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

What happens when a world-class mathematician meets ’80s college radio, Bill Gates’ top-10 favorite books, and a host with an algebra redemption arc? A surprisingly funny, fast-moving conversation. Dr. Jordan Ellenberg—John D. MacArthur Professor of Mathematics at UW–Madison and author of How Not to Be Wrong—swaps stories about The Housemartins, consulting on NUMB3RS (yes, one of his lines aired), and competing at the International Mathematical Olympiad. There’s a lot of laughter—and a fresh way to see math as culture, craft, and curiosity.

But we also get practical about math education. We discuss the love/hate split students have for math and what it implies for curriculum design; a century of “new” methods (and if anything is truly new); how movie tropes (Good Will Hunting, etc.) shape student identity in math; soccer-drills vs scrimmage as a frame for algebra practice and “honest” applications; grades as feedback vs record; AI shifting what counts as computation vs math; why benchmarks miss the point and the risk of lowering writing standards with LLMs; and a preview of Jordan’s pro-uncertainty thesis.

Listen to Learn: 

• A better answer to “Why am I learning this?” using a soccer analogy
• The two big off-ramps of math for students, and tactics that keep more students on board
• How to replace the “born genius” myth with a mindset that helps any student do math
• When a grade is a record vs. a motivator, and a simple replacement policy that turns a rough start into effort and growth
• What AI will and won’t change in math class, and why “does it help create new math?” matters more than benchmark scores

3 Big Takeaways from this Episode:

1. Math mastery comes from practice plus meaning, not a “born genius.” Jordan puts it plainly: “genius is a thing that happens, not a kind of person,” and he uses the soccer drills vs scrimmage analogy to pair targeted practice with real tasks, with algebraic manipulation as a core high school skill. He urges teachers to “throw a lot of spaghetti at the wall” so different explanations land for different students, because real innovation is iterative and cooperative.

2. Students fall off at fractions and Algebra I. How do we pull them back? Jordan names those two moments as the big off-ramps and points to multiple representations, honest applications, and frequent low‑stakes practice to keep kids in. Matt’s own algebra story shows how a replacement policy turned failure into effort and persistence, reframing grades as motivation rather than just record‑keeping.

3. AI will shift our capabilities and limits in math, but math is still a human task. Calculators and Wolfram already do student‑level work, and Jordan argues benchmarks like DeepMind vs the International Mathematical Olympiad matter less than whether tools help create new mathematics. He also warns against letting LLMs lower writing standards and says the real test is whether these systems add substantive math, not just win contests.

Resources in this Episode:

• Visit Jordan Ellenberg's website! jordanellenberg.com
• Read How Not to Be Wrong: The Power of Mathematical Thinking

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Transcript

Matt Kirchner: 0:00

Matt, welcome to the TechEd podcast. This is your host. Matt Kirkner, imagine having a pair of glasses that would allow you to look underneath the craziness and the chaos of the earth and to find order in everything, or at least most of the things that we do. We used to dream about having X ray goggles or glasses as kids, and so that's what sparked my interest a little bit in today's guest, I was reading an excerpt, actually, earlier this year from a book, a memoir by one William Henry Gates, the third also known as Bill Gates, who almost all of us, I'm sure, recognize as the co founder of Microsoft for many years, one of the wealthiest human beings on the planet, still right up there. And icon in technology and icon in entrepreneurship and business. I want to tell you that there was a paragraph in that article and it read like this. And this is Bill Gates writing about his childhood. He said, realizing early on that I had a head for math was a critical step in my story in his terrific book. And he quotes another book, he says, in his terrific book, how not to be wrong, mathematician Jordan Ellenberg observes that knowing mathematics is like wearing a pair of X ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. That book went on to say that how not to be wrong. The book by Jordan Ellenberg is one of Bill Gates favorite books. In fact, if he made a list, and he did of his top 10 favorite books, that book was on it so inspired and more than a little bit curious, I picked up a copy of the book, read it cover to cover. Thought it was fantastic. Reached out to the author of the book, Jordan Ellenberg, who today joins us on the TechEd podcast. Jordan is the John D MacArthur, professor, professor of mathematics at the University of Wisconsin, Madison. I should also mention that he is referred to as Dr Jordan Ellenberg, with his permission, I'll call him Jordan through the conversation today. But so honored Jordan to have you joining us on The TechEd podcast. Thanks for being here.

Jordan Ellenberg: 1:57

Oh, it's great to be on I love talking about this stuff. So let me start with this.

Matt Kirchner: 2:01

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

Jordan Ellenberg: 2:21

break in. Yeah, I've been on, I don't even know 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 you could not have started on a more congenial note, because that is an incredible album. I don't think anybody remembers it. It's it was actually incredibly hard to get the rights to quote lyrics from that song, because that band has been defunct for so long, it was difficult to figure out who owned the copyright. And amazingly, it's in Milwaukee. Amazingly, I tracked it down to a music publishing house that's in Milwaukee, and that's who owned the rights. And actually, I had to pay them a bundle, to be honest, to use those Did you really from that amazing song? That was unfair, since the band is not, nobody's buying that cassette anymore, the band is not making any more revenue from the use of those lyrics. But copyrights, copyright, so

Matt Kirchner: 3:12

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

Jordan Ellenberg: 3:36

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

Matt Kirchner: 3:44

you go. And speaking of copyright, there's actually all kinds of goofy rules around podcasts, and you can play that kind of music if you have the right licensing on a radio show, but you cannot play it on a podcast, regrettably. So maybe we, maybe, maybe we'll do a little bit of rendition of setting out a fence. How does that sound? All right, this is, I love it. This is the first podcast, I think, Jordan, that I've begun with a full couple of minutes on like, 1980s college radio. I actually went to school across the state from where you are, at the University of Wisconsin, Madison, at Marquette University. Got my start in broadcasting on the on the iconic WM, you are the college radio station. So I don't know that I've ever talked about that on the podcast, either. We're breaking new ground. I have talked about one of my favorite movies of all time, and that is Good Will Hunting. I saw that back in the in the late 90s with my best friend, Jeff Sherman. I still remember going to see it, loving that movie. Matt Damon, Robin Williams, as I was reading a little bit about your background, Jordan, there's a little bit of a flavor to that right? There's a scene in that movie where Minnie Driver and Matt Damon are talking about how Matt Damon could just his character Good Will Hunting could just play when it came to things like organic chemistry and so on. And I got that sense when it came to math for you, is this incredible skill or ability curiosity? Now? That you have of mathematics is that something you were just born with, did you hone it over time? A little bit of both. Tell

Jordan Ellenberg: 5:06

me about that. I mean, so I'm gonna start by saying, and this might surprise you, I have not seen that movie. Oh, come on, I'm telling you the truth. It's like, I feel like, it's like people who actually do karate, like, don't watch Karate Kid, right? It's like background, I feel like I know I would find it a little bit I don't know off putting is the wrong word, but I think so. Something I say in the book that I feel strongly about is that, you know, I say genius is a thing that happens, not a kind of person. I truly believe that. I think you can look at the world and not say, Okay, there's like, works of genius, like, there's sort of really amazing things that people do that we can, like, admire. But I think it's always a combination of the person and the circumstances and the times, and usually more than one person too, to be honest. So, you know, something I really try to get across about mathematics is that, of course, it comes easier to some people than to others. There's no question there. I mean, as a teacher, you know, we know this, but I don't think it's a good model to have this kind of goodwill, like hunting this Good Will Hunting like picture that there are sort of certain people who are set apart from whom inspiration just kind of like flows out with no effort. I think that's like a bad model. And I think you and I think, to be honest, I think you see it in all kinds of movies. I think you see it Hidden Figures. Is another one, which very popular, very successful movie, certainly very well written, well acted and well made. But I still think it presents this idea that there's all these chumps who can't do anything, and then, like, the young genius wanders in and is like, Oh, why don't you just do this instead of do that? And then everything is perfect. And, you know, real innovation is iterative, like, real innovation is usually cooperative, like, and so I think that, I think for our students, if they have that image of what it means to be good at math and what it means to be able to do math, they're gonna rightly be like, Well, I'm not an alien. I'm not a person for whom it just like flows out of me with no effort, as if it was like placed in my brain at birth. And so they may say, and people do say, oh, maybe this isn't for me. Maybe I shouldn't have studied this. And I think we lose a lot of great students that way, to be honest.

Matt Kirchner: 7:31

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

Jordan Ellenberg: 7:43

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

Matt Kirchner: 7:51

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

Jordan Ellenberg: 7:54

I'm gonna argue against myself, Matt, because I was just saying, you know, we lose a lot of students because some of these, like mistaken stereotypes about how math works beautiful mind. I have real issues with the movie as a movie, but I cannot deny that tons of people, like went into math and were inspired to study math from that movie. So I can't deny that it had that positive effect. I think it,

Matt Kirchner: 8:20

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

Jordan Ellenberg: 8:27

all? Did I watch it? I was a script consultant for it. Oh, were you really? No way. I didn't know. That's awesome. I read all the script well, just one season. For season two, they would send me 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 more accurate, like, how the mathematician would say something, you know, rephrasing. So it's very exciting. So I will say one line I wrote made it to the show. There was one line where I was like, he wouldn't say this. He would say this completely different thing. And so I feel like I can say I'm a TV writer, because, look, one sentence that I wrote was, like, aired on a major network TV, and I forgot to include pronunciation notes. So David Krumholz pronounced one of the words wrong. And I was like, oh, I should have put in a note to make it,

Matt Kirchner: 9:15

yeah, that's awesome. I love that, that it aired on, like, Friday nights, I think, for Anna. And that was, like, my thing, after a crazy week, you go and watch these and watch numbers, just we could probably do a whole show on that. I also do a whole show. You talk about Iterative innovation, and in the importance of that aspect of not just mathematics, but but, you know, various disciplines in general. You know, one of the greatest innovators of all time, some would would argue, is Bill Gates. And, of course, I was turned on to your book by that, that article I read earlier in the year, the excerpt from his memoir. Have you met him? And why do you think he loves his book so much?

Jordan Ellenberg: 9:52

I've never met him. I was completely taken by surprise, and, of course, incredibly pleased and honored that. He sort of had read the book and liked it. I can tell you that it's not like we pitched it to him, like, I can promise you, if the publishing industry knew a way to get into fortress gates to be like, Hey, have you tried this book? Like 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, I mean, 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 he actually read it. I don't think anybody like, I don't think anybody markets books to him. I think he just like says what he likes, of course. So no, I don't know anything about him as a as a person, and have not met him. But like, I, you know, we're he's a nerd. I'm a nerd. He wouldn't be mad that I said that, right? I mean, no, not enough. We have, like, similar kind of backgrounds and, like, I guess what? I would, let me put it this way, he's a nerd, so am 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 the books is, I mean, if I were, like, I'm gonna teach a certain amount of mathematical content in a certain amount of space, I wouldn't write the books the way I do, right? I mean, like, obviously, there's a lot of content. There's a lot of math in it. But what I'm excited about, what gets me, I mean, I'm writing a new book right now, so like, Okay, what gets me to sort of sit and stare at the page and write? It's like, the connections, the things that are out in the world. Like, sorry. Did that sound come through to you? Okay? Let me say it. Okay, fine. Keep going. Yeah. Yes, what, yeah, yeah, let me see what might be running, because I'm actually getting it a little bit from you

Matt Kirchner: 12:01

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

Jordan Ellenberg: 12:07

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

Matt Kirchner: 12:16

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

Jordan Ellenberg: 12:21

Oh, yeah. I thought, I thought you were gonna say, um, I thought you were 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 in New York who's just, like, constantly yelling, like pacing my natural speaking. I'm suitable for audio book.

Matt Kirchner: 12:41

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

Jordan Ellenberg: 12:55

I'm not totally it doesn't look Activity Monitor. Is anything taking a lot of CPU here. Let me see if there's, oh, let me throw this one. Hold on. I closed the original one, but there was, I think the producer one would have still been up. And how is that any better I did close one. Are you still getting a lag from

Matt Kirchner: 13:29

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

Jordan Ellenberg: 13:40

yeah. So what really excites me about writing the books is these connections between math, the stuff I've spent 30 years learning, and just like everything else in the world, whether it's, you know, society, science, politics, just the general human way of getting through life. I mean, I think sometimes we present math as if it's just some kind of abstract gauntlet that you had to run, that somebody invented, like just to be annoying, basically. And of course, right math is not like that. Right? Math is a human activity done by humans for human purposes. And every single thing we have in math, somebody created because they were trying to solve a problem that people had, right? And I think sometimes we lose sight of that, and I just it's so fun for me to kind of go back. I mean, my books always have a lot of history, because I find I got to go back to be like, Okay, why did people want to do this? Like, what problem did they have that they were trying to solve? And just, again and again, there turns out to be an interesting story there,

Matt Kirchner: 14:42

for sure, having the Jesuit education that I did post secondary, and we were required to study topics in subjects like theology and philosophy, and I was actually fascinated. We'll talk about some of that a little bit later, but the number of the philosophers that you pull into a conversation about math. Ethics was just absolutely fascinating to me. And say to your point about history, you know, learning about, you know, some of these historical figures that you've learned about another contest context, who are actually mathematicians as well, or maybe first that, that part of it was really, really fascinating. So credit to you for for being able to draw from so many different topic areas, which I think is part of the reason, you know, I can't speak for Bill Gates. And by the way, you know, I think challenge to Melissa Martin, our producer that let's get Bill Gates and Jordan Ellenberg on the same podcast, and under the pretext that that bill can finally meet, meet his hero, Jordan and and and meet the gentleman that wrote one of his top 10 favorite books. But, but I think that is one of the one of your true gifts is to be able to bring some of this stuff down to earth, in a way, and maybe tell some of the stories that are less about numbers and equations and more about human interest. Is, have you been told that before? And do you feel that way?

Jordan Ellenberg: 15:51

I mean, that's definitely what I'm trying to do. So if people say that, I definitely listen, because I'm like, yeah, yes, that's, that's although I wouldn't, I wouldn't say they're not about numbers and equations, and instead, they're about human interest. I would say they're about numbers and equations and human interest. I'm just trying to demonstrate why are humans interested in numbers and equations, which, you know, in every society that's ever existed, we have been

Matt Kirchner: 16:15

absolutely Yep, no for Mission accomplished. That was, that was exactly the point I was making. And it's really readable stuff, and I've only read one of your books, and I know that and I know there's several. We'll talk about some of the others a little bit later. Let's talk about this. You know, you start right out at the beginning of a book, Jordan talking about this whole idea of, why am I learning this? Right? And we spend a lot of time 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 it through but, but, you know, it was never easy for me to learn in kind of a traditional classroom. I won't bore our audience with that story again, because they've heard it way too many times. But you know, that was a question I had. What? Why am I sitting here learning about these equations with letters in them? And what does this have to do with anything? And what, you know, what am I ever going to use an integral? I mean, all those, you know, all those questions that we have, you draw a parallel to doing Soccer Drills actually, which I thought was just perfect, and I'm going to use it talk about that a little bit about why. Why are we studying math? Say, if you have a student who's a freshman in high school and getting into their algebra textbook and math hasn't been their thing for one reason or another. Why study math?

Jordan Ellenberg: 17:25

Yeah, so the metaphor I use in the book is it would be weird to do soccer drills 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 to school one day and somebody is like, what we're gonna do is run diagonally between these traffic cones. And by the way, you're gonna be moving this ball with your feet. Why they do that? And you'd be very reasonable to be like, Okay, but why am I doing that? Like, I guess we can do it, but like, but what's it actually for? And if you've never heard of soccer, or didn't even know that it existed like it would seem like a very strange activity to do. But that being said, when we actually coach kids in soccer, they play scrimmages and they do that so they know what soccer does, and they do the drills. And I think most soccer coaches would say, okay, learning soccer is not just about kind of playing soccer casually, like until you become incredibly good. They're like, there are sort of certain skills that you need to build, and you build with repetition. And you sort of build with repetition, like so much that it goes into your muscle memory, and you can almost do it unconsciously. And I think lots of 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 my books. I work hard on them. I'm very happy that people read them. But they're not designed that you like, become a mathematician by by reading them, right? Like, I mean, they're designed so that you're like, Okay, I get it. What's the point of actually doing this? But somebody who wanted to, like, you know, really learn math and do math, or learn math well enough to do engineering or to do physics or something like that, yeah, that person is still gonna, like, really have to become quite skilled at, like, algebraic manipulation, to give one example, which I think is sort of the key skill of high school math. And like, Sure, high school has succeeded, if a kid comes out of it with the ability to manipulate algebraic expressions, and if not, then they haven't been well served,

Matt Kirchner: 19:29

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

Jordan Ellenberg: 19:45

I mean, the first thing I want to say is, it's a challenge. Like teaching is hard. There's no magic bullet. I often say, you know, people say, like, what's the right way to teach math? And I often say, you know, there's no right way, but there are some wrong ways, you know. Anyway, I. Sort of complete, a sort of, you know, a sort of absolutely, sort of mindless focus on repetition with like no attempts to ascribe meaning to it, I think, is probably the wrong way for moat for almost all kids. But what I found as a teacher is that whatever I do in the classroom. There's, I'm going to do something, and then some kids will be like, Oh, thank god you said it that way. That finally makes sense. And other kids are like, What the hell are you talking about? Like, that's and then I'll do something else, and like the other kids will be like, so it's very it's very individual. And I tell you know what my students, who I'm training as they're going to classroom for the first time, I tell them, you just got to kind of throw a lot of spaghetti at the wall, like you actually have to try a lot of things and not just be one kind of teacher in the classroom, because different students are going to respond to different things, and it's very hard to predict what an individual student is going to respond to. And I think for most students, 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, and two thirds they're like, I don't get why he's saying it that way. That's weird. I think that's better than if 1/3 of the students love you all the time, and two thirds spend the entire semester, like, checked out. Like, you sort of want everybody to get something. So I sort of preach variety. I'll say this too. Okay, we have a super interesting collection, at the University of Wisconsin library, although our library is actually about to be closed by budget cuts, so I don't know where those books are going, so go look at them now if you're on campus, because you won't have your chance for it much longer, but it is a collection of math textbooks from Wisconsin that were used Wisconsin schools going back to the, I think, the first decade of the 20th century. So like, 100 years of math textbooks, a whole day just looking through these. And it's incredibly striking, because what you realize is that there's no new arguments in math education, like, every argument we have about, Well, should we do this, or should we do that, or should we do this other thing? I promise you, it has all been tried, and everything has its pluses and minuses. So you can go back to like nine, like people have this idea, oh, now there's this new fangled idea of, like, writing math textbooks with like social relevance that, like, talk about, like contemporary issues, or like that was being done in 1920 you know, people say, like, Well, what about this sort of focus on, like, drill and repetition that was being done in 1930 I mean, everything has its pluses and minuses. And people are like, Oh, this way we're doing it isn't working. Like, let's switch to this other thing. And it just, and it just kind of cycles, and it's, um, I mean, I think in the end, I'll say, so here's, here's an interesting fact about math and K 12. If you ask students like at that age, like, what's your favorite class, the answer that's most frequently given is math interesting, but if you ask students what's their least favorite class, right? Also, the answer that's most frequently given 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 I begin to come back to it, to come back to the beginning. Yes, I don't advocate a meaningless way of teaching it. I do think, not that it's easy to do this, but I do think sort of connecting it to the real world is useful, but it has to be in an 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 friends. Like you will do this if you can solve this algebraic equation. Like, it's not as direct as that. And kids are pretty smart, right? So if we, if we tell them that, they'll be like, come on.

Matt Kirchner: 23:59

Yeah, right. Speaking of smart kids in I'm not necessarily taking credit for being smart, but one of the things I figured out in grade school was this, and I didn't, I didn't, I didn't become disenamored with math until I got to high school. I'll admit that up front, but the I used to love doing story problems, right? I mean, so you'd have the, you know, you have your textbook, speaking of old textbooks. And you know, one page would be whatever 4040, different equations that you do, and then the other one might be eight story problems. And I love the story problems. And my teacher asked me one time, why, you know, Matthew, they called me at the time. Why do you love those story problems? And I said, and you would think the answer is, well, it's my opportunity to apply the math, right? Or it makes it real for me. And my answer was, well, 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 work to do. Was my was my application. But you know, you make an interesting observation, Jordan in in the book again, and I 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, we talk a lot on this podcast, and have all kinds of golf guests on as you know, that are talking about different approaches to education. One of the things that you said, which is not only resonates me, but could almost be the reason for existence of this podcast, is that students learn differently, and what might be interesting to 1/3 of the class may not be to the other two thirds, and the key is to find something that's interesting to as many of those people as you can also love the idea. And I was envisioning an inverted bell curve as you were talking about this. This idea that you've got some students on one end that love math and and that's their favorite subject. And the same can be true, or said for another group of students, that it's the, you know, it's their least favorite that's a fascinating way of thinking about it as well, but on this topic of rote memorization, and you've mentioned that, and we've got some folks that are saying, hey, we need to get away from that, especially in the age of AI and machine learning. We'll get into that topic here in just a moment, as we do on almost every episode of this podcast. But before we talk about that, and then we've got other teachers that are talking about getting into things like the meeting and developing ways of thinking and Guided Discovery and approximation. And what's your thought on that? I mean, it's probably a loaded question because, or maybe just the obvious one, because I think I already know the answer, but talk about one or the other, or both.

Jordan Ellenberg: 26:17

Yeah, and by the way, a great example something else I learned is this idea of discovery learning, the idea of like, Okay, what if the class didn't tell the student the material? But like, was like a sequence of questions which the student, you know, starting from the very beginning, and the student answering them would guide them to the which we think of as like, oh, this kind of novel. Slightly wooy term. I found a textbook from the 1870s no way that worked exactly that way. So nothing is new. Nothing is new, right? Nothing under the sun, as my boy Ecclesiastes used to say, so. So what I'd say, and I think you do kind of know what I'm gonna say, this is, like, this question of like, well, do we need to focus on the skills being able to do them, like, swiftly and reliably and like repeating until they're memorized. Or do we need to focus on the kind of discovery meaning context? I just feel like they like to use another sports metaphor. This is like somebody like, goes out for the baseball team and they're like, Well, should I learn to catch the ball, or should I learn to throw the ball? And you're just gonna, okay, you don't. That's actually not a choice you get to make. If you're not doing both those things, you're not playing baseball, right? It's just like a stupid question, okay, stupid is too hard, but, but it's, it's, yeah, you're not doing mathematics unless you're doing both of those things and building both of those skills. So, so I think it's a false choice. I don't think it makes sense to sort of say, are we going to emphasize one over the other? I think that you're just not doing math without both. And I know it's a tall order, right? I know we have, like, limited time in the classroom and, like, that's a lot so,

Matt Kirchner: 27:51

but yeah, well, put in the so a couple things I have. I have a saying that you can, you can analogize any business situation, in this case using either your, you know, your post secondary love interest, or the game of baseball. So, well done using baseball to analogize an answer, also wrapping in a reference to Ecclesiastes, not to, not to telegraph too much a later question. But we do have a spirituality question here in a little bit. So, so thanks for the reference to the Old Testament. You know, not quite a bit more recently than the Old Testament would be the book that that we're talking about here today, how not to be wrong, which was written, or at least published in 2014 so we're now 11 years out. AI,

Jordan Ellenberg: 28:34

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

Matt Kirchner: 28:41

exactly well it and mine, one might say, written for the same purpose. How not to be wrong. So you're tight. How's that awesome? Looking forward to that part of our discussion, but, but also to the AI part of it. So, so I mean, in as much as you can we've all, we've gone all the way back to 1872 and math books from the 1870s now, 150 years ago, more and a lot has changed in the last 10 years. So you know is AI and machine learning. Is that changing the way we should teach math, why we should teach math, whether we should teach math, talk about that in as much as we're living in this age of advancing technologies, and not just advancing, but advancing as quickly as I think we've ever seen.

Jordan Ellenberg: 29:27

It doesn't affect weather that much. I'll say, Okay, I have no I have no qualms about that. How, how, maybe, and we'll see. And I think I but I think it applies to other subjects as much as it applies to math, I think that you always have to bet that things are gonna be like they've been in the past. That's not always true, obviously, right? But look, if you have to make a bet, I. Are things going to be pretty like they've been in the past, or they're going to be radically different? I think it's always more likely they're going to be like they've been in the past, and in the past. You know, technology and computation has interfaced with math for, like, a long, long time. And every single time, the technology takes certain things that we sort of thought of as mathematical skills, like, you know, adding large sums of numbers, and we sort of reclassified those were like, Okay, that's not math anymore. That's computation. And then math is something else, something something we do on top of that, often something that is that we're enabled to do by the new computational abilities. So I think the best bet, and you know, no one knows the future for sure, is that that will happen 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 that we're not doing now. That would be my best guess. And the point is that I think the people who do those new things are not going to be able to do it without having the mathematical skills and insights and virtues the ones that we're teaching now

Matt Kirchner: 31:12

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

Jordan Ellenberg: 31:27

I mean, I think, like, I think as a writer, for instance, I mean, I think it's an interesting question as a writer, I can see that like a big train. LLM trained on, like, lots of English language, like, can produce English prose. It can't produce something that I would put in a book. You know what I mean? It can't produce something that I would put my name on. But, like, it produces things that are good enough for many purposes. So so that creates all kind of, I mean, I think it creates a lot of interesting questions about how we teach writing. But I somehow, and maybe this is just me being middle aged, but I sort of don't really believe that it's kind of fine for people to kind of let go of the skill of expressing themselves, because they feel that the machine can do it well enough. You must. Okay, so you must talk a lot about the concept of disruptive innovation, right? This kind of Clay Christensen, for sure. And I think what, I think what people sometimes miss about that concept, that I think is very important and very central to it, is that it's not always about like a superior product being better and displacing something that's worse. It's often about a worse product, right, displacing something better, and then people sort of choosing to sort of change their values to match the inferior product because it's more convenient or cheaper or faster than that? So I do worry a bit on the writing side that people will just come to accept the kind of prose that an LLM emits as like, Okay, this is prose. This is now what we Yeah, this is now what we value. No, and

Matt Kirchner: 33:28

that's worth considering and worth worrying about. You know, we've got, I do a tremendous amount of writing. In fact, I just wrote another magazine column yesterday morning as we record this. This one on the topic of kind of carrying over the idea of work hardening in manufacturing to getting new sales people ready for new jobs in in any role, including manufacturing. And I think you know, the question becomes on that particular topic, and whether or not we can have a generative transporter, GPT, such as some of the ones we talk about regularly, perplexity Claude are two of my go tos, chatgpt would be another example. It's got to be interesting to the reader first, right? I mean, if you can write really great prose, but if it's not interesting or insightful or doesn't present a new idea, maybe not a whole lot of reason to to read it. And maybe that's maybe that's a way of looking at it from a math side as well.

Jordan Ellenberg: 34:21

Yeah. Yeah. I mean, it's a very complicated space, and it's made more complicated by the fact that, you know, there's a lot of money, and money distorts, right? I mean, in other words, like, as somebody who, I mean, so I so, you know, I work on this stuff to some extent, right? So I don't know if this, I mean, not. I think this is about like my books, not about my academic work, but, you know, there's a lot of really interesting questions about how to get a machine learning protocol to produce something that's of material interest for mathematics. That's not an easy problem. It is not, at least at this moment and maybe forever. Or it is not a matter of you just ask chatgpt In English like that doesn't work. Maybe it'll work in the future. Doesn't work now, but there are things you can do. And I think it's like a very I think it's a very interesting space. But I also think that if you, I mean, I'm trying to choose my words very carefully, if you, if you work for a company that has a very big financial interest in appearing to be ahead of four or five other companies who are competing in the same space, you don't really get to talk about your work frankly, the way, like academics do, right? You're, you're, you're a scientist, but you're also a promoter. You sort of don't get to choose to only have one of those jobs, and so I think that's a challenge for sort of like figuring out what's actually going

Matt Kirchner: 35:49

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

Jordan Ellenberg: 36:07

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 get that, that that doesn't work unless people behave that way. But it's just we have to have eyes open about it. Do,

Matt Kirchner: 36:25

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 Wall Street Journal, which our audience knows. I spend a good fair amount of time with the Wall Street Journal every morning. The author, Ben Cohen, in fact, as I'm thinking about it, I think it was just this last weekend, he was writing about how there's this International Mathematical Olympiad. You might be familiar with that. I wasn't until I read this, but essentially, well, oh, okay, of course, you were right. I love I love that. I asked about numbers. It's like, yeah, no, I was an advisor. I was in the International Mathematical Olympiad. For the record, I was not, lest there be any confusion, but it's an exam for our audience. You know it well, over two days held, over two days, students are faced with three progressively challenging problems, spans, algebra, geometry, number theory, a word I had never heard of called combinatorics. Maybe you can explain that that one to us, but the Deep Mind, which is the AI model by Google, there are several of these, perfectly solve five of the six problems, but there were 26 students that actually got all six. So machine learning AI, deep mind hasn't quite caught up to at least those 26 students. So let's talk about first of all, so you were in the International Mathematical Olympia. Tell me about that experience. Let's start

Jordan Ellenberg: 37:45

there. Oh, it was great. And it was, um, you know, this is a contest that's been going on since the 70s. It's for high school students. Each country sends six people. It actually starts as a thing inside the Warsaw Pact, right? It was just communist countries, and then they kind of expanded, and it became this kind of, and a lot of your listeners, I sure don't remember the 80s, but there was, there was like this. It was the weird time of, like, you know, the threat of Global Thermonuclear War, but also this kind of spirit of, you know, let's at least pretend to have sort of, like, friendly, good natured competition. It was, it was late enough that, like, so, you know, the first one I went to was in Cuba. It was hard to get to Cuba and those, I guess it still is, but it was, like, really hard. And, you know, we went, and we, like, did a math contest. They took us to the Museum of American imperialism, and we, like, looked at all like the stuff about it. In the end, they made sure to bring the US team to sort of see the museum. I mean, it was, it was, and so that was, we kind of alternate between, like, a communist country and a Western country, and kind of like, have, like, a little bit of bragging rights, of, like, how did we do? How did the Russians do, you know, etc, etc. Very, very wholesome. I liked a lot. And it's been going on. It's been going on ever

Matt Kirchner: 39:04

since. What a cool, cool experience. You know, we had this within the last year, I want to say, maybe just a little bit longer ago. Leo Reddy, who ran the NATO desk at the State Department during the Cold War on it for three presidents, by the way, if memory serves, Reagan, Carter Ford, all three of them, and he, and he was the architect of the Helsinki Accords, which, which I didn't know until interviewing him. And then going back into the history, I came of age in the 80s, so I've got a little bit of a penchant for Cold War history and so on. But the whole idea of detente and creating some of these relationships, be they historical, philosophical, related to the humanities, in this case, related to math, was really something that a lot of folks would point to at least as at least one of the reasons, if not a key reason, that the cold war eventually ended because people started to see people as people, and less so as adversaries in a lot of cases. So what a cool experience. Say, even though you you were subject to the American appearing imperialism Museum, haven't been there either. But that sounds, that sounds a bit interesting on this topic, though. So 26 of these students, you know, bested Deep Mind in this competition, but it's still nailed five of the six problems. Well, you know, what are your thoughts on that? Are we going to get to a point where AI is out competing students in terms of, you know, raw computation and being able to do, you know, not just algebra, but as we suggested that, you know, geometry, number theory and and combinatorics. And so while we're on that topic, I don't know that I'm pronouncing that right, but tell us what that is, too. If you know,

Jordan Ellenberg: 40:36

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, you have sort of some big network with, like, 1000 entities. And you want to know, well, how many of them? Here's a classic combinatorics problem. You have some network network, and you want to know how many connections in the network? Do I have to break before the network falls apart into two pieces? That's actually a critical question. If you were running supply chains or you're running a communications network, that's a hard combinatorics problem called Max cut, actually, and it's like that kind of question. So, and actually, that's one of the areas where machine learning methods have been most successful. Like my own work in that area has mostly been about like, okay, how can we kind of coax a transformer into, sort of generating 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 is something I do have a kind of a strong opinion about, which is that I don't believe in benchmarks. Benchmarks are very popular, and there's a good reason that they have a purpose. So when I say I don't believe in them, they have a very good purpose, but I don't think they speak very much to the question of, what is the eventual effect of AI on mathematics. They have a purpose. If, like, let's say you're an investor and you're like, Okay, I want to get a sense of whether I think Google is ahead of anthropic technically. Then right? It's very reasonable to be like, I want there to be like, a 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 for mathematics. Got it that has not happened very much yet, but I don't believe it couldn't happen. But in other words, like winning a context is somehow that's that's artificial, like, that's not actually what matters. And so like, the benchmark that matters is, like, does the thing actually work? And we'll see,

Matt Kirchner: 42:46

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

Jordan Ellenberg: 42:50

let me answer your question a different way, though, because you said you didn't. I answered a question you didn't really ask. So let me answer the question you did ask, which is, like, is it ahead of students? The thing is, in many ways, yes, but that's been true for decades already. In other words, like, what we ask students to do, like, like, let's say, like, a kid who's taking even a college level class like calculus or linear algebra, I promise. I mean, maybe I shouldn't tell this in this college students lit listening, but like, Wolfram Alpha can do your calculus homework already. Like, that's not new. That does not take the power of a transformer. So in terms of, like, student level work, and I think one reason that I'm not too doomy about it is that that has been true for a long time, and yet, like, we're still teaching math, and students are still learning math, and I don't feel like college students today are like, more degraded than college students of the past.

Matt Kirchner: 43:47

Am I think about my wife, who's a both an undergraduate and master's degree in engineer and still has her science calculator that she carried around with her back in the 80s, when, when we were listening to, you know, actually the, you know, the house Martin's album London zero Hall follower just come out, and we were using the science calculator back then, and it's so into your point. I hope first Polish the best calculator, of course, Oh yeah, absolutely, with kind of like that gold finish on it. I mean, you know, that's exactly the one. Yes, I see that was, that was the

Jordan Ellenberg: 44:18

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

Matt Kirchner: 44:23

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

Jordan Ellenberg: 44:28

people, and then we're going to come back to doing serious business. But this reminds me of when I went to see, this is a very okay, this is a very Wisconsin moment. But I went to see violent femmes play their entire first album at the Sylvie in Madison. Yeah, incredible concert, incredible show. They still bring it at the age they're at, but also, literally, every single person in that 2000 person venue was, like, born within two years before me and two years after me. It's like, an incredible it's like, it's like, incredibly demographic. So that's who would listen to our podcast. Like, exactly. Exactly, people born at the exact same time as us, all right, ever do we agree? Greatest fan ever to come from

Matt Kirchner: 45:07

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

Jordan Ellenberg: 45:25

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

Matt Kirchner: 45:29

right? Exactly. So, 1986 the same, same year that the house, Martin Zelman came out the London zero, how far? And they did two of them. I think they were fantastic. That was one of them that summer. I saw the violent femmes play at the Rock stage at Summerfest, when there was still a rock stage, largest outdoor music festival in the world. And the opening band, and nobody had heard of them, was the bodeens, and it was amazing. So I saw the bodes open up for the violent femmes, which was amazing. So I'm Wow, figuring out that was really cool show. So just about four weeks ago, I was at Summerfest, again, the killers were playing huge killers. Fan love the killers, and they covered American music by the violent femmes in that concert, which is just awesome.

Jordan Ellenberg: 46:20

Wow. So, so,

Matt Kirchner: 46:22

yeah, so we got Yeah, so, yes, violent femmes. You know, there's, there's all kinds of connections to to Wisconsin music history. But that 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 up on that, on that concert, and sounded like it was just phenomenal. I it was great. It was great, awesome. So now I have to segue from that to oh, this is perfect, actually. So 1986 saw that concert, violent femmes, proteins. I was in high school. Speaking of high school, how's that? Melissa, speaking of high school, I hated algebra. In high school. I just when I was I was I was thinking about this, this podcast this morning, Jordan and I went my high school algebra teacher was Mel DODDS. Is his name? God bless. Mel DODDS. He was an icon basketball coach, and I just, for whatever reason, I looked his name up thinking about this topic this morning, found his obituary. He's been gone now for 10 years. I failed the first semester of algebra. Literally failed. Got an F. And he came to me at the end of my first semester, and this is what he said, I think he just wanted to get rid of me. He said, Whatever you whatever grade you get for the second semester, I will go back and give you for the first semester. And he said, so don't give up on it. You get an A for the first semester, we'll go back and give you an A for the second for if you get an A for the second semester, we'll go back and give you an A for the first semester. And so I ended up getting a D my second semester, which meant my grade for my first semester was also a D, which means that was enough to pass and get on to to geometry that following year, and then Algebra Two. And I actually, again, to portend a little bit of our future conversation, I got religion about at least education, and kind of cleaned up my act after that. But so I'm a student, I just struggled like crazy with algebra. And in fact, you kind of mentioned there's two inflection points in a student's academic journey relative to math, and one is learning fractions, which I remember doing in probably fourth or fifth grade. The other one is algebra, which I got into freshman year of high school, and that's, and that's where you say, 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 they fall off the math train. What should we do to keep students like me engaged in math? Maybe it's as simple as having someone who says, All right, you're smarter than this. What you do second semester. We'll give you for first but what are those things that teachers should be doing to make sure that we hang on to those students and keep them fired

Jordan Ellenberg: 48:48

up? First of all, I love that grading policy. I think it because I think it speaks to this very interesting question that I think we don't ask ourselves and reflect on enough as teachers, of like, what are grades actually for? Because in some sense, the truth is, when you really think about it, they have a lot of different purposes which are kind different purposes which are kind of incompatible. Like, if the purpose of the grade is to like, record how you did for some future person to look at, then the people the teacher will be like, Well, why should I change your F like that accurately reports how you did. But if the point of a grade is to give a student feedback and help them learn, which is kind of a little more what I think like that, then what your teacher did was exactly right, because, like, he created the motivation in you to like, be like, Okay, you actually can like. He wouldn't say that if he didn't believe you could pass the class, right? So that both demonstrates his faith in you and sort of gives you some motivation to succeed. But the truth is, the grades are both of those things, right? I mean, we teach in college, we know people are gonna look at our students. GPA, we know that, like, part of what we're doing is, like, providing information for future schools, future employers, etc, so like, like, everything else, the answer is always, like, it's both

Matt Kirchner: 49:55

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, and then 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 it through school. Actually studied accounting in undergrad. So for a kid, the fail of algebra, that was my career choice. Spent a few years in public accounting and then ended up several years later, as CEO of a manufacturing company headquartered in Milwaukee. I ran into Mel Dodd son at a charity event. Just by coincidence, he was sitting next to me. I noticed the last name where he was from. I'm like, by any chance, are you related to he's like, Oh, for sure. He's like, Yeah, Mel, dads is my dad. And I'm like, I wonder if he'd remember me. He said, I guarantee you he will remember you, because he remembers every single, every single student he ever had. And I happened to have my CEO business card with me. And I said, you know, give him his business card. Let him know I remember him. Let him know for thank him for giving me that break, that freshman year in math, things turned out okay, if he was wondering. And so that was that story ended. Well, at any rate, you said you had a question, and please feel free to pose it,

Jordan Ellenberg: 51:10

and you just gotta hope that he didn't see the business card. And think it's gotta be a different guy, like, couldn't be the guy who barely skate by with a D in my class. That's awesome. So okay, now I gotta remember what I was all right, we were talking about. So one thing I find that 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 unload about you, about my bad math experience when I was nine, when I was 12, or when I was 16? Because, think about it, they've gone through their whole life. They have nobody to tell after this trauma, like when race, you know, until me. So I want to, we're going to get on the couch, and I want to explore this with you. I want to know what happened that you felt UK you so you failed first semester of algebra. Do you feel like mal DODDS was at fault? Do you feel like you were at fault? What went wrong in the interaction between you algebra and Mal DODDS? Since you're obviously like a competent person, he's in a quantitative field, tell me go through it with me. Like what you feel went wrong?

Matt Kirchner: 52:16

Let it all out. No, absolutely I first of all, the problem was all me, and it was certainly not him or his way of teaching, or, you know, obviously, given the story I told, he took an interest in my success and wanted to see me be successful, you know, whether or not for me, there were more applied ways to learn it maybe, maybe not. I mean, I was never a great classroom learner. That was certainly no fault of his. That was the model that was education then, and to many, in many cases, still is today. But I got religion my sophomore year about education. I could tell a 15 minute story. I'll tell the abridged version, and that's all about I just I didn't see the connection between education to what I was going to do after high school and good one of my very best friends, in fact, I'll give him credit. His name is Mark Davis, and we're still, still really good buddies. It kind 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 of Jordan Ellenberg, but, but the kid that that really could just everything just made sense to him. He didn't have to spend tons of time buried in a book to get it. It was, he was just a natural. And he said, you know, we're gonna get to the end of our high school journey. And we had our, you know, same friend group. He's like, we're all going to have all these options of what we wanted to do after high school, whether we want to go to college, where we want to go to college, what we want to study. He's like, if you don't figure this out, you're not going to have any choices when we get done, and you're going to be stuck getting, will get, taking whatever life gives you. And so and that that actually, that conversation changed my life for one reason or another. We just have those moments in our life, and so, so I got serious about studying. I got serious about my academics. I was a kid that had probably told the story on the podcast before finished my freshman year with a 1.8 grade point average, graduated high school almost at a 3.0 and so you're pretty good math guy. You can imagine that I really picked up my pace there in those last three years to pull the to pull the average up as high as I did. But, but for me, it was, it was all on me, and I didn't see the connection. I didn't take an interest in academics until I saw a purpose in it. And I also felt like, you know, up until that point, yeah, I was doing academics for the sake of doing academics, or that perhaps because, you know, to please my parents or to whatever, and that, you know, if that wasn't a high enough bar or big enough goal or the reward wasn't strong enough, why keep doing it. That was the part of it. And then once I put a connection between, hey, the better you do in school, the more options you're going to have, regardless of what you want to do that, you know, the deeper you can go. That that was that spark that kind of lit the fire under me. And I was never a four, oh, student, even through college, but I figured it out well enough to get through it, maybe a longer answer, that you could hear that

Jordan Ellenberg: 54:52

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

Matt Kirchner: 55:01

Yep, 100% so great observation,

Jordan Ellenberg: 55:07

yeah, and that's something I think we struggle with, because as teachers, we can control what we do and we can control what the school does, but we can't control the social environment the student is in, and if, if the kid is around a bunch of their friends who are like, God, why are you wasting your time doing your homework where you can, when you can, just like chat, GPT, all your assignments? If that's you know that that's a that's a hard current

Matt Kirchner: 55:30

to fight against, sure is Yeah, and then we certainly encourage teachers now, because I think in a lot of ways, my my theory that that's been bouncing around in my head Jordan is that it used to be that school was where we went to learn and home was where we went to 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 school, but then you go home, and we actually called it homework, and that was where we wrote essays, and that's where we studied for exams. That's where we went through our notes. You know, we applied the the work that we learned in school, and I think now with so many different ways to deliver liver learning. And to your earlier point, you and I agree 100% every learner learns differently, and the magic of education is to figure out where and how we can resonate best with an individual student or group of students, based upon how they learn, the more effective 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

Jordan Ellenberg: 56:23

I just want to say, I want to say something optimistic, because I actually am an optimist. Like, I feel like I said some slightly negative things, but I want to emphasize, I mean, one thing I love about being a professor and spending my life like, among like, you know, these young folks, is that, I mean it really, it's a very soul refreshing workplace. You can't be too pessimistic when you're around these folks all the time. And I just will say that, like, I have an unshakable faith from, like, my years of experience being a teacher, that people like learning and they crave it like they truly do. I think we can get cynical and talk about like, oh, all the ways that people like avoid effort, blah, blah, blah, but I think fundamentally, it's just extremely human to be excited about learning and value it, and we just have to make sure that people are seeing that they actually are learning. Are not doing tasks for the sake of tasks, for the sake of busy work, but because they're gonna learn something. And I'm enough of an optimist about like the human race to feel like people do respond to that. There's something fundamental in us that gets excited about encountering new things, learning new things, mastering new things. We are built to do it.

Matt Kirchner: 57:29

We are, for sure, it's exploration in the same way that we can explore space. We can explore the you know, what's what's under the ground, what you know, what have you this is just another form of exploration. And that's a little bit of the sense I got from Bill Gates, is comments about your book, right? Is that, you know, how do we make sense of this chaos and this craziness? We do it by exploring. We do it by asking ourselves questions. We do it by going deeper. And for a teacher, professor, instructor, whatever you know, workforce, trainer, whatever that whatever that vocation is, and I use the vocation intentionally, whatever that calling is, there's so many opportunities not just to deliver knowledge, which is important, but to inspire students and show them they're capable of doing something they didn't know they were capable of doing, or that they have an interest in something that they didn't know they had an interest in. I think I was horrible at art, but I had an art teacher that took an interest in some of the creative things I was doing and and all of a sudden I had, like, found this whole in middle school creative side of myself I didn't know existed. And so that's the real magic that happens inside and out of the classroom. And I got to imagine, that's a big part of why you've chosen the location you have.

Jordan Ellenberg: 58:36

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

Matt Kirchner: 58:37

it better. Awesome. Well, great. So we'll keep going on the topic of the book, and it's called how not to be wrong. And again, you've written many books, several books, but this is the one that I I read, if I got it, and it took, you know, I mean, I read through, I'd read the whole book. It was awesome. You get to the final chapter, and the kind of the takeaway for me was a little bit about, you know, math is a little bit less about absolutes and getting to exactly the right answer, and a little bit more about understanding our world in terms of probability. So we can't perfectly predict anything. We can kind of, we can handicap it a little bit. We can understand the present in the future a little bit better based upon data. And whether that's you know, whether that's the lottery, whether it's you know, something going on in the world of AI or machine learning in these days is that the right takeaway is, Did I did I get it right? And what would you add to that?

Jordan Ellenberg: 59:27

Yeah, well, I'd say it's funny that you say that, because I think that's one of the strands that's going on in that book. But actually that is, in some sense, like the premise of the book I'm writing right now. I mean, that's what I'm really so you're sort of jumped ahead awesome to the book I'm working on right now, which is about uncertainty and whose theme is really that I think people have this mistaken idea that what math is for is to diminish or even dispel uncertainty for your life, because people. Are uncomfortable with it. They're like, I want answers. I want an answer with three decimal places like that would make me feel more secure, because I hate all this uncertainty I have to live with. Like, math come and save me from this, and then I have, like, I think, a negative, but really a positive message, which is like, nope, math is not going to save you from that, because uncertainty is the way the world really is, right? If you try to, like, neurotically get it out of your life, you're just failing to look at the actual world. But then the good news is that, guess what, math is actually filled with tools for, like, helping you think about uncertainty in a useful and productive way. And so the whole theme of the new book is, like, all about the many ways that the math helps with that, and fundamentally, the message is, like, it's not uncertainty that's the problem. It's our inability to tolerate uncertainty. That's the problem, whether because we don't have the quantitative tools or we just sort of haven't built, like, the psychological strength to tolerate it, but like, that's, um, so it's kind of a pro uncertainty manifesto. That's what I'm trying to work on right now. What do you think my elevator pitch?

Matt Kirchner: 1:01:08

Yeah. Oh, 100% Yeah. Are you kidding me? I, in fact, I'm hoping for an advanced copy and and signed by Jordan Ellenberg. That would make an advance

Jordan Ellenberg: 1:01:15

copy, but it's gonna be I'm still a year away. I've written like a third of it.

Matt Kirchner: 1:01:20

Well, yeah, good Lord willing. We'll both be around here in a year. It's interesting. You I was working over the weekend. We built a model a couple years ago using Azure Data Factory and Azure for one of the companies that I'm involved with that was accurately predicting EBITDA, or net cash flow within we got it to where it was 14 months out, one and a half percent accurate to to what the net EBITDA it was for 1414, months out. And we were refining that over the weekend, and had the same thought about, look, this is a really, really cool model, and it takes a ton of stuff into account, but there's even more stuff that it doesn't solve for, doesn't take into account. And so that whole aspect of uncertainty as you were just referencing it was resonating in my head. The other thing you're resonating my head. I'm, I'm a big believer that, you know, in Celestine Prophecy, you know nothing, nothing happens by accident. There's no such thing as coincidence. And your reference earlier to Ecclesiastes, believe it or not, I was just I rode my bike back and forth to work every every day last week, and which I don't get to do most weeks because I've got business meetings or I've got places. Got places I need to be during the work day. But last week was such that I didn't have that. And I got back on my bike this year, after about a five year hiatus. I was I was big into bike racing. I was doing a ton of cycle cross racing. My son was racing for the truck Junior Devo team. Everything revolved around cycling. I ran into a woman I used to race with about a year ago, and she, if you're familiar with with five word stories, when a Hemingway's kind of little tools. And yeah, Melissa certainly is our producer. Love five word stories. And she told me this little five word story. And and I we used to race together, and I said, are you still racing? And because I had this kind of guilt that I had gotten away from it. And and her five word story was, No, we had our time. And so those five words, and I was like, wow, that she didn't say it was a five word story, but I'm like, that says everything in five words, right? That is a five year story. And it kind of put that whole thing into perspective to me. And then, of course, you know, the whole time to Ecclesiastes into it, everything, there is a season not to go too far down the spiritual rabbit hole, but it's a good segue into our next conversation, and that is, I found you going back in the book several times to the issues of questions of spirituality, the existence of God, and honestly, and maybe it's on purpose, it was a little bit like, Oh, this guy's, he's an atheist, oh, He's an agnostic. Okay, wait, maybe he's, you know, we're in So at any rate, without giving anything away that you don't want to, why are those types of questions so important to you, and why did you keep coming back to that question of the existence of God and of spirituality throughout the book?

Jordan Ellenberg: 1:03:55

Well, part of it, I'll give two answers, and I'll say a little bit about myself, like, Okay, so one answer is just that, as I said at the beginning, you know, math is a constant in every society like this, what it says to be some fundamental part of humanity that we think quantitatively, we reason mathematically and so and but thinking about who made the universe like what it's all for, that's also a constant in every society, right? So how can you write about something that's like, like, math, that's like, sort of so big and so omnipresent in our way of thinking? And how is it not gonna intersect with those questions, right? Because those are two big things that humans have always done and are always built to do. I find that there's also a lot of poetry in my books, which I'm very surprised by. But that's also sort of like, 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. So that's one reason, just because, you know, in olden times, there was not such a distinction between mathematics and philosophy and people like Blaise Pascal, I wrote a lot about. That book were, he did. They were very serious method editions and very serious philosophers, and very, in Pascal's case, like a true religious mystic, right? I mean, like a true devotee. So, so that's one reason, because I think,

Matt Kirchner: 1:05:14

if I'm not mistaken, yeah, exactly.

Jordan Ellenberg: 1:05:20

But it's funny, because I feel like people write me email, and they like and they and, you know, they write me email sort of doctor to find a point on it, but to correct my atheism, they like write to you, like, I just wanted to sort of rebut some of your atheistic argument. I'm not an atheist. I'm Jewish. I believe in God, like I'm a I'm not Orthodox, as you can see from the fact I'm not wearing a Yamaga. Like I'm not strict, but I would say I'm a religious person. And there's, there's lot. 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, I think that stuff is really valuable. Like, the next book after that shape is with, like, a wonderful Talmudic story, which I think is fantastic, which, which sort of speaks to somehow, to me, it sort of exactly goes with, like, what math is all about. Actually, can I tell the story? Because it's so good, because, I mean, I'm gonna abridge it, because the Talmud does like to go on and on, and I'm gonna give like, the story. Give like, the short version, but like, you know, basically, you know, a bunch of rabbis are arguing over whether a particular piece of pottery is like, clean or unclean. This is the kind of stuff the Talmud is full of. And they argue and they argue, and each one has, like, a reference for why they think their view is correct and but one guy is clearly winning. One guy is clearly getting the best of the argument based on the text of what's in the Torah. But his opponent is like, not happy about this. And he's like, you know, look like, let God come down and, like, tell us who's right, who's right about this. Like, is this thing clean or unclean? Yep. And then, like, there's this whole sequence of miracles. And like, the walls fall down, and the river flows in 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 amazing thing happens, which is that the first Rabbi does not give up. He says, But God, like, you know, didn't you say that the Torah is here on Earth? And, like, this is how we're supposed to decide these matters of law. He really just like talks back, right? Yeah. And then there's this amazing moment where I don't think this happens like anywhere else in the text, where it said, God laughs, God laughs. And he says, My children have defeated me. My children have defeated me. And then he like pieces out, and it's an amazing story about beautiful story, the responsibility that we're given as human beings to, like, with these incredible and I would say, I don't want to get too deep into it, but I mean, I guess I would say these, like, God given capacities that we have, like, that's a responsibility, but it's also our 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 of stuff on a podcast,

Matt Kirchner: 1:08:28

kind of topics,

Jordan Ellenberg: 1:08:32

but people, but people do write me and be like, you know, I'm here to correct your atheism. And I'm like, come on, what I write about in that book is like, I don't like it when people are like, I'm gonna prove that God exists with a statistical test. I'm like, come on. Like that is not respectful. Like that is like, you know, what I see, what I say in the book, is, like, you know, when God wants you to know he's there, like, he lights a bush on fire. He does not, like, hide it in, like, the fourth decimal place of a statistical test. Like, come on, that's so that's awesome. So sorry to get a little bit salty, but I feel like, no, for sure, things that are not true,

Matt Kirchner: 1:09:08

yeah, for sure. And that's probably the first rabbi. I won't call it a rabbi jokeness To show you Rabbi story that we've probably had on the podcast as well. So we're breaking all kinds of new ground, which I hope to do with the final two questions. In the interest of time, we've got our unfortunately for me, because I'm really enjoying this conversation time, bring our time to a close here with Jordan Ellenberg, but Jordan, I want to wrap two questions into one, and that is this, you know, the first one is, and I think we've learned a little bit about it already, but is there something that you believe about education that would surprise people? And then, you know, the second one is, if you could go back to, you know, your 14 year old days, and you know the Potomac area in Washington, DC, when you're a Washington, DC or 15 year old kid, what advice would you give that, that young man, I mean,

Jordan Ellenberg: 1:09:55

to the first thing, maybe I'll say something that I think would surprise my younger self, because I think that's a good Gage for. Like, what's surprising? I mean, I think I've come to understand over many years of teaching that here's a word I made up, that, like, schooliness is not the same thing as intelligence. And I think, like, you know, a sort of mental roadblock that a lot of us in education have to get over is that anybody who's a teacher or a professor is probably somebody who really liked school and function really well in the school environment, because otherwise, why the hell did I never leave? Right? Why am I 53, years old and have, like, never left a college campus? Because obviously, like, I really like this environment, and it really works for me, and it exactly suits my temperament. And I think it's easy to fall into a trap of thinking that schooliness is like what intelligence is, or like what learning is. And as I've gotten older, I just think you come to see that that's one model, and it does work for a lot of people. Like that's why it has persisted, like, not changed that much for like, 100 years in this country. I don't want it to. I think it's, I think University of Wisconsin, Madison is an incredible institution that serves 10s of 1000s of students incredibly well, but it also doesn't work for everyone, right? And I think I was gonna say that's a problem I don't know how to solve, but it's not even a problem, right? I mean, it's just as you say, just that, as you say, like people are different. And I just think it's useful for us to sort of think hard about what do we have to offer for people who truly want to learn, which I, as I said, I optimistically, think, is basically everyone, right? But for whom this particular structure does not work very well, and that can be like for all manner of, for all manner of reasons, right, like, I mean, but, um, but I think that's something, I think is like we can get better at, and broaden and certainly look like at Wisconsin. I mean, you probably know about the Wisconsin Idea, right? This is the animating principle of this institution, that the boundaries of the university are the boundaries of this state. I'm not saying we always fully live by it, but like a fundamental founding idea, which I've come to see, is not just a marketing slogan, but is really part of the DNA of this institution, is that we're not here just for the 18 to 21 year olds who are enrolled in our courses and are inside our walls. Right? Obviously, that's a big part of what we do. But in the end, the reason that we exist is to serve the intellectual needs of the entire state of Wisconsin, which includes, like, a lot of people who are never going to be enrolled in any institution of higher learning. But like, you know, we, in many ways, we are living up to that. I think it's always something that we can press on.

Matt Kirchner: 1:12:53

No question well, in history being the great indicator, obviously a phenomenal institution. I think, as you know, both of my both of my kids are badgers and as is our producer, Melissa Martin, by the way, is also a former cheerleader at the University of Wisconsin, Madison, that that could be a whole podcast in and of itself as well. But to the last question that we that we had for you, Jordan, go back to your your your sophomore year of high school. You have one opportunity to give that young man one piece of advice. What would that be.

Jordan Ellenberg: 1:13:22

I mean, I think I would just say, like, you know, trust your instincts about what you find interesting and what you want to do. I think like kids. And I think this is actually more true now than it was in 1986 we really kind of say to them, like, okay, figure out what you should do. Like, figure out what you're best at, and specialize and only do that. And I think sort of, I sort of accidentally didn't do that, but I for a long time, I felt a bit of bad conscience about like, Aren't I supposed to be focusing on math, because that's what I do. Like, that's my thing. And I think I would tell my 15 year old self, like, actually, the way you learn is by when you feel, when that weird feeling Kindles, of like I want to, I just feel moved to go and learn this or master that, or build that skill. You know, maybe that's your soul telling you something like, maybe actually listen to that and don't worry so much about whether it's productive or like is on the track. I'll close with a story, please. I remember I was talking to an undergrad at UW Madison who took my class. Great student. She had had one plan to study geosciences, but she was cooling on it, and she was like, No, I think I want to go another direction, but she had, but she had an arrangement she was going to go to Antarctica for a year, and like, work in this lab. And she's like, I'm really excited about it, but I also have sort of felt like this is not my future. And. Go in another career direction. So, like, I don't know if I can afford to, like, like, waste a year, even though I'm excited about it, I'm like, shouldn't I sort of get started on this new path? Because, like, I have, like, a plan, and I got to do what's towards the plan, and I just, like, in my best, you know, Dad voice, because now I'm old enough 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, the mom who could have gone to Antarctica, or do you want to be the mom who did go to Antarctica? Antarctica? Like, that's the question that's before you, right, because you're gonna end up in the same place. But like, which do you want to be?

Matt Kirchner: 1:15:40

I love that Absolutely. That's great advice. And I love the idea that you know, this whole idea of you know, not just following your interest, but if something you find interesting, something sparks your curiosity, sparks your imagination, that is your opportunity to learn. Chase that down. That's the advice that Jordan Ellenberg would give his 15 year old self. It's the advice that I took on my own when I chased down Jordan Ellenberg, when I reached out and said, Hey, read your book. Thought it was amazing. Have this podcast. Would you like to join me? So glad I did. Jordan, this was such a wonderful conversation. You're doing so many cool things and can't thank you enough for being with us.

Jordan Ellenberg: 1:16:12

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

Matt Kirchner: 1:16:15

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

Jordan Ellenberg: 1:16:26

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

Matt Kirchner: 1:16:38

Love it. Yep, absolutely. That's it's awesome advice as well. That's advice I would give to my 15 year old self, actually, is, is, in another couple years, this amazing album is gonna gonna come out, go and go and grab it, in that case, on vinyl or maybe on a CD. But at any rate, so glad that Jordan joined us. You'll check out all those resources. We'll have them linked up on the show notes. They are the best show notes in the business. So check those out. We'll put those up at TechEd 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 on social media. We are all over social. You'll find us on tick tock. You'll find us on YouTube. You can check us out on Facebook. We're on Instagram. We are on LinkedIn, wherever you go for your social media, you will find the TechEd podcast. When you do say hello, we'd love to hear from you and can't wait to see you all next week. I'm Matt Kirkner, thanks for joining us. That was really.