Love It or Hate It: A Surprisingly Human (And Very Fun) Conversation About Math - Dr. Jordan Ellenberg, Mathematics Professor at the University of Wisconsin - The TechEd Podcast

Episode Transcript
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Matt Kirchner (00:00):
Matt, welcome to the TechEd podcast. This is your

(00:03):
host. Matt Kirkner, imaginehaving a pair of glasses that
would allow you to lookunderneath the craziness and the
chaos of the earth and to findorder in everything, or at least
most of the things that we do.
We used to dream about having Xray goggles or glasses as kids,
and so that's what sparked myinterest a little bit in today's
guest, I was reading an excerpt,actually, earlier this year from

(00:24):
a book, a memoir by one WilliamHenry Gates, the third also
known as Bill Gates, who almostall of us, I'm sure, recognize
as the co founder of Microsoftfor many years, one of the
wealthiest human beings on theplanet, still right up there.
And icon in technology and iconin entrepreneurship and
business. I want to tell youthat there was a paragraph in

(00:45):
that article and it read likethis. And this is Bill Gates
writing about his childhood. Hesaid, realizing early on that I
had a head for math was acritical step in my story in his
terrific book. And he quotesanother book, he says, in his
terrific book, how not to bewrong, mathematician Jordan
Ellenberg observes that knowingmathematics is like wearing a
pair of X ray specs that revealhidden structures underneath the

(01:08):
messy and chaotic surface of theworld. That book went on to say
that how not to be wrong. Thebook by Jordan Ellenberg is one
of Bill Gates favorite books. Infact, if he made a list, and he
did of his top 10 favoritebooks, that book was on it so
inspired and more than a littlebit curious, I picked up a copy
of the book, read it cover tocover. Thought it was fantastic.

(01:31):
Reached out to the author of thebook, Jordan Ellenberg, who
today joins us on the TechEdpodcast. Jordan is the John D
MacArthur, professor, professorof mathematics at the University
of Wisconsin, Madison. I shouldalso mention that he is referred
to as Dr Jordan Ellenberg, withhis permission, I'll call him
Jordan through the conversationtoday. But so honored Jordan to

(01:52):
have you joining us on TheTechEd podcast. Thanks for being
here.

Jordan Ellenberg (01:57):
Oh, it's great to be on I love talking about
this stuff. So let me start withthis.

Anybody who can quote in a book about
mathematics the house Martins inLondon, zero, hell four, which,
for my money, is one of thegreatest albums ever recorded
back in 1986 is my kind of guy.
So really, really lookingforward to this conversation, as
I was doing a little bit ofresearch on your background.
Jordan, go ahead and

break in.
Yeah, I've been on, I don't evenknow how many dozens of podcasts
I've been on. I've been a lot,and nobody has ever brought up
the house Martins before. So youcould not have started on a more
congenial note, because that isan incredible album. I don't
think anybody remembers it. It'sit was actually incredibly hard
to get the rights to quotelyrics from that song, because

(02:43):
that band has been defunct forso long, it was difficult to
figure out who owned thecopyright. And amazingly, it's
in Milwaukee. Amazingly, Itracked it down to a music
publishing house that's inMilwaukee, and that's who owned
the rights. And actually, I hadto pay them a bundle, to be
honest, to use those Did youreally from that amazing song?
That was unfair, since the bandis not, nobody's buying that

(03:06):
cassette anymore, the band isnot making any more revenue from
the use of those lyrics. Butcopyrights, copyright, so

exactly, well, it's fascinating, because
they're, you know, they'reactually Marxist, which I, you
know, full admission, I am not,but they are. And for years and
years, they refused to put theirmusic on any type of a streaming
service. You couldn't find it oniTunes. You know, for I just, I
happen to be as we're warming upfor this episode, I was playing
a couple of tracks from fromthat album, just because it's so
good. So so it's on Spotify.
Now, something must have changedalong the

background possible to bring themselves to
death, like running behind ouras our outro this episode, there

you go. And speaking of copyright, there's
actually all kinds of goofyrules around podcasts, and you
can play that kind of music ifyou have the right licensing on
a radio show, but you cannotplay it on a podcast,
regrettably. So maybe we, maybe,maybe we'll do a little bit of
rendition of setting out afence. How does that sound? All
right, this is, I love it. Thisis the first podcast, I think,
Jordan, that I've begun with afull couple of minutes on like,

(04:07):
1980s college radio. I actuallywent to school across the state
from where you are, at theUniversity of Wisconsin,
Madison, at MarquetteUniversity. Got my start in
broadcasting on the on theiconic WM, you are the college
radio station. So I don't knowthat I've ever talked about that
on the podcast, either. We'rebreaking new ground. I have
talked about one of my favoritemovies of all time, and that is

(04:27):
Good Will Hunting. I saw thatback in the in the late 90s with
my best friend, Jeff Sherman. Istill remember going to see it,
loving that movie. Matt Damon,Robin Williams, as I was reading
a little bit about yourbackground, Jordan, there's a
little bit of a flavor to thatright? There's a scene in that
movie where Minnie Driver andMatt Damon are talking about how
Matt Damon could just hischaracter Good Will Hunting

(04:48):
could just play when it came tothings like organic chemistry
and so on. And I got that sensewhen it came to math for you, is
this incredible skill or abilitycuriosity? Now? That you have of
mathematics is that somethingyou were just born with, did you
hone it over time? A little bitof both. Tell

me about that.
I mean, so I'm gonna start bysaying, and this might surprise
you, I have not seen that movie.
Oh, come on, I'm telling you thetruth. It's like, I feel like,
it's like people who actually dokarate, like, don't watch Karate
Kid, right? It's likebackground, I feel like I know I
would find it a little bit Idon't know off putting is the

(05:27):
wrong word, but I think so.
Something I say in the book thatI feel strongly about is that,
you know, I say genius is athing that happens, not a kind
of person. I truly believe that.
I think you can look at theworld and not say, Okay, there's
like, works of genius, like,there's sort of really amazing

(05:49):
things that people do that wecan, like, admire. But I think
it's always a combination of theperson and the circumstances and
the times, and usually more thanone person too, to be honest.
So, you know, something I reallytry to get across about
mathematics is that, of course,it comes easier to some people
than to others. There's noquestion there. I mean, as a

(06:11):
teacher, you know, we know this,but I don't think it's a good
model to have this kind ofgoodwill, like hunting this Good
Will Hunting like picture thatthere are sort of certain people
who are set apart from whominspiration just kind of like
flows out with no effort. Ithink that's like a bad model.
And I think you and I think, tobe honest, I think you see it in

(06:33):
all kinds of movies. I think yousee it Hidden Figures. Is
another one, which very popular,very successful movie, certainly
very well written, well actedand well made. But I still think
it presents this idea thatthere's all these chumps who
can't do anything, and then,like, the young genius wanders
in and is like, Oh, why don'tyou just do this instead of do
that? And then everything isperfect. And, you know, real

(06:54):
innovation is iterative, like,real innovation is usually
cooperative, like, and so Ithink that, I think for our
students, if they have thatimage of what it means to be
good at math and what it meansto be able to do math, they're
gonna rightly be like, Well, I'mnot an alien. I'm not a person

(07:17):
for whom it just like flows outof me with no effort, as if it
was like placed in my brain atbirth. And so they may say, and
people do say, oh, maybe thisisn't for me. Maybe I shouldn't
have studied this. And I thinkwe lose a lot of great students
that way, to be honest.

You know, that's a really, really important, I
think distinction. And, youknow, you could throw in a
beautiful mind too. Is another,another film, and there's,
there's, you know, dozens ofthem probably, that have the
Prodigy or the natural genius.
What's that?

Hated it? Did you? Yeah, love the book. The
book is amazing, by the way,Sylvia NAS book,

but not the film.
I'll have to go back and readthe book, although

I'm gonna argue against myself, Matt,
because I was just saying, youknow, we lose a lot of students
because some of these, likemistaken stereotypes about how
math works beautiful mind. Ihave real issues with the movie
as a movie, but I cannot denythat tons of people, like went
into math and were inspired tostudy math from that movie. So I

(08:14):
can't deny that it had thatpositive effect. I think it,

yeah, awesome. So while we're on that topic, how
about the show numbers? Did youwatch that one back in the
probably the early zeros. Wasthat one that you tuned into at

all? Did I watch it? I was a script
consultant for it. Oh, were youreally? No way. I didn't know.
That's awesome. I read all thescript well, just one season.
For season two, they would sendme and another mathematician and
my colleague, Alice Silverberg,the scripts before they aired,
and we would sort of shoot back,like, all of our comments about,
like, what could be made moreaccurate, like, how the

(08:48):
mathematician would saysomething, you know, rephrasing.
So it's very exciting. So I willsay one line I wrote made it to
the show. There was one linewhere I was like, he wouldn't
say this. He would say thiscompletely different thing. And
so I feel like I can say I'm aTV writer, because, look, one
sentence that I wrote was, like,aired on a major network TV, and
I forgot to includepronunciation notes. So David

(09:09):
Krumholz pronounced one of thewords wrong. And I was like, oh,
I should have put in a note tomake it,

yeah, that's awesome. I love that, that it
aired on, like, Friday nights, Ithink, for Anna. And that was,
like, my thing, after a crazyweek, you go and watch these and
watch numbers, just we couldprobably do a whole show on
that. I also do a whole show.
You talk about Iterativeinnovation, and in the
importance of that aspect of notjust mathematics, but but, you
know, various disciplines ingeneral. You know, one of the
greatest innovators of all time,some would would argue, is Bill

(09:39):
Gates. And, of course, I wasturned on to your book by that,
that article I read earlier inthe year, the excerpt from his
memoir. Have you met him? Andwhy do you think he loves his
book so much?

I've never met him. I was completely taken by
surprise, and, of course,incredibly pleased and honored
that. He sort of had read thebook and liked it. I can tell
you that it's not like wepitched it to him, like, I can
promise you, if the publishingindustry knew a way to get into
fortress gates to be like, Hey,have you tried this book? Like

(10:13):
they would do it. But it's like,I mean, it's like, only Oprah is
more guarded, right? I mean,like, nobody knows. Like, how I
think it's, I think it's, Imean, let me put it this way.
From what he wrote about it,it's clear that it's, I mean, I
think it's organic and heactually read it. I don't think
anybody like, I don't thinkanybody markets books to him. I
think he just like says what helikes, of course. So no, I don't

(10:40):
know anything about him as a asa person, and have not met him.
But like, I, you know, we'rehe's a nerd. I'm a nerd. He
wouldn't be mad that I saidthat, right? I mean, no, not
enough. We have, like, similarkind of backgrounds and, like, I
guess what? I would, let me putit this way, he's a nerd, so am

(11:01):
I, but he's also not narrow,right? I think he's not a guy
whose mind just works in like,one channel. And so what I'm
always trying to do with thebooks is, I mean, if I were,
like, I'm gonna teach a certainamount of mathematical content
in a certain amount of space, Iwouldn't write the books the way
I do, right? I mean, like,obviously, there's a lot of
content. There's a lot of mathin it. But what I'm excited

(11:23):
about, what gets me, I mean, I'mwriting a new book right now, so
like, Okay, what gets me to sortof sit and stare at the page and
write? It's like, theconnections, the things that are
out in the world. Like, sorry.
Did that sound come through toyou? Okay? Let me say it. Okay,
fine. Keep going. Yeah. Yes,what, yeah,

(11:57):
yeah, let me see what might berunning, because I'm actually
getting it a little bit from you

too. Matt, okay, yeah, go ahead. Take your time
slightly. I

don't know it seems good. Let me see what's
let me see what might be, uh,running, um. The

little delay is giving me an opportunity to keep
up with you in my brain. So Iactually appreciate it.

Oh, yeah. I thought, I thought you were
gonna say, um, I thought youwere gonna say, can you do mine,
like, talking 60% as fast, like,when I do the audio book,
there's like, a guy in my ear inNew York who's just, like,
constantly yelling, like pacingmy natural speaking. I'm
suitable for audio book.

Yeah. I sit on Milwaukee, and there's a the
president of that company saysthat ours is the only podcast he
can't listen to on 1.5 speedbecause we talk too fast. You're
in good company.

I'm not totally it doesn't look Activity
Monitor. Is anything taking alot of CPU here. Let me see
if there's, oh, let me throwthis one. Hold on. I closed the

(13:20):
original one, but there was, Ithink the producer one would
have still been up. And how isthat any better I did close one.
Are you still getting a lag from

Yeah, let's give it a shot. Yeah, and we were and
we're getting through it. Imean, I you know, yeah, for
sure. Okay,

yeah. So what really excites me about writing
the books is these connectionsbetween math, the stuff I've
spent 30 years learning, andjust like everything else in the
world, whether it's, you know,society, science, politics, just
the general human way of gettingthrough life. I mean, I think
sometimes we present math as ifit's just some kind of abstract

(14:04):
gauntlet that you had to run,that somebody invented, like
just to be annoying, basically.
And of course, right math is notlike that. Right? Math is a
human activity done by humansfor human purposes. And every
single thing we have in math,somebody created because they
were trying to solve a problemthat people had, right? And I
think sometimes we lose sight ofthat, and I just it's so fun for

(14:25):
me to kind of go back. I mean,my books always have a lot of
history, because I find I got togo back to be like, Okay, why
did people want to do this?
Like, what problem did they havethat they were trying to solve?
And just, again and again, thereturns out to be an interesting
story there,

for sure, having the Jesuit education that I did
post secondary, and we wererequired to study topics in
subjects like theology andphilosophy, and I was actually
fascinated. We'll talk aboutsome of that a little bit later,
but the number of thephilosophers that you pull into
a conversation about math.
Ethics was just absolutelyfascinating to me. And say to
your point about history, youknow, learning about, you know,

(15:04):
some of these historical figuresthat you've learned about
another contest context, who areactually mathematicians as well,
or maybe first that, that partof it was really, really
fascinating. So credit to youfor for being able to draw from
so many different topic areas,which I think is part of the
reason, you know, I can't speakfor Bill Gates. And by the way,
you know, I think challenge toMelissa Martin, our producer

(15:24):
that let's get Bill Gates andJordan Ellenberg on the same
podcast, and under the pretextthat that bill can finally meet,
meet his hero, Jordan and andand meet the gentleman that
wrote one of his top 10 favoritebooks. But, but I think that is
one of the one of your truegifts is to be able to bring
some of this stuff down toearth, in a way, and maybe tell
some of the stories that areless about numbers and equations

(15:45):
and more about human interest.
Is, have you been told thatbefore? And do you feel that
way?

I mean, that's definitely what I'm trying to
do. So if people say that, Idefinitely listen, because I'm
like, yeah, yes, that's, that'salthough I wouldn't, I wouldn't
say they're not about numbersand equations, and instead,
they're about human interest. Iwould say they're about numbers
and equations and humaninterest. I'm just trying to
demonstrate why are humansinterested in numbers and
equations, which, you know, inevery society that's ever

(16:13):
existed, we have been

absolutely Yep, no for Mission accomplished.
That was, that was exactly thepoint I was making. And it's
really readable stuff, and I'veonly read one of your books, and
I know that and I know there'sseveral. We'll talk about some
of the others a little bitlater. Let's talk about this.
You know, you start right out atthe beginning of a book, Jordan
talking about this whole ideaof, why am I learning this?

(16:36):
Right? And we spend a lot oftime here in the TechEd podcast,
talking to teachers, educators,and that's a big thing for us,
right? I struggled, and I've,you know, I did fine through
school. I mean, I made itthrough but, but, you know, it
was never easy for me to learnin kind of a traditional
classroom. I won't bore ouraudience with that story again,
because they've heard it way toomany times. But you know, that
was a question I had. What? Whyam I sitting here learning about

(16:57):
these equations with letters inthem? And what does this have to
do with anything? And what, youknow, what am I ever going to
use an integral? I mean, allthose, you know, all those
questions that we have, you drawa parallel to doing Soccer
Drills actually, which I thoughtwas just perfect, and I'm going
to use it talk about that alittle bit about why. Why are we
studying math? Say, if you havea student who's a freshman in
high school and getting intotheir algebra textbook and math

(17:19):
hasn't been their thing for onereason or another. Why study
math?

Yeah, so the metaphor I use in the book is it
would be weird to do soccerdrills if you didn't know there
was such a thing as soccer,right? It would be, it would be
weird if so, if you went toschool one day and somebody is
like, what we're gonna do is rundiagonally between these traffic

(17:46):
cones. And by the way, you'regonna be moving this ball with
your feet. Why they do that? Andyou'd be very reasonable to be
like, Okay, but why am I doingthat? Like, I guess we can do
it, but like, but what's itactually for? And if you've

(18:07):
never heard of soccer, or didn'teven know that it existed like
it would seem like a verystrange activity to do. But that
being said, when we actuallycoach kids in soccer, they play
scrimmages and they do that sothey know what soccer does, and
they do the drills. And I thinkmost soccer coaches would say,
okay, learning soccer is notjust about kind of playing

(18:28):
soccer casually, like until youbecome incredibly good. They're
like, there are sort of certainskills that you need to build,
and you build with repetition.
And you sort of build withrepetition, like so much that it
goes into your muscle memory,and you can almost do it
unconsciously. And I think lotsof men unconsciously. And I
think lots of math is like that,right? I mean, it would be cool.
Let me put it this way.
Obviously, I'm very proud of mybooks. I work hard on them. I'm

(18:49):
very happy that people readthem. But they're not designed
that you like, become amathematician by by reading
them, right? Like, I mean,they're designed so that you're
like, Okay, I get it. What's thepoint of actually doing this?
But somebody who wanted to,like, you know, really learn
math and do math, or learn mathwell enough to do engineering or
to do physics or something likethat, yeah, that person is still

(19:11):
gonna, like, really have tobecome quite skilled at, like,
algebraic manipulation, to giveone example, which I think is
sort of the key skill of highschool math. And like, Sure,
high school has succeeded, if akid comes out of it with the
ability to manipulate algebraicexpressions, and if not, then
they haven't been well served,

fair enough and and so what's your message to a
teacher? Maybe, if I'm a teacherthat's teaching, whether it's
math, physics, chem, you know, alot of those courses, I think,
are probably the ones wherestudents ask those questions,
how do we make that more realfor students. What you What's
your suggestion there?

I mean, the first thing I want to say is,
it's a challenge. Like teachingis hard. There's no magic
bullet. I often say, you know,people say, like, what's the
right way to teach math? And Ioften say, you know, there's no
right way, but there are somewrong ways, you know. Anyway, I.
Sort of complete, a sort of, youknow, a sort of absolutely, sort

(20:06):
of mindless focus on repetitionwith like no attempts to ascribe
meaning to it, I think, isprobably the wrong way for moat
for almost all kids. But what Ifound as a teacher is that
whatever I do in the classroom.
There's, I'm going to dosomething, and then some kids
will be like, Oh, thank god yousaid it that way. That finally
makes sense. And other kids arelike, What the hell are you

(20:27):
talking about? Like, that's andthen I'll do something else, and
like the other kids will belike, so it's very it's very
individual. And I tell you knowwhat my students, who I'm
training as they're going toclassroom for the first time, I
tell them, you just got to kindof throw a lot of spaghetti at
the wall, like you actually haveto try a lot of things and not
just be one kind of teacher inthe classroom, because different
students are going to respond todifferent things, and it's very

(20:48):
hard to predict what anindividual student is going to
respond to. And I think for moststudents, if like, a third of
the stuff you say they're like,that's it. That's the way to
explain it. Now I get it, andtwo thirds they're like, I don't
get why he's saying it that way.
That's weird. I think that'sbetter than if 1/3 of the
students love you all the time,and two thirds spend the entire

(21:10):
semester, like, checked out.
Like, you sort of want everybodyto get something. So I sort of
preach variety. I'll say thistoo. Okay, we have a super
interesting collection, at theUniversity of Wisconsin library,
although our library is actuallyabout to be closed by budget
cuts, so I don't know wherethose books are going, so go
look at them now if you're oncampus, because you won't have

(21:32):
your chance for it much longer,but it is a collection of math
textbooks from Wisconsin thatwere used Wisconsin schools
going back to the, I think, thefirst decade of the 20th
century. So like, 100 years ofmath textbooks, a whole day just
looking through these. And it'sincredibly striking, because

(21:54):
what you realize is that there'sno new arguments in math
education, like, every argumentwe have about, Well, should we
do this, or should we do that,or should we do this other
thing? I promise you, it has allbeen tried, and everything has
its pluses and minuses. So youcan go back to like nine, like
people have this idea, oh, nowthere's this new fangled idea
of, like, writing math textbookswith like social relevance that,

(22:15):
like, talk about, likecontemporary issues, or like
that was being done in 1920 youknow, people say, like, Well,
what about this sort of focuson, like, drill and repetition
that was being done in 1930 Imean, everything has its pluses
and minuses. And people arelike, Oh, this way we're doing
it isn't working. Like, let'sswitch to this other thing. And

(22:36):
it just, and it just kind ofcycles, and it's, um, I mean, I
think in the end, I'll say, sohere's, here's an interesting
fact about math and K 12. If youask students like at that age,
like, what's your favoriteclass, the answer that's most
frequently given is mathinteresting, but if you ask

(23:01):
students what's their leastfavorite class, right? Also, the
answer that's most frequentlygiven is math. So it's out there
on the end of the distribution,right? I mean, it has lovers and
haters, but, but I do think Ibegin to come back to it, to
come back to the beginning. Yes,I don't advocate a meaningless

(23:23):
way of teaching it. I do think,not that it's easy to do this,
but I do think sort ofconnecting it to the real world
is useful, but it has to be inan honest way. Like in other
words, you can't tell a kid,okay, there's a direct line
where, like you will be richer,like you will be like, have more

(23:47):
friends. Like you will do thisif you can solve this algebraic
equation. Like, it's not asdirect as that. And kids are
pretty smart, right? So if we,if we tell them that, they'll be
like, come on.

Yeah, right.
Speaking of smart kids in I'mnot necessarily taking credit
for being smart, but one of thethings I figured out in grade
school was this, and I didn't, Ididn't, I didn't become
disenamored with math until Igot to high school. I'll admit
that up front, but the I used tolove doing story problems,
right? I mean, so you'd havethe, you know, you have your
textbook, speaking of oldtextbooks. And you know, one

(24:20):
page would be whatever 4040,different equations that you do,
and then the other one might beeight story problems. And I love
the story problems. And myteacher asked me one time, why,
you know, Matthew, they calledme at the time. Why do you love
those story problems? And Isaid, and you would think the
answer is, well, it's myopportunity to apply the math,
right? Or it makes it real forme. And my answer was, well,

(24:40):
when we get all those equations,we have to do 40 of them, and
when we do the story problems,they can only fit eight on the
pages, so there's just less workto do. Was my was my
application. But you know, youmake an interesting observation,
Jordan in in the book again, andI remember the numbers you say
it's hard to get through. Life,if you don't know that six times
eight is 48 and and you know, wetalk a lot on this podcast, and

(25:03):
have all kinds of golf guests onas you know, that are talking
about different approaches toeducation. One of the things
that you said, which is not onlyresonates me, but could almost
be the reason for existence ofthis podcast, is that students
learn differently, and whatmight be interesting to 1/3 of
the class may not be to theother two thirds, and the key is
to find something that'sinteresting to as many of those
people as you can also love theidea. And I was envisioning an

(25:25):
inverted bell curve as you weretalking about this. This idea
that you've got some students onone end that love math and and
that's their favorite subject.
And the same can be true, orsaid for another group of
students, that it's the, youknow, it's their least favorite
that's a fascinating way ofthinking about it as well, but
on this topic of rotememorization, and you've
mentioned that, and we've gotsome folks that are saying, hey,

(25:47):
we need to get away from that,especially in the age of AI and
machine learning. We'll get intothat topic here in just a
moment, as we do on almost everyepisode of this podcast. But
before we talk about that, andthen we've got other teachers
that are talking about gettinginto things like the meeting and
developing ways of thinking andGuided Discovery and
approximation. And what's yourthought on that? I mean, it's
probably a loaded questionbecause, or maybe just the

(26:10):
obvious one, because I think Ialready know the answer, but
talk about one or the other, orboth.

Yeah, and by the way, a great example
something else I learned is thisidea of discovery learning, the
idea of like, Okay, what if theclass didn't tell the student
the material? But like, was likea sequence of questions which
the student, you know, startingfrom the very beginning, and the
student answering them wouldguide them to the which we think
of as like, oh, this kind ofnovel. Slightly wooy term. I

(26:39):
found a textbook from the 1870sno way that worked exactly that
way. So nothing is new. Nothingis new, right? Nothing under the
sun, as my boy Ecclesiastes usedto say, so. So what I'd say, and
I think you do kind of know whatI'm gonna say, this is, like,
this question of like, well, dowe need to focus on the skills
being able to do them, like,swiftly and reliably and like

(27:01):
repeating until they'rememorized. Or do we need to
focus on the kind of discoverymeaning context? I just feel
like they like to use anothersports metaphor. This is like
somebody like, goes out for thebaseball team and they're like,
Well, should I learn to catchthe ball, or should I learn to
throw the ball? And you're justgonna, okay, you don't. That's
actually not a choice you get tomake. If you're not doing both

(27:23):
those things, you're not playingbaseball, right? It's just like
a stupid question, okay, stupidis too hard, but, but it's,
it's, yeah, you're not doingmathematics unless you're doing
both of those things andbuilding both of those skills.
So, so I think it's a falsechoice. I don't think it makes
sense to sort of say, are wegoing to emphasize one over the
other? I think that you're justnot doing math without both. And

(27:45):
I know it's a tall order, right?
I know we have, like, limitedtime in the classroom and, like,
that's a lot so,

but yeah, well, put in the so a couple things I
have. I have a saying that youcan, you can analogize any
business situation, in this caseusing either your, you know,
your post secondary loveinterest, or the game of
baseball. So, well done usingbaseball to analogize an answer,
also wrapping in a reference toEcclesiastes, not to, not to

(28:13):
telegraph too much a laterquestion. But we do have a
spirituality question here in alittle bit. So, so thanks for
the reference to the OldTestament. You know, not quite a
bit more recently than the OldTestament would be the book that
that we're talking about heretoday, how not to be wrong,
which was written, or at leastpublished in 2014 so we're now
11 years out. AI,

you're gonna read two books, right, the Old
Testament and how not to bewrong. Read the Old Testament
documents

exactly well it and mine, one might say, written
for the same purpose. How not tobe wrong. So you're tight. How's
that awesome? Looking forward tothat part of our discussion,
but, but also to the AI part ofit. So, so I mean, in as much as
you can we've all, we've goneall the way back to 1872 and

(29:01):
math books from the 1870s now,150 years ago, more and a lot
has changed in the last 10years. So you know is AI and
machine learning. Is thatchanging the way we should teach
math, why we should teach math,whether we should teach math,
talk about that in as much aswe're living in this age of
advancing technologies, and notjust advancing, but advancing as

(29:24):
quickly as I think we've everseen.

It doesn't affect weather that much. I'll
say, Okay, I have no I have noqualms about that. How, how,
maybe, and we'll see. And Ithink I but I think it applies
to other subjects as much as itapplies to math, I think that

(29:51):
you always have to bet thatthings are gonna be like they've
been in the past. That's notalways true, obviously, right?
But look, if you have to make abet, I. Are things going to be
pretty like they've been in thepast, or they're going to be
radically different? I thinkit's always more likely they're
going to be like they've been inthe past, and in the past. You
know, technology and computationhas interfaced with math for,

(30:13):
like, a long, long time. Andevery single time, the
technology takes certain thingsthat we sort of thought of as
mathematical skills, like, youknow, adding large sums of
numbers, and we sort ofreclassified those were like,
Okay, that's not math anymore.
That's computation. And thenmath is something else,
something something we do on topof that, often something that is

(30:34):
that we're enabled to do by thenew computational abilities. So
I think the best bet, and youknow, no one knows the future
for sure, is that that willhappen again, that there will be
certain things that we now do,that we think of as mathematics,
that we'll be able to mechanize,and then we'll do new things on
top of that, like stuff thatwe're not doing now. That would

(30:56):
be my best guess. And the pointis that I think the people who
do those new things are notgoing to be able to do it
without having the mathematicalskills and insights and virtues
the ones that we're teaching now

for sure, yeah, I mean, the whole complexity can
do or tell You, go on. Sayagain. Oh, you know, go ahead,
competition.

I mean, I think, like, I think as a
writer, for instance, I mean, Ithink it's an interesting
question as a writer, I can seethat like a big train. LLM
trained on, like, lots ofEnglish language, like, can
produce English prose. It can'tproduce something that I would

(31:50):
put in a book. You know what Imean? It can't produce something
that I would put my name on.
But, like, it produces thingsthat are good enough for many
purposes. So so that creates allkind of, I mean, I think it
creates a lot of interestingquestions about how we teach
writing. But I somehow, andmaybe this is just me being

(32:16):
middle aged, but I sort of don'treally believe that it's kind of
fine for people to kind of letgo of the skill of expressing
themselves, because they feelthat the machine can do it well
enough. You must. Okay, so youmust talk a lot about the
concept of disruptiveinnovation, right? This kind of
Clay Christensen, for sure. AndI think what, I think what

(32:38):
people sometimes miss about thatconcept, that I think is very
important and very central toit, is that it's not always
about like a superior productbeing better and displacing
something that's worse. It'soften about a worse product,
right, displacing somethingbetter, and then people sort of

(32:58):
choosing to sort of change theirvalues to match the inferior
product because it's moreconvenient or cheaper or faster
than that? So I do worry a biton the writing side that people
will just come to accept thekind of prose that an LLM emits
as like, Okay, this is prose.

(33:23):
This is now what we Yeah, thisis now what we value. No, and

that's worth considering and worth worrying
about. You know, we've got, I doa tremendous amount of writing.
In fact, I just wrote anothermagazine column yesterday
morning as we record this. Thisone on the topic of kind of
carrying over the idea of workhardening in manufacturing to
getting new sales people readyfor new jobs in in any role,
including manufacturing. And Ithink you know, the question

(33:51):
becomes on that particulartopic, and whether or not we can
have a generative transporter,GPT, such as some of the ones we
talk about regularly, perplexityClaude are two of my go tos,
chatgpt would be anotherexample. It's got to be
interesting to the reader first,right? I mean, if you can write
really great prose, but if it'snot interesting or insightful or
doesn't present a new idea,maybe not a whole lot of reason

(34:12):
to to read it. And maybe that'smaybe that's a way of looking at
it from a math side as well.

Yeah. Yeah. I mean, it's a very complicated
space, and it's made morecomplicated by the fact that,
you know, there's a lot ofmoney, and money distorts,
right? I mean, in other words,like, as somebody who, I mean,
so I so, you know, I work onthis stuff to some extent,
right? So I don't know if this,I mean, not. I think this is
about like my books, not aboutmy academic work, but, you know,

(34:43):
there's a lot of reallyinteresting questions about how
to get a machine learningprotocol to produce something
that's of material interest formathematics. That's not an easy
problem. It is not, at least atthis moment and maybe forever.
Or it is not a matter of youjust ask chatgpt In English like

(35:03):
that doesn't work. Maybe it'llwork in the future. Doesn't work
now, but there are things youcan do. And I think it's like a
very I think it's a veryinteresting space. But I also
think that if you, I mean, I'mtrying to choose my words very
carefully, if you, if you workfor a company that has a very
big financial interest inappearing to be ahead of four or

(35:27):
five other companies who arecompeting in the same space, you
don't really get to talk aboutyour work frankly, the way, like
academics do, right? You're,you're, you're a scientist, but
you're also a promoter. You sortof don't get to choose to only
have one of those jobs, and so Ithink that's a challenge for
sort of like figuring out what'sactually going

on. No question, yeah, having worked in and
around companies, whetherthey're public companies or
quasi public companies, where,you know, literally, your stock
market and your fortune and yournet worth can be affected by
somebody saying the wrong thingor leading investors in a
direction that maybe isn't partof the company line, and so on.
I mean, those are some of thepeople doing the research. Is

that. And I'm really not trying to criticize
that, because like that,because, you know, the business
world, in the corporate world,is like an essential part of
scientific innovation. And I getthat, that that doesn't work
unless people behave that way.
But it's just we have to haveeyes open about it. Do,

yep, 100% you and I agree. 100% I was reading an
article just a couple weeks ago,maybe even last week again, as
we record this in the WallStreet Journal, which our
audience knows. I spend a goodfair amount of time with the
Wall Street Journal everymorning. The author, Ben Cohen,
in fact, as I'm thinking aboutit, I think it was just this
last weekend, he was writingabout how there's this
International MathematicalOlympiad. You might be familiar

(36:47):
with that. I wasn't until I readthis, but essentially, well, oh,
okay, of course, you were right.
I love I love that. I askedabout numbers. It's like, yeah,
no, I was an advisor. I was inthe International Mathematical
Olympiad. For the record, I wasnot, lest there be any
confusion, but it's an exam forour audience. You know it well,

(37:08):
over two days held, over twodays, students are faced with
three progressively challengingproblems, spans, algebra,
geometry, number theory, a wordI had never heard of called
combinatorics. Maybe you canexplain that that one to us, but
the Deep Mind, which is the AImodel by Google, there are
several of these, perfectlysolve five of the six problems,

(37:29):
but there were 26 students thatactually got all six. So machine
learning AI, deep mind hasn'tquite caught up to at least
those 26 students. So let's talkabout first of all, so you were
in the InternationalMathematical Olympia. Tell me
about that experience. Let'sstart

there. Oh, it was great. And it was, um, you
know, this is a contest that'sbeen going on since the 70s.
It's for high school students.
Each country sends six people.
It actually starts as a thinginside the Warsaw Pact, right?
It was just communist countries,and then they kind of expanded,
and it became this kind of, anda lot of your listeners, I sure

(38:06):
don't remember the 80s, butthere was, there was like this.
It was the weird time of, like,you know, the threat of Global
Thermonuclear War, but also thiskind of spirit of, you know,
let's at least pretend to havesort of, like, friendly, good
natured competition. It was, itwas late enough that, like, so,
you know, the first one I wentto was in Cuba. It was hard to

(38:29):
get to Cuba and those, I guessit still is, but it was, like,
really hard. And, you know, wewent, and we, like, did a math
contest. They took us to theMuseum of American imperialism,
and we, like, looked at all likethe stuff about it. In the end,
they made sure to bring the USteam to sort of see the museum.
I mean, it was, it was, and sothat was, we kind of alternate
between, like, a communistcountry and a Western country,

(38:52):
and kind of like, have, like, alittle bit of bragging rights,
of, like, how did we do? How didthe Russians do, you know, etc,
etc. Very, very wholesome. Iliked a lot. And it's been going
on. It's been going on ever

since. What a cool, cool experience. You know,
we had this within the lastyear, I want to say, maybe just
a little bit longer ago. LeoReddy, who ran the NATO desk at
the State Department during theCold War on it for three
presidents, by the way, ifmemory serves, Reagan, Carter
Ford, all three of them, and he,and he was the architect of the
Helsinki Accords, which, which Ididn't know until interviewing

(39:25):
him. And then going back intothe history, I came of age in
the 80s, so I've got a littlebit of a penchant for Cold War
history and so on. But the wholeidea of detente and creating
some of these relationships, bethey historical, philosophical,
related to the humanities, inthis case, related to math, was
really something that a lot offolks would point to at least as

(39:49):
at least one of the reasons, ifnot a key reason, that the cold
war eventually ended becausepeople started to see people as
people, and less so asadversaries in a lot of cases.
So what a cool experience. Say,even though you you were subject
to the American appearingimperialism Museum, haven't been
there either. But that sounds,that sounds a bit interesting on
this topic, though. So 26 ofthese students, you know, bested

(40:11):
Deep Mind in this competition,but it's still nailed five of
the six problems. Well, youknow, what are your thoughts on
that? Are we going to get to apoint where AI is out competing
students in terms of, you know,raw computation and being able
to do, you know, not justalgebra, but as we suggested
that, you know, geometry, numbertheory and and combinatorics.
And so while we're on thattopic, I don't know that I'm

(40:33):
pronouncing that right, but tellus what that is, too. If you
know,

oh, combinatorics means counting.
Okay, recently it's like, like,like, problems, or, I know,
counting. I can count, you know,or general questions, like, you
know, if you want to know, youhave sort of some big network
with, like, 1000 entities. Andyou want to know, well, how many
of them? Here's a classiccombinatorics problem. You have
some network network, and youwant to know how many

(41:00):
connections in the network? Do Ihave to break before the network
falls apart into two pieces?
That's actually a criticalquestion. If you were running
supply chains or you're runninga communications network, that's
a hard combinatorics problemcalled Max cut, actually, and
it's like that kind of question.
So, and actually, that's one ofthe areas where machine learning
methods have been mostsuccessful. Like my own work in
that area has mostly been aboutlike, okay, how can we kind of

(41:23):
coax a transformer into, sort ofgenerating interesting
information about combinatorics,which is pretty fun. And I've
worked with my guys are great.
I've worked with them, actually,on one of the projects. So
here's what I think. This issomething I do have a kind of a
strong opinion about, which isthat I don't believe in
benchmarks. Benchmarks are verypopular, and there's a good
reason that they have a purpose.

(41:45):
So when I say I don't believe inthem, they have a very good
purpose, but I don't think theyspeak very much to the question
of, what is the eventual effectof AI on mathematics. They have
a purpose. If, like, let's sayyou're an investor and you're
like, Okay, I want to get asense of whether I think Google
is ahead of anthropictechnically. Then right? It's
very reasonable to be like, Iwant there to be like, a

(42:07):
competition with fixed rules,and I see who wins. For me, the
only benchmark that matters is,do machines actually, like, help
us produce material that is,like, really substantive,
substantively useful formathematics. Got it that has not

(42:27):
happened very much yet, but Idon't believe it couldn't
happen. But in other words, likewinning a context is somehow
that's that's artificial, like,that's not actually what
matters. And so like, thebenchmark that matters is, like,
does the thing actually work?
And we'll see,

right? Got it?
Okay, fair enough, yeah. So whenwe talk about benchmarks,

let me answer your question a different way,
though, because you said youdidn't. I answered a question
you didn't really ask. So let meanswer the question you did ask,
which is, like, is it ahead ofstudents? The thing is, in many
ways, yes, but that's been truefor decades already. In other
words, like, what we askstudents to do, like, like,
let's say, like, a kid who'staking even a college level

(43:12):
class like calculus or linearalgebra, I promise. I mean,
maybe I shouldn't tell this inthis college students lit
listening, but like, WolframAlpha can do your calculus
homework already. Like, that'snot new. That does not take the
power of a transformer. So interms of, like, student level
work, and I think one reasonthat I'm not too doomy about it
is that that has been true for along time, and yet, like, we're

(43:36):
still teaching math, andstudents are still learning
math, and I don't feel likecollege students today are like,
more degraded than collegestudents of the past.

Am I think about my wife, who's a both an
undergraduate and master'sdegree in engineer and still has
her science calculator that shecarried around with her back in
the 80s, when, when we werelistening to, you know, actually
the, you know, the houseMartin's album London zero Hall
follower just come out, and wewere using the science
calculator back then, and it'sso into your point. I hope first

(44:08):
Polish the best calculator, ofcourse, Oh yeah, absolutely,
with kind of like that goldfinish on it. I mean, you know,
that's exactly the one. Yes, Isee that was, that was the

one that she she's nostalgia tech and college
rock podcast that would beamazing.

That would be, yeah, maybe, maybe we'll
collaborate on that. Maybe wefound a new new, new opportunity
only

people, and then we're going to come back to
doing serious business. But thisreminds me of when I went to
see, this is a very okay, thisis a very Wisconsin moment. But
I went to see violent femmesplay their entire first album at
the Sylvie in Madison. Yeah,incredible concert, incredible
show. They still bring it at theage they're at, but also,
literally, every single personin that 2000 person venue was,

(44:52):
like, born within two yearsbefore me and two years after
me. It's like, an incredibleit's like, it's like, incredibly
demographic. So that's who wouldlisten to our podcast. Like,
exactly. Exactly, people born atthe exact same time as us, all
right, ever do we agree?
Greatest fan ever to come from

Wisconsin, violent times, yeah, yeah,
certainly right up there. Iyeah, I would say they're right
up there. I was a long time BoDeans fan as well. So, so Okay,
so now we're going down thispath. We'll just keep it going.
Melissa can edit it out if shedoesn't like it, but it's gonna

be so the I raise her hand when we hit the
first band she's heard of,

right? Exactly.
So, 1986 the same, same yearthat the house, Martin Zelman
came out the London zero, howfar? And they did two of them. I
think they were fantastic. Thatwas one of them that summer. I
saw the violent femmes play atthe Rock stage at Summerfest,
when there was still a rockstage, largest outdoor music

(45:50):
festival in the world. And theopening band, and nobody had
heard of them, was the bodeens,and it was amazing. So I saw the
bodes open up for the violentfemmes, which was amazing. So
I'm Wow, figuring out that wasreally cool show. So just about
four weeks ago, I was atSummerfest, again, the killers
were playing huge killers. Fanlove the killers, and they

(46:12):
covered American music by theviolent femmes in that concert,
which is just awesome.

Wow. So, so,

yeah, so we got Yeah, so, yes, violent femmes.
You know, there's, there's allkinds of connections to to
Wisconsin music history. Butthat must have been awesome. I
saw that actually in the paper,I think our local paper, the
Journal Sentinel, Milwaukee.
Journal Sentinel, did a write upon that, on that concert, and
sounded like it was justphenomenal. I it was great. It
was great, awesome. So now Ihave to segue from that to oh,

(46:46):
this is perfect, actually. So1986 saw that concert, violent
femmes, proteins. I was in highschool. Speaking of high school,
how's that? Melissa, speaking ofhigh school, I hated algebra. In
high school. I just when I was Iwas I was thinking about this,
this podcast this morning,Jordan and I went my high school
algebra teacher was Mel DODDS.

(47:07):
Is his name? God bless. MelDODDS. He was an icon basketball
coach, and I just, for whateverreason, I looked his name up
thinking about this topic thismorning, found his obituary.
He's been gone now for 10 years.
I failed the first semester ofalgebra. Literally failed. Got
an F. And he came to me at theend of my first semester, and
this is what he said, I think hejust wanted to get rid of me. He

(47:28):
said, Whatever you whatevergrade you get for the second
semester, I will go back andgive you for the first semester.
And he said, so don't give up onit. You get an A for the first
semester, we'll go back and giveyou an A for the second for if
you get an A for the secondsemester, we'll go back and give
you an A for the first semester.
And so I ended up getting a D mysecond semester, which meant my

(47:50):
grade for my first semester wasalso a D, which means that was
enough to pass and get on to togeometry that following year,
and then Algebra Two. And Iactually, again, to portend a
little bit of our futureconversation, I got religion
about at least education, andkind of cleaned up my act after
that. But so I'm a student, Ijust struggled like crazy with
algebra. And in fact, you kindof mentioned there's two

(48:11):
inflection points in a student'sacademic journey relative to
math, and one is learningfractions, which I remember
doing in probably fourth orfifth grade. The other one is
algebra, which I got intofreshman year of high school,
and that's, and that's where yousay, that's where students
quote, fall off the math train.
And maybe I'm quoting your book,maybe those were my words, but
that's where, that's where theyfall off the math train. What

(48:32):
should we do to keep studentslike me engaged in math? Maybe
it's as simple as having someonewho says, All right, you're
smarter than this. What you dosecond semester. We'll give you
for first but what are thosethings that teachers should be
doing to make sure that we hangon to those students and keep
them fired

up? First of all, I love that grading policy.
I think it because I think itspeaks to this very interesting
question that I think we don'task ourselves and reflect on
enough as teachers, of like,what are grades actually for?
Because in some sense, the truthis, when you really think about
it, they have a lot of differentpurposes which are kind
different purposes which arekind of incompatible. Like, if
the purpose of the grade is tolike, record how you did for

(49:08):
some future person to look at,then the people the teacher will
be like, Well, why should Ichange your F like that
accurately reports how you did.
But if the point of a grade isto give a student feedback and
help them learn, which is kindof a little more what I think
like that, then what yourteacher did was exactly right,
because, like, he created themotivation in you to like, be

(49:29):
like, Okay, you actually canlike. He wouldn't say that if he
didn't believe you could passthe class, right? So that both
demonstrates his faith in youand sort of gives you some
motivation to succeed. But thetruth is, the grades are both of
those things, right? I mean, weteach in college, we know people
are gonna look at our students.
GPA, we know that, like, part ofwhat we're doing is, like,
providing information for futureschools, future employers, etc,

(49:52):
so like, like, everything else,the answer is always, like, it's
both

Okay, for sure, let me, let me do a lot. One
more thing before we you. Yeah,let me go one more thing before
and then, and then we'll, andthen we'll come back to the to
the question that you've got,really excited for that. But you
know this Mel DODDS experience,right? So I was, you know, fast
forward 15 years. Maybe made itthrough school. Actually studied

(50:15):
accounting in undergrad. So fora kid, the fail of algebra, that
was my career choice. Spent afew years in public accounting
and then ended up several yearslater, as CEO of a manufacturing
company headquartered inMilwaukee. I ran into Mel Dodd
son at a charity event. Just bycoincidence, he was sitting next
to me. I noticed the last namewhere he was from. I'm like, by

(50:38):
any chance, are you related tohe's like, Oh, for sure. He's
like, Yeah, Mel, dads is my dad.
And I'm like, I wonder if he'dremember me. He said, I
guarantee you he will rememberyou, because he remembers every
single, every single student heever had. And I happened to have
my CEO business card with me.
And I said, you know, give himhis business card. Let him know
I remember him. Let him know forthank him for giving me that
break, that freshman year inmath, things turned out okay, if

(51:01):
he was wondering. And so thatwas that story ended. Well, at
any rate, you said you had aquestion, and please feel free
to pose it,

and you just gotta hope that he didn't see
the business card. And thinkit's gotta be a different guy,
like, couldn't be the guy whobarely skate by with a D in my
class. That's awesome. So okay,now I gotta remember what I was
all right, we were talkingabout. So one thing I find that

(51:30):
I do a lot of therapy, because,like, when I go around, I go and
give talks about math and, like,it is very common occurrence
that someone will come up to me.
It was like, I have to unloadabout you, about my bad math
experience when I was nine, whenI was 12, or when I was 16?
Because, think about it, they'vegone through their whole life.
They have nobody to tell afterthis trauma, like when race, you
know, until me. So I want to,we're going to get on the couch,

(51:52):
and I want to explore this withyou. I want to know what
happened that you felt UK you soyou failed first semester of
algebra. Do you feel like malDODDS was at fault? Do you feel
like you were at fault? Whatwent wrong in the interaction
between you algebra and MalDODDS? Since you're obviously
like a competent person, he's ina quantitative field, tell me go
through it with me. Like whatyou feel went wrong?

Let it all out.
No, absolutely I first of all,the problem was all me, and it
was certainly not him or his wayof teaching, or, you know,
obviously, given the story Itold, he took an interest in my
success and wanted to see me besuccessful, you know, whether or
not for me, there were moreapplied ways to learn it maybe,
maybe not. I mean, I was never agreat classroom learner. That
was certainly no fault of his.
That was the model that waseducation then, and to many, in

(52:38):
many cases, still is today. ButI got religion my sophomore year
about education. I could tell a15 minute story. I'll tell the
abridged version, and that's allabout I just I didn't see the
connection between education towhat I was going to do after
high school and good one of myvery best friends, in fact, I'll

(52:59):
give him credit. His name isMark Davis, and we're still,
still really good buddies. Itkind of sat me down at the
beginning of our sophomore year.
And he was straight A student,the kid that, you know, he
wasn't quite at the level ofJordan Ellenberg, but, but the
kid that that really could justeverything just made sense to
him. He didn't have to spendtons of time buried in a book to
get it. It was, he was just anatural. And he said, you know,
we're gonna get to the end ofour high school journey. And we

(53:19):
had our, you know, same friendgroup. He's like, we're all
going to have all these optionsof what we wanted to do after
high school, whether we want togo to college, where we want to
go to college, what we want tostudy. He's like, if you don't
figure this out, you're notgoing to have any choices when
we get done, and you're going tobe stuck getting, will get,
taking whatever life gives you.
And so and that that actually,that conversation changed my

(53:41):
life for one reason or another.
We just have those moments inour life, and so, so I got
serious about studying. I gotserious about my academics. I
was a kid that had probably toldthe story on the podcast before
finished my freshman year with a1.8 grade point average,
graduated high school almost ata 3.0 and so you're pretty good
math guy. You can imagine that Ireally picked up my pace there
in those last three years topull the to pull the average up

(54:02):
as high as I did. But, but forme, it was, it was all on me,
and I didn't see the connection.
I didn't take an interest inacademics until I saw a purpose
in it. And I also felt like, youknow, up until that point, yeah,
I was doing academics for thesake of doing academics, or that
perhaps because, you know, toplease my parents or to

(54:23):
whatever, and that, you know, ifthat wasn't a high enough bar or
big enough goal or the rewardwasn't strong enough, why keep
doing it. That was the part ofit. And then once I put a
connection between, hey, thebetter you do in school, the
more options you're going tohave, regardless of what you
want to do that, you know, thedeeper you can go. That that was
that spark that kind of lit thefire under me. And I was never a

(54:44):
four, oh, student, even throughcollege, but I figured it out
well enough to get through it,maybe a longer answer, that you
could hear that

coming from a peer. You no doubt had heard the
same thing from teachers,principals, your parents.
There's certain things that'sdifferent when it comes from a
friend or a. Here, 100%

Yep, 100% so great observation,

yeah, and that's something I think we
struggle with, because asteachers, we can control what we
do and we can control what theschool does, but we can't
control the social environmentthe student is in, and if, if
the kid is around a bunch oftheir friends who are like, God,
why are you wasting your timedoing your homework where you
can, when you can, just likechat, GPT, all your assignments?
If that's you know that that's athat's a hard current

to fight against, sure is Yeah, and then we
certainly encourage teachersnow, because I think in a lot of
ways, my my theory that that'sbeen bouncing around in my head
Jordan is that it used to bethat school was where we went to
learn and home was where we wentto practice. So you go to
school, you get a lecture,you'd, you know, you do your do
your little projects at school,maybe do some problems in

(55:52):
school, but then you go home,and we actually called it
homework, and that was where wewrote essays, and that's where
we studied for exams. That'swhere we went through our notes.
You know, we applied the thework that we learned in school,
and I think now with so manydifferent ways to deliver liver
learning. And to your earlierpoint, you and I agree 100%
every learner learnsdifferently, and the magic of
education is to figure out whereand how we can resonate best

(56:12):
with an individual student orgroup of students, based upon
how they learn, the moreeffective we're going to be and
and so that, to me, you know,really kind of speaks to the to
the future of education. And

I just want to say, I want to say something
optimistic, because I actuallyam an optimist. Like, I feel
like I said some slightlynegative things, but I want to
emphasize, I mean, one thing Ilove about being a professor and
spending my life like, amonglike, you know, these young
folks, is that, I mean itreally, it's a very soul
refreshing workplace. You can'tbe too pessimistic when you're

(56:44):
around these folks all the time.
And I just will say that, like,I have an unshakable faith from,
like, my years of experiencebeing a teacher, that people
like learning and they crave itlike they truly do. I think we
can get cynical and talk aboutlike, oh, all the ways that
people like avoid effort, blah,blah, blah, but I think
fundamentally, it's justextremely human to be excited
about learning and value it, andwe just have to make sure that

(57:05):
people are seeing that theyactually are learning. Are not
doing tasks for the sake oftasks, for the sake of busy
work, but because they're gonnalearn something. And I'm enough
of an optimist about like thehuman race to feel like people
do respond to that. There'ssomething fundamental in us that
gets excited about encounteringnew things, learning new things,
mastering new things. We arebuilt to do it.

We are, for sure, it's exploration in the same way
that we can explore space. Wecan explore the you know, what's
what's under the ground, whatyou know, what have you this is
just another form ofexploration. And that's a little
bit of the sense I got from BillGates, is comments about your
book, right? Is that, you know,how do we make sense of this
chaos and this craziness? We doit by exploring. We do it by
asking ourselves questions. Wedo it by going deeper. And for a

(57:52):
teacher, professor, instructor,whatever you know, workforce,
trainer, whatever that whateverthat vocation is, and I use the
vocation intentionally, whateverthat calling is, there's so many
opportunities not just todeliver knowledge, which is
important, but to inspirestudents and show them they're
capable of doing something theydidn't know they were capable of
doing, or that they have aninterest in something that they
didn't know they had an interestin. I think I was horrible at

(58:15):
art, but I had an art teacherthat took an interest in some of
the creative things I was doingand and all of a sudden I had,
like, found this whole in middleschool creative side of myself I
didn't know existed. And sothat's the real magic that
happens inside and out of theclassroom. And I got to imagine,
that's a big part of why you'vechosen the location you have.

Yeah, I couldn't, I couldn't say

it better.
Awesome. Well, great. So we'llkeep going on the topic of the
book, and it's called how not tobe wrong. And again, you've
written many books, severalbooks, but this is the one that
I I read, if I got it, and ittook, you know, I mean, I read
through, I'd read the wholebook. It was awesome. You get to
the final chapter, and the kindof the takeaway for me was a
little bit about, you know, mathis a little bit less about

(58:58):
absolutes and getting to exactlythe right answer, and a little
bit more about understanding ourworld in terms of probability.
So we can't perfectly predictanything. We can kind of, we can
handicap it a little bit. We canunderstand the present in the
future a little bit better basedupon data. And whether that's
you know, whether that's thelottery, whether it's you know,
something going on in the worldof AI or machine learning in

(59:19):
these days is that the righttakeaway is, Did I did I get it
right? And what would you add tothat?

Yeah, well, I'd say it's funny that you say
that, because I think that's oneof the strands that's going on
in that book. But actually thatis, in some sense, like the
premise of the book I'm writingright now. I mean, that's what
I'm really so you're sort ofjumped ahead awesome to the book
I'm working on right now, whichis about uncertainty and whose

(59:48):
theme is really that I thinkpeople have this mistaken idea
that what math is for is todiminish or even dispel
uncertainty for your life,because people. Are
uncomfortable with it. They'relike, I want answers. I want an
answer with three decimal placeslike that would make me feel
more secure, because I hate allthis uncertainty I have to live

(01:00:09):
with. Like, math come and saveme from this, and then I have,
like, I think, a negative, butreally a positive message, which
is like, nope, math is not goingto save you from that, because
uncertainty is the way the worldreally is, right? If you try to,
like, neurotically get it out ofyour life, you're just failing
to look at the actual world. Butthen the good news is that,

(01:00:30):
guess what, math is actuallyfilled with tools for, like,
helping you think aboutuncertainty in a useful and
productive way. And so the wholetheme of the new book is, like,
all about the many ways that themath helps with that, and
fundamentally, the message is,like, it's not uncertainty
that's the problem. It's ourinability to tolerate

(01:00:52):
uncertainty. That's the problem,whether because we don't have
the quantitative tools or wejust sort of haven't built,
like, the psychological strengthto tolerate it, but like,
that's, um, so it's kind of apro uncertainty manifesto.
That's what I'm trying to workon right now. What do you think
my elevator pitch?

Matt Kirchner (01:01:08):
Yeah. Oh, 100% Yeah. Are you kidding me? I, in
fact, I'm hoping for an advancedcopy and and signed by Jordan
Ellenberg. That would make anadvance

Jordan Ellenberg (01:01:15):
copy, but it's gonna be I'm still a year away.
I've written like a third of it.

Well, yeah, good Lord willing. We'll both be
around here in a year. It'sinteresting. You I was working
over the weekend. We built amodel a couple years ago using
Azure Data Factory and Azure forone of the companies that I'm
involved with that wasaccurately predicting EBITDA, or
net cash flow within we got itto where it was 14 months out,
one and a half percent accurateto to what the net EBITDA it was

(01:01:44):
for 1414, months out. And wewere refining that over the
weekend, and had the samethought about, look, this is a
really, really cool model, andit takes a ton of stuff into
account, but there's even morestuff that it doesn't solve for,
doesn't take into account. Andso that whole aspect of
uncertainty as you were justreferencing it was resonating in
my head. The other thing you'reresonating my head. I'm, I'm a

(01:02:04):
big believer that, you know, inCelestine Prophecy, you know
nothing, nothing happens byaccident. There's no such thing
as coincidence. And yourreference earlier to
Ecclesiastes, believe it or not,I was just I rode my bike back
and forth to work every everyday last week, and which I don't
get to do most weeks becauseI've got business meetings or
I've got places. Got places Ineed to be during the work day.
But last week was such that Ididn't have that. And I got back

(01:02:28):
on my bike this year, afterabout a five year hiatus. I was
I was big into bike racing. Iwas doing a ton of cycle cross
racing. My son was racing forthe truck Junior Devo team.
Everything revolved aroundcycling. I ran into a woman I
used to race with about a yearago, and she, if you're familiar
with with five word stories,when a Hemingway's kind of

(01:02:48):
little tools. And yeah, Melissacertainly is our producer. Love
five word stories. And she toldme this little five word story.
And and I we used to racetogether, and I said, are you
still racing? And because I hadthis kind of guilt that I had
gotten away from it. And and herfive word story was, No, we had
our time. And so those fivewords, and I was like, wow, that

(01:03:09):
she didn't say it was a fiveword story, but I'm like, that
says everything in five words,right? That is a five year
story. And it kind of put thatwhole thing into perspective to
me. And then, of course, youknow, the whole time to
Ecclesiastes into it,everything, there is a season
not to go too far down thespiritual rabbit hole, but it's
a good segue into our nextconversation, and that is, I
found you going back in the bookseveral times to the issues of

(01:03:31):
questions of spirituality, theexistence of God, and honestly,
and maybe it's on purpose, itwas a little bit like, Oh, this
guy's, he's an atheist, oh, He'san agnostic. Okay, wait, maybe
he's, you know, we're in So atany rate, without giving
anything away that you don'twant to, why are those types of
questions so important to you,and why did you keep coming back
to that question of theexistence of God and of

(01:03:52):
spirituality throughout thebook?

Well, part of it, I'll give two answers, and
I'll say a little bit aboutmyself, like, Okay, so one
answer is just that, as I saidat the beginning, you know, math
is a constant in every societylike this, what it says to be
some fundamental part ofhumanity that we think
quantitatively, we reasonmathematically and so and but

(01:04:15):
thinking about who made theuniverse like what it's all for,
that's also a constant in everysociety, right? So how can you
write about something that'slike, like, math, that's like,
sort of so big and soomnipresent in our way of
thinking? And how is it notgonna intersect with those
questions, right? Because thoseare two big things that humans
have always done and are alwaysbuilt to do. I find that there's

(01:04:39):
also a lot of poetry in mybooks, which I'm very surprised
by. But that's also sort oflike, also sort of like a human
constant that we always sort of,we all sing, we all say poems.
So, I mean, so so that. Sothat's one reason, just because,
you know, in olden times, therewas not such a distinction
between mathematics andphilosophy and people like
Blaise Pascal, I wrote a lotabout. That book were, he did.

(01:05:01):
They were very serious methodeditions and very serious
philosophers, and very, inPascal's case, like a true
religious mystic, right? I mean,like a true devotee. So, so
that's one reason, because Ithink,

if I'm not mistaken, yeah, exactly.

But it's funny, because I feel like
people write me email, and theylike and they and, you know,
they write me email sort ofdoctor to find a point on it,
but to correct my atheism, theylike write to you, like, I just
wanted to sort of rebut some ofyour atheistic argument. I'm not
an atheist. I'm Jewish. Ibelieve in God, like I'm a I'm

(01:05:41):
not Orthodox, as you can seefrom the fact I'm not wearing a
Yamaga. Like I'm not strict, butI would say I'm a religious
person. And there's, there'slot. I mean, I try not to overdo
it, but I mean, there is, like,a certain amount of Jewish
learning in the books. I mean, Ithink that stuff is really
valuable. Like, the next bookafter that shape is with, like,

(01:06:03):
a wonderful Talmudic story,which I think is fantastic,
which, which sort of speaks tosomehow, to me, it sort of
exactly goes with, like, whatmath is all about. Actually, can
I tell the story? Because it'sso good, because, I mean, I'm
gonna abridge it, because theTalmud does like to go on and
on, and I'm gonna give like, thestory. Give like, the short

(01:06:23):
version, but like, you know,basically, you know, a bunch of
rabbis are arguing over whethera particular piece of pottery is
like, clean or unclean. This isthe kind of stuff the Talmud is
full of. And they argue and theyargue, and each one has, like, a
reference for why they thinktheir view is correct and but

(01:06:50):
one guy is clearly winning. Oneguy is clearly getting the best
of the argument based on thetext of what's in the Torah. But
his opponent is like, not happyabout this. And he's like, you
know, look like, let God comedown and, like, tell us who's
right, who's right about this.
Like, is this thing clean orunclean? Yep. And then, like,

(01:07:11):
there's this whole sequence ofmiracles. And like, the walls
fall down, and the river flowsin the opposite direction. And
then finally, like, God says,like, okay, like, like, you're
right, the first guy is wrong,who seems to have the best of it
in the text. And then an amazingthing happens, which is that the
first Rabbi does not give up. Hesays, But God, like, you know,
didn't you say that the Torah ishere on Earth? And, like, this

(01:07:36):
is how we're supposed to decidethese matters of law. He really
just like talks back, right?
Yeah. And then there's thisamazing moment where I don't
think this happens like anywhereelse in the text, where it said,
God laughs, God laughs. And hesays, My children have defeated

(01:07:56):
me. My children have defeatedme. And then he like pieces out,
and it's an amazing story aboutbeautiful story, the
responsibility that we're givenas human beings to, like, with
these incredible and I wouldsay, I don't want to get too
deep into it, but I mean, Iguess I would say these, like,
God given capacities that wehave, like, that's a

(01:08:17):
responsibility, but it's alsoour power, and We're sort of
supposed to use it. You and I,and I are very, very well a
little too. I mean, this kind ofstuff on a podcast,

kind of topics,

but people, but people do write me and be
like, you know, I'm here tocorrect your atheism. And I'm
like, come on, what I writeabout in that book is like, I
don't like it when people arelike, I'm gonna prove that God
exists with a statistical test.
I'm like, come on. Like that isnot respectful. Like that is
like, you know, what I see, whatI say in the book, is, like, you
know, when God wants you to knowhe's there, like, he lights a

(01:08:53):
bush on fire. He does not, like,hide it in, like, the fourth
decimal place of a statisticaltest. Like, come on, that's so
that's awesome. So sorry to geta little bit salty, but I feel
like, no, for sure, things thatare not true,

yeah, for sure.
And that's probably the firstrabbi. I won't call it a rabbi
jokeness To show you Rabbi storythat we've probably had on the
podcast as well. So we'rebreaking all kinds of new
ground, which I hope to do withthe final two questions. In the
interest of time, we've got ourunfortunately for me, because
I'm really enjoying thisconversation time, bring our
time to a close here with JordanEllenberg, but Jordan, I want to
wrap two questions into one, andthat is this, you know, the

(01:09:29):
first one is, and I think we'velearned a little bit about it
already, but is there somethingthat you believe about education
that would surprise people? Andthen, you know, the second one
is, if you could go back to, youknow, your 14 year old days, and
you know the Potomac area inWashington, DC, when you're a
Washington, DC or 15 year oldkid, what advice would you give

(01:09:51):
that, that young man, I mean,

to the first thing, maybe I'll say something
that I think would surprise myyounger self, because I think
that's a good Gage for. Like,what's surprising? I mean, I
think I've come to understandover many years of teaching that
here's a word I made up, that,like, schooliness is not the
same thing as intelligence. AndI think, like, you know, a sort
of mental roadblock that a lotof us in education have to get

(01:10:18):
over is that anybody who's ateacher or a professor is
probably somebody who reallyliked school and function really
well in the school environment,because otherwise, why the hell
did I never leave? Right? Why amI 53, years old and have, like,
never left a college campus?
Because obviously, like, Ireally like this environment,
and it really works for me, andit exactly suits my temperament.
And I think it's easy to fallinto a trap of thinking that

(01:10:40):
schooliness is like whatintelligence is, or like what
learning is. And as I've gottenolder, I just think you come to
see that that's one model, andit does work for a lot of
people. Like that's why it haspersisted, like, not changed
that much for like, 100 years inthis country. I don't want it

(01:11:02):
to. I think it's, I thinkUniversity of Wisconsin, Madison
is an incredible institutionthat serves 10s of 1000s of
students incredibly well, but italso doesn't work for everyone,
right? And I think I was gonnasay that's a problem I don't
know how to solve, but it's noteven a problem, right? I mean,
it's just as you say, just that,as you say, like people are

(01:11:23):
different. And I just think it'suseful for us to sort of think
hard about what do we have tooffer for people who truly want
to learn, which I, as I said, Ioptimistically, think, is
basically everyone, right? Butfor whom this particular
structure does not work verywell, and that can be like for

(01:11:45):
all manner of, for all manner ofreasons, right, like, I mean,
but, um, but I think that'ssomething, I think is like we
can get better at, and broadenand certainly look like at
Wisconsin. I mean, you probablyknow about the Wisconsin Idea,
right? This is the animatingprinciple of this institution,
that the boundaries of theuniversity are the boundaries of

(01:12:09):
this state. I'm not saying wealways fully live by it, but
like a fundamental foundingidea, which I've come to see, is
not just a marketing slogan, butis really part of the DNA of
this institution, is that we'renot here just for the 18 to 21
year olds who are enrolled inour courses and are inside our
walls. Right? Obviously, that'sa big part of what we do. But in

(01:12:29):
the end, the reason that weexist is to serve the
intellectual needs of the entirestate of Wisconsin, which
includes, like, a lot of peoplewho are never going to be
enrolled in any institution ofhigher learning. But like, you
know, we, in many ways, we areliving up to that. I think it's
always something that we canpress on.

No question well, in history being the great
indicator, obviously aphenomenal institution. I think,
as you know, both of my both ofmy kids are badgers and as is
our producer, Melissa Martin, bythe way, is also a former
cheerleader at the University ofWisconsin, Madison, that that
could be a whole podcast in andof itself as well. But to the
last question that we that wehad for you, Jordan, go back to
your your your sophomore year ofhigh school. You have one

(01:13:16):
opportunity to give that youngman one piece of advice. What
would that be.

I mean, I think I would just say, like,
you know, trust your instinctsabout what you find interesting
and what you want to do. I thinklike kids. And I think this is
actually more true now than itwas in 1986 we really kind of
say to them, like, okay, figureout what you should do. Like,

(01:13:47):
figure out what you're best at,and specialize and only do that.
And I think sort of, I sort ofaccidentally didn't do that, but
I for a long time, I felt a bitof bad conscience about like,
Aren't I supposed to be focusingon math, because that's what I
do. Like, that's my thing. And Ithink I would tell my 15 year
old self, like, actually, theway you learn is by when you

(01:14:08):
feel, when that weird feelingKindles, of like I want to, I
just feel moved to go and learnthis or master that, or build
that skill. You know, maybethat's your soul telling you
something like, maybe actuallylisten to that and don't worry
so much about whether it'sproductive or like is on the
track. I'll close with a story,please. I remember I was talking

(01:14:32):
to an undergrad at UW Madisonwho took my class. Great
student. She had had one plan tostudy geosciences, but she was
cooling on it, and she was like,No, I think I want to go another
direction, but she had, but shehad an arrangement she was going
to go to Antarctica for a year,and like, work in this lab. And

(01:14:54):
she's like, I'm really excitedabout it, but I also have sort
of felt like this is not myfuture. And. Go in another
career direction. So, like, Idon't know if I can afford to,
like, like, waste a year, eventhough I'm excited about it, I'm
like, shouldn't I sort of getstarted on this new path?
Because, like, I have, like, aplan, and I got to do what's
towards the plan, and I just,like, in my best, you know, Dad

(01:15:16):
voice, because now I'm oldenough to kind of dad voice the
undergrads like, I was like,when you're like, a 38 year old
Mom, do you want to be like, themom who could have gone to
Antarctica, or do you want to bethe mom who did go to
Antarctica? Antarctica? Like,that's the question that's
before you, right, becauseyou're gonna end up in the same

(01:15:37):
place. But like, which do youwant to be?

I love that Absolutely. That's great advice.
And I love the idea that youknow, this whole idea of you
know, not just following yourinterest, but if something you
find interesting, somethingsparks your curiosity, sparks
your imagination, that is youropportunity to learn. Chase that
down. That's the advice thatJordan Ellenberg would give his
15 year old self. It's theadvice that I took on my own
when I chased down JordanEllenberg, when I reached out

(01:16:01):
and said, Hey, read your book.
Thought it was amazing. Havethis podcast. Would you like to
join me? So glad I did. Jordan,this was such a wonderful
conversation. You're doing somany cool things and can't thank
you enough for being with us.

Great to talk to you. Thank you so much. This
is really fun,

fun for me as well. And thanks to Jordan
Ellenberg for joining us on thisepisode of The TechEd podcast.
All kinds of resources that wetalked about music resources. We
talked about his books. Wetalked about others as well.
Please,

seriously, go find London zero, hole four. Now
I think it is streaming, right?
This is like one of the greatforgotten albums of our time. We
both, Matt and I are in 100% inagreement. We demand that you
listen to it.

Love it. Yep, absolutely. That's it's awesome
advice as well. That's advice Iwould give to my 15 year old
self, actually, is, is, inanother couple years, this
amazing album is gonna gonnacome out, go and go and grab it,
in that case, on vinyl or maybeon a CD. But at any rate, so
glad that Jordan joined us.
You'll check out all thoseresources. We'll have them
linked up on the show notes.
They are the best show notes inthe business. So check those

(01:17:00):
out. We'll put those up atTechEd podcast.com/ellenberg
that is TechEd podcast.com/e l,l, e n, B, E R, G. When you're
down there, check us out also onsocial media. We are all over
social. You'll find us on ticktock. You'll find us on YouTube.
You can check us out onFacebook. We're on Instagram. We
are on LinkedIn, wherever you gofor your social media, you will

(01:17:22):
find the TechEd podcast. Whenyou do say hello, we'd love to
hear from you and can't wait tosee you all next week. I'm Matt
Kirkner, thanks for joining us.
That was really.

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Love It or Hate It: A Surprisingly Human (And Very Fun) Conversation About Math - Dr. Jordan Ellenberg, Mathematics Professor at the University of Wisconsin

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