematics for Human
Flourishing.
Anything else you want to plughere?
Are you on TikTok or what?
Francis Su (33:44):
Ha ha ha.
Um, anything else I want toplug?
No, I mean, I think that likethat book is, as you notice, I
put a lot of heart into it.
You know, there's lots ofpersonal stories and that's,
part of the way in, I think, to,for people to begin to see
themselves in mathematics is tosee themselves as part of the
story.
And, um, you read some of my ownjourney of discouragement, but
(34:06):
also, why I think math should berich, should be part of
everybody's experience, right?
Like, if you think about what'sgoing on in AI these days,
people think of computation AIis, okay, we can just leave all
the math to, to the robots,right?
And I would say, yes, there's alot of routine stuff that should
(34:28):
be left to robots.
But, we're missing out if youlet robots do all the math,
Vanessa Vakharia (34:33):
Okay.
Like, should this episode becalled"Is mathematical virtue
the antidote to AI?"
Francis Su (34:40):
Yes, that's how you're going to get more people
to, to engage with it is like,this has implications for what
we're, what, the way we'rethinking about technology,
right?
Like, is technology
Vanessa Vakharia (34:51):
Totally!
Francis Su (34:51):
And part of the wisdom I think we, we need to
have around technology is beingable to say what's, routine that
I can actually,
Vanessa Vakharia (35:00):
Mm hmm.
Francis Su (35:01):
That I can automate and what's actually important to
focus on.
Isn't that also what life isabout?
Like, what should I be spendingmy time and energy thinking
about?
And I would say if you're notspending part of your time
enjoying some of themathematical patterns around
you, whether you think of themas mathematical or not, then
(35:22):
that's a life that's maybe notas rich as one in which you do
see some of the patterns aroundyou.
Vanessa Vakharia (35:29):
This is such an incredible conversation
because also I find that it'sreally hard, I know we're not
talking about spirituality, butit's hard to talk about things
in a spiritual way, because Ifeel that when I do, I got a lot
of flack from like math people,you know, not wanting the two to
meet.
Francis Su (35:45):
Yes, yes.
And I and I I think that's amistake like I think that like
people would be much more opento math if they could see how it
connects to their spiritualnatures.
I mean, you see some of thatthread running through the book,
but all these human desires areactually spiritual desires.
Like we, we have a spiritualconnection to beauty.
(36:06):
We have a spiritual connectionto, to seeking truth, right?
To, to seeking meaning, right?
These are all spiritual desiresas well.
Vanessa Vakharia (36:16):
Okay, this has been amazing, beyond, so
exciting.
Francis Su (36:20):
It's been fun for me too.
Vanessa Vakharia (36:22):
Great, well thanks for making it happen and
uh, bye.
Francis Su (36:26):
Bye bye.
Vanessa Vakharia (36:29):
I love him.
Can I say that?
I just love the guy.
I just left this interview withsuch a concrete outlook on how
math trauma can affect ourstudents far beyond their
performance in our classroomsand I appreciate so much Dr.
Su's ability to take what oftenseems vague and unapproachable
and turn it into something wecan all access and action in our
very own classrooms.
(36:49):
And come on, how cute was thatpart about teaching his son how
to count with his fingers?
I mean, stop.
Go get his book, The Mathematicsof Human Flourishing.
Seriously, you will not regretit.
If something in this episodeinspired you, please tweet us
@maththerapy and you can alsofollow me personally@themathguru
on Instagram, Twitter, andTikTok.
(37:10):
Math Therapy is hosted by me,Vanessa Vakharia, it was created
by me and Sabina Wex, and it'sproduced and edited by David
Kochberg.
Our theme music is by GoodnightSunrise.
And guys, if you know someonewho needs math therapy or just
needs to hear someone elsegetting math therapy, please,
please, please share thispodcast, and rate or review it
on whatever podcast app you use.
(37:31):
Those things actually make sucha big difference for us.
I'm determined to change theculture surrounding math and I
need your help, so spread theword.
Until next time, peace, love,and pi.
It's kind of like learning your musical scales, if
you want to play a concerto.
You don't learn music to startlearning to play scales.
People put the emphasis onthinking about math as learning
scales, versus listening to asymphony.
I just want people to experiencethe symphony, even if they don't
end up becoming professionalmusicians.
Vanessa Vakharia (00:23):
Hi, I'm Vanessa Vakharia, aka The Math
Guru, and you're listening toMath Therapy, a podcast that
explores the root causes of mathtrauma, and the empowering ways
we can heal from it.
Whether you think you're a mathperson or not, you're about to
find out that math people don'tactually exist.
But the scars that math classleft on many of us definitely
do.
Oh, and don't worry, nocalculators or actual math were
(00:46):
involved in the making of thispodcast.
Okay, let me ask you guys this.
What comes to mind when you hearthe words mathematics for human
flourishing?
Like really think about it.
"Mathematics for HumanFlourishing".
What a beautiful sentiment.
And it is also the title of anincredible book by Dr.
Francis Su and the reason I hadto have him on the podcast.
(01:08):
I devoured that book cover tocover and was so deeply moved by
the way he views mathematics,and the awe he believes it could
inspire in our students.
And I just, I can't wait for youguys to hear him explain how
finding the beauty and wonder inmath can make it possible for
all of us to truly flourish ashumans.
Francis, welcome to the podcast!I'm so excited to have you.
(01:30):
There's a lot I want to talk toyou about.
Truthfully, I have you on thepodcast as like a fan, like I
read your book and I was like,I'm a huge fan.
But, as I was like, Oh, I'mhaving him on the podcast, I
should like just do a littlemore research, I started kind of
like looking into you and, Ifound the reflection questions
you had written for your bookand that actually opened up like
(01:52):
a whole new thing in me.
And so, I actually have so manyquestions just about the first
thing I saw on your website,which was that you call yourself
a mathematical explorer.
Francis Su (02:04):
Yeah.
Well, I mean, I guess one ofthe, the ways that I think about
math, I think is a veryimportant aspect of math is the
exploratory nature of math,which a lot of people don't see.
And, I could call myself amathematician, but for some
people, when they hear thatterm, they think professional
mathematician who does research,for instance, like, one set of
(02:24):
people like college professorsthink mathematician is just
someone who does mathematicalresearch, but maybe other people
who are familiar with what amathematician does, who knows
what they think about when theythink about a mathematician?
And so I prefer to use the termmathematical explorer, because I
think that maybe is a littlemore accessible.
(02:45):
People don't have preconceivednotions about what it means to
be a mathematician.
Vanessa Vakharia (02:50):
Well, yeah, I would say that if you tell
anyone you're a mathematician,like, no one other than a
mathematician is going to thinkanything good.
Francis Su (02:58):
Yes, yes.
Vanessa Vakharia (02:59):
Like, that's not, that's not a good vibe.
Also, do you know, um, DeborahPeart at all, and like the work
she does around the term"mather"?
Francis Su (03:06):
Yes.
Vanessa Vakharia (03:07):
So it's like making me think about that.
Francis Su (03:09):
Yes, yeah, I mean I appreciate all these reframings
that help people get out of theusual mode when they think about
a particular word.
Vanessa Vakharia (03:18):
So like, why do you think that the word
mathematician has such a badreputation?
Francis Su (03:24):
That's a great question.
I think when people think ofmathematician, they think of, a
reclusive hermit who works on,you know, difficult problem for
many years and avoids people.
And, you know, to some extentthat narrative is, is sometimes
fed by media, right.
Or fed by stereotypes thatpeople have around who can be a
(03:44):
mathematician, and uh, what theydo.
And of course you hear thesestories about, you know, these
very, very hard centuries oldproblems that someone's been
working on, in silence untilthey suddenly solve it, right?
Like, that's one narrative thatoften gets press, but it's maybe
not the most common narrative orthe way that we do math.
Vanessa Vakharia (04:06):
Well, yeah, my whole master's thesis, it, well,
it's called Imagining a WorldWhere Paris Hilton Loves Math,
and it was entirely about mediarepresentations of
mathematicians, especially forwomen, and how it like, turns
them off the subject entirely,because who would be like, ooh,
you know what I want to do?
I want to be a recluse and,like, never have a romantic
relationship and have nofriends, but, like, all do math.
(04:28):
You know,
Francis Su (04:28):
Right.
That's right.
Vanessa Vakharia (04:29):
But it's, it's crazy because I wrote it in
2010, and you would think somuch has changed, but like
still, you're hard pressed tofind, a representation of a
mathematician that doesn't fitinto one of these tropes.
Francis Su (04:42):
Yes,
Vanessa Vakharia (04:43):
Like, think about the Queen's Gambit.
Did you watch that?
Francis Su (04:46):
Yes.
I love that.
I love that series.
Vanessa Vakharia (04:49):
Okay, but what did you think of, what was her
name?
The main character?
Francis Su (04:54):
I, yeah, I don't remember her name.
Vanessa Vakharia (04:55):
Well, whatever, but what did you think
of her?
Francis Su (04:57):
Well, I mean, there are some ways in which her
character broke stereotypes,right?
This is maybe for the listeners.
The main character is a girl whoplays chess and does a lot of
mathematical thinking, but shehas a very difficult life and,
the series tries to unpack alittle bit about her journey
into chess.
And it's been a little whilesince I watched it, so maybe you
(05:19):
should start with what youthought was recycling old
tropes.
Vanessa Vakharia (05:23):
I just think it's interesting.
Cause when I watched it, I waslike, yes, a woman who plays
chess..
And then I started looking at itas like, the full picture.
And I was like, but hold on asecond.
What did she have to do to be agreat mathematical thinker?
Oh, she had all of theseproblems.
She had to do all of thesedrugs.
They kind of made it seem likeshe had like severe mental
health issues.
Francis Su (05:43):
Yes.
Yes.
Vanessa Vakharia (05:44):
Right?
So I was like, wait, this isjust the same trope now of being
like, the only way you can begood at math is if there's
something like wrong with you inevery
Francis Su (05:51):
Yes.
No, that's very true.
That's very true.
Yeah, I mean that's similar toGood Will Hunting, right?
Like, Good Will Hunting is, itfollows that.
Vanessa Vakharia (05:59):
A Beautiful Mind.
Francis Su (06:00):
Yes, Beautiful Mind, um, to some extent Jeff
Goldblum, uh, in, uh, uh,Jurassic Park, is this sort of
crazy mathematician who is alittle, you know, he's a little
weird in some sense and, yeah,all these things sort of feed
into that, that stereotype.
But there are ways which Iappreciated Queen's Gambit, they
do a pretty good job of, helpingpeople see what it means to
(06:25):
visualize math or visualizechess, like doing chess on the
ceiling.
I, I love some of those scenes.
Vanessa Vakharia (06:31):
I loved that.
Well, and like, so I run a mathtutoring center.
We tutor math, and literally,I'm not kidding, after that came
out, I had at least 10 femalestudents being like, do you guys
tutor chess?
Like it worked in a way, right?
Like it, it got women, like aton of my teenage students, like
getting into chess.
So, okay.
Well, anyway, so MathematicalExplorer it is, and that's what
(06:51):
we're using from now on becauseit sounds way cooler and way
more fun.
And I think really touches onthat exploratory nature of what
mathematics could be.
This thing filled with likecuriosity.
And what you talk about ismathematics for human
flourishing.
That's the title of your bookand that's what it's about.
And I guess my first question islike, what is human flourishing
(07:14):
to you?
Francis Su (07:15):
Yeah, the way I like to think about human flourishing
is it's both a state of beingand doing and so the being
aspect is it's beyond happiness.
It's a beyond joy.
In fact, you could be goingthrough very difficult
circumstances and still beflourishing in those
circumstances.
(07:36):
It's a state of living andacting in accordance with,
living to your fullestpotential, maybe it's one way of
putting it.
And acting in accordance withyour values.
It's a holistic state of being.
I mean, one way of thinkingabout it is, is the way the
ancient Greeks thought abouthuman flourishing, right?
(07:58):
It's the ultimate good in lifein some sense, right?
It's the highest good is one inwhich you are, maybe in, in
modern parlance, it's, you're ina state of flow and that's the
way some people in thepsychology literature talk about
being in flow, right?
You are so, absorbed orengrossed in, in this case, it
could be maybe a, solving aproblem, but, generally
(08:19):
speaking, outside themathematical context, it's um,
I, I hate to use this term"living your best life" because
that also sounds like it hassomething to do with
Vanessa Vakharia (08:29):
So YOLO.
Francis Su (08:29):
circumstances.
Vanessa Vakharia (08:30):
It means YOLO.
Francis Su (08:31):
Yes,
Vanessa Vakharia (08:32):
You could have titled your book, Mathematics
for YOLO.
Okay, cool.
Francis Su (08:36):
But let me give you an example.
I mean, like, for instance, whenmy, um, my mother was dying,
that's, that, that's a difficultsituation, right?
But, you know, sometimes whenyou have difficult situations
you're living through, you canstill, you know, that, that
started lots of conversations,hard conversations, good
conversations, richconversations.
(08:58):
And somehow you're like, oh,really in the moment, you are
really loving someone through adifficult time, that could also
be a state of human flourishing.
Vanessa Vakharia (09:10):
It's so crazy because, first of all, you said
it so beautifully.
And I, I feel like we're, I usedifferent words, but to me, this
sounds like you're talking aboutliving in alignment, really,
with like your values, whateverthat is.
And it feels really spiritual tome in the sense that it, like,
has nothing to do with thematerial world, it's something
so internal, but, so you're on apodcast called Math Therapy, and
(09:32):
my whole, thing really is theidea that, like, yes, it's very
cool to learn math andmathematical thinking and all of
that, but to me, the skillsstudents have the capacity to
learn in math class are onesthat I really believe can lead
them to a lifetime of joy.
In, I always say, helpingstudents break myth around math
ability that have been like puton them can help lead them to a
(09:54):
place where they truly believethey're capable of anything.
I can think of no greater, morenoble cause than to help young
people discover how to do that.
Francis Su (10:03):
Yes.
Right.
Right.
Yeah.
I mean, living life is hard.
Vanessa Vakharia (10:07):
It's hard.
Francis Su (10:08):
It's hard, and how do we, how do we move through
the world?
You know, I think mathematicscertainly helps people, to see
the world more clearly and movethrough it in ways that if you
don't have that experience, evenhaving the experience of beauty
in seeing mathematics, that's toour detriment, right?
That's, there's something we'remissing by, not experiencing
(10:32):
some of those things.
Vanessa Vakharia (10:33):
So how do you tie those ideas of human
flourishing, this beautifulincredible thing that it'd be so
great for every human to be ableto like actualize, and doing
that through mathematics?
Like tie those together for me.
Francis Su (10:48):
Yeah.
Uh, well, I guess the way that Itry to do that in the book is to
connect with everybody'sexperience of, of having deep
human desires, right?
Like we all have a deep desirefor community, to be in
connection with other people.
We all have a deep desire formeaning.
nobody wants to live a life thatsomehow feels meaningless.
(11:09):
So we automatically makeconnections, between events and
people and ideas.
And the same thing happens inmath, right?
You, you make connectionsbetween something you're just
learning and something thatyou've seen in another context.
We all have a deep desire forfreedom and being able to have
agency to make choices in whatwe do.
(11:30):
Um, we all have a, a deep desirefor beauty to experience, that
feeling of transcendence, whichpeople experience in other
contexts, but only people who domath professionally begin to see
the sort of transcendent side oflike, oh, whoa, you know, this
idea is connected to this oneand it's so beautiful.
(11:51):
Right?
And, you know, this is part ofwhy, you know, you see, in a
beautiful mind, you've got thislike, um, characters who
experienced that beauty.
And then, of course, everyonelooks at that and says, oh,
they're crazy, you know, ratherthan, oh, I want some of that,
right?
I want to be able to see theconnectedness of ideas and feel
like I have a window intosomething that I otherwise
(12:14):
wouldn't see.
Vanessa Vakharia (12:15):
Yeah, I think part of that reason is because
that character never is able tolike get a girlfriend.
You know, like, so you're like,yeah, I'd like to feel like
that, but not at the expense oflike my social life.
But that being said, but, butwhat's so interesting about what
you said is you're talking aboutmath in this incredibly like
liberating way, but how is itthat you are talking about it
(12:38):
this way yet, I would say thatmost people I know would think
of math as like one of the mostrestrictive things.
One of the things that wouldabsolutely not lead to freedom.
Francis Su (12:48):
Yes.
Yes.
and that's, that's because mathhas this other side, right?
The side of, um,
Vanessa Vakharia (12:54):
The dark side.
Francis Su (12:56):
Ha, well it doesn't have to be dark, but it's often
taught that way.
Like, you know, some of these,basic understandings, that you
need in order to experience someof that beauty and joy, is some
basic, you know, basic numberfacts, right?
And, you know, I think thosethings are, are important, but
it's sometimes often taughtlike, Hey, just try to be a
better human calculator.
(13:17):
And, you know, what I like tosay is the world doesn't need
better human calculators.
Yes.
It's important that we know ourbasic facts and that having a
fluency, there's that technicalside, but people often confuse
that, fluency with.
the deeper joy or the deeperpossibilities inherent in
learning math.
And you know, there, there areways in which that's, you know,
(13:39):
that, that takes practice andit's, it's kind of like learning
your musical scales, right?
If you want to play a concerto,right?
But, you don't learn music tostart learning to play scales.
Right?
Like people put the, you know,maybe switch the emphasis on
thinking about math as learningscales, versus listening to a
symphony.
(13:59):
And I just want people toexperience the symphony, even if
they don't end up becomingprofessional musicians,
Vanessa Vakharia (14:08):
And even if they can't like write the
symphony themselves, like theycan still listen to it.
Francis Su (14:13):
Yes, and enjoy, experience that.
If you think about what we do inmath, often we teach people to
learn scales before theyactually experience the
symphony.
And some people think, well,gosh, you know, kids can't
experience a symphony until theylearn the scales.
And I'm like, no, no, you cangive them glimpses of what's
possible.
Vanessa Vakharia (14:32):
But they've heard music.
That's the other, Okay.
But now I'm obsessed with thisidea because I'm like, okay,
hold on.
So I'm like, well, of course,again, I'm in a band.
So like tons of people go toconcerts and they're not I can't
get into this because I don'tknow how to play the guitar.
Francis Su (14:47):
Right.
Vanessa Vakharia (14:48):
But why is it different for math?
is it because there's so muchguilt and shame around not being
able to like understand everybit of it?
Whereas like, there's no guiltand shame around not being able
to perform an instrument.
Francis Su (15:00):
Yeah, I think that there, there's some aspect of
that, right?
Like there's this idea that, Oh,I can't teach kids, I can't show
kids the beautiful side of math,until they learn their times
tables.
Vanessa Vakharia (15:12):
Hmm.
Mm
Francis Su (15:13):
And so, of course, part of that, the thing that I
say is that that's theexploratory side that the
playful side of mathematics isoften what gets people
interested and helps them seethat, oh, actually, math is
actually fun.
Right?
And they begin to enjoy thoseaspects of mathematical
thinking.
You know, think about what'sgoing on in the world today,
(15:33):
right?
Like where we have calculators,computers that can do a lot of
the routine stuff for us, right?
It's valuable, it's importantfor kids to know how to multiply
7 times 5 quickly, so you're notalways reaching for a
calculator.
Yes.
But, as an example, do we reallyneed to teach long division?
You know, there's, there's alittle bit of a debate, right?
(15:55):
Like, what would I like kids tolearn, that I think is way more
valuable, is having a certainnumber sense, right?
Being able to say that, oh, if Imultiply, 39 times 4, I should
get something that's about 160.
Because that's almost 40 times4, right?
That, that's a skill that'suseful in today's modern world.
(16:15):
We can let calculators andcomputers and AI do the, the
routine stuff, but what we needare people with virtues who are
able to say, ah, I thinksomething went wrong with that
computer, right?
Like I think the answer, ormaybe somebody entered the
numbers wrong, but I know that,you know, 39 times 4 isn't gonna
(16:37):
give me 2000, right?
Like so
Vanessa Vakharia (16:38):
Right.
Francis Su (16:39):
That, that's what we need.
We need people who are able todo the checks and say ah
something went wrong somewhere.
Vanessa Vakharia (16:44):
But I love that you just said people with
virtues.
What a way to put it.
Francis Su (16:49):
Yeah.
And of course, that's theargument.
the big argument I'm making inthe book is that math is more
than just a bunch of skills likelearning how to multiply numbers
and factor a quadratic.
Like skills are things thatcalculators and computers can do
because they can be automated,but virtues are always going to
be in demand, right?
If you have a job that dependson having skills, that job's in
(17:11):
jeopardy, right?
Vanessa Vakharia (17:12):
Right.
Right.
Yeah.
Francis Su (17:15):
But if you have people who actually have the
capacity to think, to reason, tovisualize, to abstract, to
define, to quantify, those,virtues are always going to be
in demand.
Those are the things that agreat math education builds, and
unfortunately, people don't getthat impression when they leave
a math class Maybe we don't do agood enough sales job as
(17:38):
teachers.
Vanessa Vakharia (17:38):
We do not.
No, I've never, no.
Francis Su (17:43):
Yeah, and when people say, well, why do I need
to know this stuff?
The reason is often because theythink math is just skills, like,
why do I need to know how tofactor a quadratic?
Well, people who go off in STEMand subjects, um, but most
people never need to factor aquadratic in their daily lives.
But will they actually need tobe able to think, and to reason,
Vanessa Vakharia (18:04):
Yes.
Francis Su (18:05):
and to understand?
Yes!
Vanessa Vakharia (18:07):
And that's what I always say too.
I'm like, it's like the mathadjacent skills you're building.
Obviously we would love to go inand change the curriculum and
the content and all, but likethe only thing I think you could
do to convince a, like a childor a teenager or whatever that
it was important is to be like,you're going to be building
skills that will be important inthe areas of your life that
matter.
Like, you know what I mean?
Like factoring a quadratic.
Okay.
First of all, I actually lovefactoring quadratics.
(18:29):
Regardless of whether it'suseful.
Okay.
That's one of my favoritethings, but I'm always like, no,
it's like the thinking, it's thelike ability to like problem
solve and to work through it.
Like all of that stuff.
But like, okay, but hold on, wehave to back up.
Cause you said something thatI'm like, still like shell
shocked over.
kind of.
I'm still thinking about themusic thing, Think about it from
the students.
Okay, let's not even use theword student.
(18:51):
Think about it from thelearner's perspective, okay?
I'm a learner of life.
I'm just a person.
I go to a rock concert.
I listen to a band.
I love the band, I leave.
In no way am I like walking intothe concert being like fuck like
I might not understand this andlike I don't know how to do it,
and like I'm, right?
And then so like same person, Iwalk into a math class and my
(19:13):
teacher shows me this likereally cool math thing, like I
don't know whatever it is cool,it's like cool stuff, it's not
like, but I'm like, I would feellike I, I'd be so blocked.
By a previous math trauma orlike by whatever, I don't know
that I'd be able to do whatyou're wanting, I don't think we
can just show kids cool stuffwithout doing all this like prep
(19:34):
work emotionally.
Well, what do you think though?
Do you think I'm like, no, maybeI'm wrong.
Francis Su (19:39):
Yeah.
Vanessa Vakharia (19:41):
People don't have like, music trauma.
Francis Su (19:44):
Yeah.
Why, and why is that?
Vanessa Vakharia (19:47):
Tell me you're the guest.
You're
Francis Su (19:49):
Yes.
Yes.
Well, I mean, I'm just thinkingout loud here, which is what I
think math helps us to do often.
But, you know, if I think aboutmusic, people have early
introduction to music, so it'snot unfamiliar.
Vanessa Vakharia (20:04):
Lullabies, even.
Francis Su (20:05):
Lullabies.
People sing.
you know, I have a three yearold and I.
I'm basically, doing littlemathematical things just to get
him ready, right?
Like, back when we were, I waschanging his diaper, I would say
what's one plus one.
And he'd say two.
And that's, of course, that'sall memory, right?
He's not doing anyunderstanding.
(20:25):
But I have to say, so now he'sthree, three and a half.
just the other day, for thefirst time I saw him thinking
about this, right?
So we do, you know, one plus oneis two, two plus two is four.
And he knows these things byheart now, but then I, you know,
recently I started doing this,one plus one is, Oh, count them
two, right?
And so, this was maybe a monthago or so he, I said, what's one
(20:50):
plus one.
And he did this.
And he thought of,
Vanessa Vakharia (20:54):
Okay, wait.
Everyone needs to know whatyou're doing.
This is a podcast.
Francis Su (20:57):
yes, oh I'm sorry, yes, yes.
I'm holding up fingers, and thenputting them together, right?
So two plus two, I'd hold up twoon one hand, two on the other
hand, and then I put themtogether, and then we, you know,
then we start counting them,right?
And so the funny thing is he'svery good at just reciting, but
the other day he actually pausedand that's how I knew he was
(21:19):
thinking.
And I saw his eyes move andthink, right.
And so I put up, you know, oneplus one and he's like looking
and then thinking, and then hesays two.
And I say, two plus two.
And then he pauses in a way henever did that before and then
he goes four and then just totest him I mean, we don't recite
this one.
I said what's one plus two?
Vanessa Vakharia (21:39):
Oh my god.
Francis Su (21:41):
We've never practiced that one before and I
could see the gears turning andhe said three!
Vanessa Vakharia (21:46):
No, he didn't! Mazel.
Oh my god.
That's incredible.
Francis Su (21:51):
But see that, he's not afraid to engage that way
because we did all this prepwork, but it wasn't like, he
would get the answer wrong lots,like, sometimes he wouldn't
remember 2 plus 2 is 4.
He'd say 5 or whatever, and Idon't shame him, right?
I don't say, you're wrong, it's4, and now you don't get your
supper.
You know, like, um, it's sofunny how kids learn through
(22:16):
revision and I don't make themfeel bad that they don't get it
the first time.
But then of course when hebegins to see it, has a insight,
I'm like, whoa, that's cool.
That's great So so maybe I meanthat like with music is like
that, too.
People have an introduction inmusic and I guess maybe they
don't necessarily learn how toplay music until much later
Vanessa Vakharia (22:39):
Or ever though.
Like they could never learn itand they wouldn't learn, they
wouldn't feel dumb about beinglike, oh man, I can't play what
the band is playing, like,
Francis Su (22:49):
Yes.
Vanessa Vakharia (22:50):
Because I'm also thinking, like, I literally
just thought of this questionnow with you.
So, speaking of learning throughrevision, like, that's literally
what we're doing.
And we're not like, no, like,take back your previous answer.
So, first of all, that's adirect application of what
you're talking about in termsof, like, translatable
mathematical skill.
But I'm also thinking out loud,is it because there are no
stakes attached to music the waythey are with math?
Francis Su (23:11):
Yeah, or less.
Less so.
Vanessa Vakharia (23:13):
No one's going to call you dumb if you don't
know how to play music.
Francis Su (23:16):
That's right.
And, one could argue, I'm notsure I'm gonna stand by this,
but I'll just say it.
Like, one could argue that mathis such a necessary skill to
have in a way that music isn't,but you know, the thing is,
like, I, that's, that's part ofthe whole flourishing aspect.
Like, I would say, if you liveda life where you never
(23:36):
experienced music, that would bea real shame, right?
That like maybe, you know,something like music is, you
don't need that to live, butmusic is part of what makes life
worth living, right?
Like it's part of why you live.
Vanessa Vakharia (23:55):
That's, whoa.
That's fucking deep and I know,I see what you're saying of
being like, I don't know if I'mgonna say, like I know what
you're saying.
I'm like, I don't know but thenI'm kind of like well, hold on,
what does it mean to even needsomething to live?
Francis Su (24:07):
Yeah.
I mean, you could go throughyour whole life and not listen
to much music and, but I wouldsay that there's, you've lost
something if you haven'tactually, haven't actually
experienced music.
You know, right.
And the other thing, of course,is that there's lots of
different ways to experiencemusic, lots of different kinds
(24:28):
of music.
And to get to your point, we'revery limited in what we think of
as math.
We think of math is just thosecalculator skills.
And it's actually much larger,like math includes, of course, I
like to call them virtues, beingable to visualize, right?
Being able to define, toquantify, to abstract, like
(24:50):
these are all different ways ofbeing mathematical and we don't
often talk about that or discussthat or assess that.
But that's why I love theQueen's Gambit, right?
Like you, you saw this girlpracticing her chess skills by
visualization and, you know,laying awake at night and
looking up at the ceiling,right?
(25:11):
I can't tell you the number oftimes that I, I do that as a
mathematician thinking about ahard problem.
I try to visualize it in someway that's completely different
than the way I was thinkingabout it before.
Vanessa Vakharia (25:20):
Oh, and I love, and also doesn't that
speak to the way we would lovepeople to think about ideas that
they're so polarized against?
Looking at it, reframing it in adifferent way from a different
perspective and a differentcontext.
Francis Su (25:33):
Yes, that's how you have empathy for other people,
even if you don't agree withthem, like, it would be great if
every person could argue to givethe best argument for why their
ideological opponent has aparticular point of view, right?
Like,
Vanessa Vakharia (25:51):
Wait, I love that.
Like, you have to find one thingin the other person's argument
that, like, speaks to you insome way that's, like
meaningful.
Francis Su (26:00):
Yeah, yeah.
I mean
Vanessa Vakharia (26:01):
You should tell this to Chris.
This is great for his debatestuff.
Francis Su (26:06):
uh, yeah, yeah.
Sorry.
Who?
Chris?
Chris who?
Vanessa Vakharia (26:09):
Chris Luzniak, who thinks you're very nice, who
I just interviewed.
Francis Su (26:12):
Oh, I see.
Yes, and of course that's what Ilike about Chris Luzniak's work
is, which, uh, for the listenerwho doesn't know is, um, he
frames math around thinkingabout debates.
And how engaging it is to havedebates.
So you're not, debating whethertwo plus two equals four, but
you're debating what's the beststrategy to get to this or that
(26:33):
answer.
And that, that is really moreabout what math is about.
So he's actually like, gettingat an aspect of math that, hits
at the community aspect, right?
Being able to have interestingconversations about how you
might try to solve a problem.
Vanessa Vakharia (26:47):
Hmm.
Mm hmm.
Francis Su (26:48):
That's really more about, as a professional
mathematician, that's more likewhat my life is like is I have
I'm having debates, little mini,discussions with my
collaborators and how we'regoing to approach this or that
problem.
That's way more interesting andengaging than.
having debates over facts, whichI hope we don't have debates
over.
Vanessa Vakharia (27:09):
Well, yeah, exactly.
And also it's like that, but Ithink that's what people think.
They think that's the only wayto talk about math.
Okay.
I'm, I'm actually looking at my,list of questions and I haven't
asked you one thing I wanted toask.
And I kind of love that becausethis is the best, but I do,
there's one thing, I mean,there's one final question I'm
going to ask you.
Um.
But also how funny is that?
I was like, Oh, I didn't askactually one of these questions,
(27:30):
but this has been the best convoanyhow.
Here's my question.
Do you know Gabor Mate?
I'm listening to his book onAudible.
It's just about, it's abouttrauma, and I'm writing a book
on math trauma and math therapy,and the way he frames it made me
want to ask you about it.
He talks about trauma as awound.
He's like, you know, when wetalk about trauma, we make it
(27:51):
this whole big thing, but it'snot like trauma is basically
like any wound you have, aninternal wound.
And with a wound, it eitherscars over, so it becomes rigid
and immovable and you can't growover it, or it doesn't scar
over, so anytime anyone touchesthat wound, it hurts again.
So like, I think about mathtrauma that way.
(28:12):
You know, you have an experiencewith math that it just leaves a
little bit of a wound.
Either you, you can't, uh, dowhat we were saying, you can't
go to a math rock concert andtake in the math because you
just don't feel like you cangrow, or it hurts and you feel,
you know, whatever.
So, do you feel the way that weare currently teaching math,
which I would say is obviouslynot in any way towards the end
(28:32):
goal of human flourishing inmost classrooms, do you think
there's something about teachingmath in the way we are that
leads to that wound or leads tothat wound being re touched or
re triggered?
Francis Su (28:46):
Mm Yeah, I mean, I, I do.
I think that there's a hugeemphasis.
And again, I understand why,where it comes from, but there's
a huge emphasis in the earlygrades on speed as a measure of
ability.
When, you know, if you even lookat in college or advanced
levels, speed isn't even athing, right?
(29:06):
But I understand, I understandwhy we do it.
It's because we want kids to befluent in their math facts.
And that's, that's valuable.
But maybe we should rethink,just to start in one place,
maybe we should rethink how weuse speed and why we, can we
design activities, strategiesfor getting kids to learn their
(29:28):
math facts without shame andwithout speed being a factor.
If you just do that, and I thinkthere are many ways that you
could do that, I think thatwould go a long way to, helping
kids not experience that wound.
That's not the only thing,there's lots of different ways
that we could change.
I think we've got to change alot of how we assess math,
right?
We got to give studentsexperiences where they reflect
(29:51):
on some of the joyful aspects ofmath, right?
Actually, I, what I like to doin my class is actually have
students write and doreflections.
So, part of, part of that is, istrying to heal some math trauma,
and, um, part of that is justgetting them to realize that,
that I think, as a teacher, thatthere are these other things
that are equally important,right?
(30:13):
I do want my students to, tolearn the skills that they're
supposed to learn in this orthat class, but I want them to
also have, times when they, theyactually reflect.
You know, like, what's, what'sthe most beautiful idea that
you've seen so far in thisclass?
And why is it beautiful to you?
These kinds of things should bepart of our assessments.
Vanessa Vakharia (30:32):
Okay, We're on to the final questions.
But okay, I'm asking one moreand then we're honestly final
questions, which are like, bang,bang, like quick.
But like, here's the thing.
Francis Su (30:40):
Speed, oh no,
Vanessa Vakharia (30:41):
No, I, speed, speed.
You're being tested.
The rubric is only speed.
No, if we're all, kind of like,math needs to change.
Math needs to change.
Why isn't it?
Francis Su (30:50):
Yes, um, it's complicated.
It's complicated.
Vanessa Vakharia (30:55):
Okay.
Okay.
Francis Su (30:56):
I don't know.
I don't know if there's any easyanswers that question.
Part of it is we teach what weknow and how It's easier to be
in our comfort zone than to notbe in our comfort zone.
Part of it is that we needstructures around us as teachers
that encourage us to beexperimental and, uh, and don't
discourage us, right?
(31:16):
Like all of us want to, there'sno teacher who doesn't want to
improve their craft, but I knowif I have limited time and I
don't get rewarded for tryingthings that are risky, that I'm
just going to default to whatI've done before.
Vanessa Vakharia (31:31):
Yeah.
Francis Su (31:32):
And, that's not, the fault of the teacher if you
don't have people around you andstructures around you that
encourage you to try somethingdifferent.
Vanessa Vakharia (31:41):
Beautifully put.
Clapping at that one.
David probably hates this in themic.
Final two questions.
Number one.
What is the one thing you'd liketo see change about the way math
is taught in schools?
One thing.
Francis Su (31:53):
Uh, assessments.
Let's change what we value andhelp students see that too.
Because students only see whatthey're tested on.
Vanessa Vakharia (32:02):
A million percent, yes, we are so aligned
right now, an hour in and we areon the same page.
Finally, second question, whatwould you say to someone who is
like, very cool that you saidall this, Francis, but like, I'm
just not a math person.
Francis Su (32:17):
Oh, um, again, that's complicated.
But I usually start with theirexperiences and help them see
what they're already doing ismathematical, right?
Um, people think of math aslike, okay, can you compute this
or that?
Right?
But, you know, if an artist isvery visual, then I'd say, hey,
(32:39):
help them see that visualizationis a huge part of what it means
to do math as well.
And, they've honed this throughyears of experience doing
visualization, that they'reactually doing something
mathematical.
Vanessa Vakharia (32:52):
Just beautiful.
Is there anything I haven'tasked you that you feel you'd
like to say to our listeners?
Francis Su (32:59):
Um, I, I hope that every person is able to see that
math can be a part of theirlives in a rich and fruitful
way, even if it's not somethingthey regularly do or regularly
enjoy.
Vanessa Vakharia (33:13):
That's very lovely.
And I think you have to readFrancis's book, even if you
like, hate math.
No, seriously, like, even if youhate math, I would just read it.
Because it's like, I, I wasreading, like, I failed grade 11
math twice.
Like I, I've gone from one sideto the other and I was reading
it, jaw agaping, like, Oh myGod, exactly.
Like, so like, even if you'relistening to this and you're
(33:35):
like, ugh, I feel your book ismath therapy.
So I would read your book,Mathematics for Human
Flourishing.
Anything else you want to plughere?
Are you on TikTok or what?
Francis Su (33:44):
Ha ha ha.
Um, anything else I want toplug?
No, I mean, I think that likethat book is, as you notice, I
put a lot of heart into it.
You know, there's lots ofpersonal stories and that's,
part of the way in, I think, to,for people to begin to see
themselves in mathematics is tosee themselves as part of the
story.
And, um, you read some of my ownjourney of discouragement, but
(34:06):
also, why I think math should berich, should be part of
everybody's experience, right?
Like, if you think about what'sgoing on in AI these days,
people think of computation AIis, okay, we can just leave all
the math to, to the robots,right?
And I would say, yes, there's alot of routine stuff that should
(34:28):
be left to robots.
But, we're missing out if youlet robots do all the math,
Vanessa Vakharia (34:33):
Okay.
Like, should this episode becalled"Is mathematical virtue
the antidote to AI?"
Francis Su (34:40):
Yes, that's how you're going to get more people
to, to engage with it is like,this has implications for what
we're, what, the way we'rethinking about technology,
right?
Like, is technology
Vanessa Vakharia (34:51):
Totally!
Francis Su (34:51):
And part of the wisdom I think we, we need to
have around technology is beingable to say what's, routine that
I can actually,
Vanessa Vakharia (35:00):
Mm hmm.
Francis Su (35:01):
That I can automate and what's actually important to
focus on.
Isn't that also what life isabout?
Like, what should I be spendingmy time and energy thinking
about?
And I would say if you're notspending part of your time
enjoying some of themathematical patterns around
you, whether you think of themas mathematical or not, then
(35:22):
that's a life that's maybe notas rich as one in which you do
see some of the patterns aroundyou.
Vanessa Vakharia (35:29):
This is such an incredible conversation
because also I find that it'sreally hard, I know we're not
talking about spirituality, butit's hard to talk about things
in a spiritual way, because Ifeel that when I do, I got a lot
of flack from like math people,you know, not wanting the two to
meet.
Francis Su (35:45):
Yes, yes.
And I and I I think that's amistake like I think that like
people would be much more opento math if they could see how it
connects to their spiritualnatures.
I mean, you see some of thatthread running through the book,
but all these human desires areactually spiritual desires.
Like we, we have a spiritualconnection to beauty.
(36:06):
We have a spiritual connectionto, to seeking truth, right?
To, to seeking meaning, right?
These are all spiritual desiresas well.
Vanessa Vakharia (36:16):
Okay, this has been amazing, beyond, so
exciting.
Francis Su (36:20):
It's been fun for me too.
Vanessa Vakharia (36:22):
Great, well thanks for making it happen and
uh, bye.
Francis Su (36:26):
Bye bye.
Vanessa Vakharia (36:29):
I love him.
Can I say that?
I just love the guy.
I just left this interview withsuch a concrete outlook on how
math trauma can affect ourstudents far beyond their
performance in our classroomsand I appreciate so much Dr.
Su's ability to take what oftenseems vague and unapproachable
and turn it into something wecan all access and action in our
very own classrooms.
(36:49):
And come on, how cute was thatpart about teaching his son how
to count with his fingers?
I mean, stop.
Go get his book, The Mathematicsof Human Flourishing.
Seriously, you will not regretit.
If something in this episodeinspired you, please tweet us
@maththerapy and you can alsofollow me personally@themathguru
on Instagram, Twitter, andTikTok.
(37:10):
Math Therapy is hosted by me,Vanessa Vakharia, it was created
by me and Sabina Wex, and it'sproduced and edited by David
Kochberg.
Our theme music is by GoodnightSunrise.
And guys, if you know someonewho needs math therapy or just
needs to hear someone elsegetting math therapy, please,
please, please share thispodcast, and rate or review it
on whatever podcast app you use.
(37:31):
Those things actually make sucha big difference for us.
I'm determined to change theculture surrounding math and I
need your help, so spread theword.
Until next time, peace, love,and pi.
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