We're Talking About Math With Author Jordan Ellenberg (Don't Be Scared)

In this podcast, author Jordan Ellenberg shows us that the power of mathematical thinking can lead you to smarter, happier, and richer outcomes.

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This video was recorded on August 16, 2023

David Gardner: Most students in most modern day cultures have a requirement to learn two foreign languages. The first is a language spoken orally by people, a border, or ocean, or half a world away, call that a foreign tongue. The second is a language universally required of all students. This foreign language has its own grammar, highly logical at that, its own rules, and translations, and axioms, call that language math. In 2014, mathematician Jordan Ellenberg wrote a book, not for other mathematicians, but for all of us. For you and me. The numerate, the innumerate, the low GPA folk, the high GPA folk, the book lovers, the math-phobes, in how not to be wrong, the power of mathematical thinking. Ellenberg unlocks the doors of mathematical concepts and invites us all into a world where math is not just numbers and equations, but a way of thinking, a philosophy that underpins every aspect of our lives. This week on Rule Breaker Investing come with us then into the mysterious world of mathematics.

Maths, universal language underlies our daily decisions, our perceptions of the world, even our understanding of beauty and art. You can certainly try to ignore the math if you like, generally to your detriment, or you can lean in, switch on, you can stop saying, I'm bad at math and start to pay at least a little more attention. Our world increasingly relies on data and logic. This should not sound like a threat. After this week's conversation, I sure hope it won't. In any way, don't you. This week anyway, not want to be wrong. Only on Rule Breaker Investing.

Authors in August for a sixth consecutive year, continues. How many great authors are we getting to connect with once again? This year so far, Neil King, an American ramble kicking off this month. Sunny vendor back and selling without selling out last week and now this week, perhaps the boldest chiller promise of all, is this a promise? How not to be wrong? Mathematician, Jordan Ellenberg is in the house this week. Before we get started, let me mention again that next week author a more tolls makes a return visit to Rule Breaker Investing. This time we're talking through his latest novel, The Lincoln Highway. It's 576 pages of goodness to greatness. I gave you a head-start last week, Dear reader. August is maybe the best month to do lots of reading, or maybe you read it when it came out two years ago. Anyway, next week, we get to check back in with a more tolls. Man, August has become one of my favorite months. Jordan Ellenberg grew up in Potomac, Maryland. The child of two statisticians, child prodigy is not an overblown statement to describe his intellect as he competed in and won international math Olympiads and their ilk at precocious ages. As an adult, Jordan went into, yeah, math and teach us today. The university was constant at Madison where he focuses not just on his expertise, arithmetic, geometry, but writing. That's right, he's teaching writing this fall as well. In fact, speaking of writing, in 2014, as I mentioned at the top, Jordan wrote a best-seller entitled, How Not to Be Wrong: The Power of Mathematical Thinking. Finally, in 2023, I picked up a copy nine years later, Read it, loved it, and I'm happy and honored to have Jordan Ellenberg join us this week on Rule Breaker Investing. Jordan, let's start our conversation about math. Talking about a place where many first learn it schools. Do US schools teach math properly? If you could wave your magic wand, Bibbidi-Bobbidi-Boo, what would you change?

Jordan Ellenberg: Do I have to make that exact sound? [laughs] Well, we can discuss that. [laughs] This is a huge question. We really jumped right into the cold deep part of the water.

David Gardner: You bet, yeah.

Jordan Ellenberg: Here's one thing about me, I haven't teaching math a long time. Let me caveat everything I say with the fact that I teach college, I don't teach in K-12 schools. I have two kids who are going through that K-12 process. So I see schools as a parent, but not as a teacher. There's a lot I don't know about what it's like to have a room full of eighth-graders in front of you. Just want it seems a little terrifying to have 30. [laughs] But here's what I've learned. Have been teaching math for a couple of decades, and what I'd say I've learned is that there's no one right way to do it. I think I spent a lot of time at the beginning of my career being like, I'm going to figure out the exact right way to present this material so that everybody likes it and everybody gets it. The truth is, I think kids are pretty different from each other. I think there's no one approach is going to be right for everyone. I do think there's some wrong ways, by the way. But I think as a teacher over the years, I've learned to take a grab bag approach where I adopt a bunch of different styles and hopefully everybody in the class has those moments where they're like, oh, today Ellenberg nailed, I don't know what the hell he was doing the last three weeks when he was doing it some stupid way, but at least he finally said something, so I get it. But for some other students is going to be a different day. Student has more than one day that they liked. But you see the point that I think as a teacher, I've tried to learn not to be doctrinaire and not to be like, this is the right way to do it and just rather be like who's in front of me, what's working, look at their eyes while I'm talking, and is there something in there right now? If there's not, maybe I'm actually just going to stop this class in the middle and veer off course from what I was going to do. That said, that's not that useful. If you're interested in educational policy.

Yeah. If you want to know, what would I do if I could wave my magic one, I'm going to come back to that boop-oop-a-doop question. One thing I'd say, and I think everybody who teaches college would say that we see students, come in not fully having mastered algebraic skills. If you want to know what we see students lacking when they come into college. It's algebra, it's not calculus, it's not like multi-variable advanced calculus, it's algebra, very basic stuff. You can make it through the more advanced courses if you're algebra skills are weak, but make it through in a scrambling way, and at some point that runs out for kids who are going to consider going on in engineering or any technical subject like that. I think why do we have trouble teaching algebra and graduating student with algebraic skills? The reason is very simple. It's because algebra is actually quite hard. It's a massive conceptual leap over what we've done before in the classroom. Here's what I would say. I think we have a way of thinking about the way classes work in school where either you pass and you move on to the next course, or you flunk and you have to take it again. If you flunk, that's bad man. That's embarrassing, and people are like, "Oh, my god, that kid was held back." I don't know how to get here, but I would love a world in which it's normalized to take classes twice. I think we would be better off if more kids took algebra twice because that is like there are going to be some kids who can just like latch onto it the first time because of how it's taught, or a nice rapport between them and the teacher. But we're definitely passing lots of kids out of algebra who know it, but not really. Then that kneecaps you later.

David Gardner: At one point, page 104 to be precise and how not to be wrong, Jordan, you briefly used the phrase math train, as in there are two moments in the course of education where a lot of kids fall off the math train. You mentioned the first is fractions, but math is a train. People can fall off, is it? Because it seems like getting bad grades, snowballs because of the way math builds up from one lesson to the next. I get you on the idea of taking algebra twice. In fact, you mentioned that there are two moments in the course of education in your book where people fall off the train. The second is, of course, that dangerous twist and the track in your words, algebra.

Jordan Ellenberg: The other one is fractions. Besides algebra.

David Gardner: That's the first one, fractions are the first exactly.

Jordan Ellenberg: Fraction are the first and algebra is the second. Absolutely. It's funny because I think exactly what I'm saying is, man, it would be great if it were less like a train where man, if you need to get off the train to pee or something, if you're off you're off the train is gone. If you're behind it. I wish it could be less like that. It's funny that I use that metaphor and the book probably without even thinking about it, we all do sort of buying into this idea that's how it should be.

David Gardner: When you talk about algebra being hard to teach because it's hard, hard to learn because it's hard. One of the things we've learned from a Motley Fool standpoint, we often bemoan that financial literacy isn't better taught in schools. I see you nodding your head and we want our kids to leave school, not just learning algebra perhaps, but understanding compounding returns. They may know the math to do it, but they don't necessarily have the right language or concepts that they can pull in and make use of, in they're practical day-to-day life. What we've discovered as a consequence of looking harder at this is the number 1 reason we think that financial literacy is not more prevalent in our schools is because the teachers themselves don't feel literate or confident enough to teach it. Do you think that's also happening with algebra or not? By the way, we don't have to keep going down this way. We're not sitting in judgment of US math education, but I'm curious your viewpoint.

Jordan Ellenberg: Maybe if we pay teachers more, they would have more money to save and they would have more experience with investment that they could use to give hands-on advice for their students.

David Gardner: There you go.

Jordan Ellenberg: Let me meet your question with a question before we move on, do you think the basics of financial literacy are hard? In other words, do you think students graduate not getting it because it's conceptually difficult, which is what I would say about algebra or calculus or even fractions, or would you say we're just not bothering to teach it?

David Gardner: Love the question and I would say emphatically, the concepts are not difficult. At least if I can wrap my mind around them. I was really good in math up to about calculating the speed of change in curves and motion. I think I got algebra, but once we hit calculus, I was the AB track, not the BC, I'm a fast study calculating baseball on-base plus slugging percentages and Strat-O-Matic baseball and dice games and numbers and statistics I've always really loved. That's really all I think you need to know to understand most of finance.

Jordan Ellenberg: Can I say, we're going to come back to this finance algebra I have a metaphor to do. But before we do that, I just want to say, can you believe, because it sounds like you grew up as a baseball stats nerd like me, can you believe we live in a world where you go to the baseball game and on the giant scoreboard they're showing the OPS and the WHIP?

David Gardner: I cannot believe it.

Jordan Ellenberg: These things we thought were only for the nerds. These will never catch on with like general baseball fans, and now it's on the diamond vision. Incredible.

David Gardner: I totally have said the same to my baseball loving friends, my sabermetric friends, my Bill James back in the day, loving friends. I'm one of those people too. I can't believe it and I love it.

Jordan Ellenberg: I don't think Bill James ever thought he would become mainstream.

David Gardner: I agree.

Jordan Ellenberg: No way. He thought he was writing like weird nerdy books for nerds.

David Gardner: That's right. He was told that he never played the game and so what he said wasn't relevant to until I guess Billy Beane started listening in Oakland. Now everybody has all the numbers that they need. Maybe too many numbers in some cases, maybe we'll come back to that. But I'm glad I'm talking. Not surprised that I'm talking to a fellow baseball fan. I am a few years older than you. We've established this before we came on line together, but but not that many. Jordan, you and I both pretty much grew up in an era where the calculator was invented and made its way into schools a bit tamer than when smartphones showed up for our kids. But all of a sudden, there we were in the 1970s, many of us were faced with the question as to whether long division was necessary, and I'm glad I learned it. But now we have and you know this question has got to come at some point in this interview. Now we have AI, artificial intelligence already here, slash on its way. Jordan, are there aspects of math that you think truly no longer need to be learned as a consequence of an age where machines can do it bigger, faster, more accurately. By the way, it seems like they can code for us too.

Jordan Ellenberg: I use it for that. I know this very well. Boy, again, you're opening up like a big depot from which we can head off in a lot of different directions. But first of all, the intersection of AI with mathematics is a fascinating area and, we just don't know how it's going to look and it's a very exciting thing to think about. You know, most of my research life, I'm a number theorist, which means I work in the most classical precinct, the mathematics and think about thousand year-old questions. It's pretty exciting to spend some time thinking about questions that literally could not have been asked 12 months ago. That's pretty solid into my usual way of working in research.

David Gardner: It's incredible.

Jordan Ellenberg: If people are listening, I would definitely recommend we had a great workshop at the National Academy of Sciences about artificial intelligence to assist mathematical reasoning. We have a lot of research, mathematicians and industry people just talking about how are these developments going to change mathematical practice. I would definitely recommend checking out some of the talks there if you're interested in this. But in terms of education, in terms of what happens in the classroom, I tend to not be at catastrophist about this stuff. You'll definitely find people who disagree with me about this. But, for us in the math department, we're in a moment where my colleagues who write essay assignments, who teach in the English department or history or philosophy. There's a lot of freak out going on. Like what are we going to do? How are we going to assess our students when they can produce, I would not say good, but passable examples of English writing more or less on a given theme? [laughs] Like, what are we going to do in a world where students can press a button on a website and produce a not-great but adequate solution to a homework assignment. In the math room, we're just like, well, welcome to where we've lived for the last 15 years, because this is not new for us, what we teach in calculus or in high school math or whatever especially calculus, which is what I see in college. Absolutely 100%. Any student can go on innumerable websites and generate fully worked out solutions to just about question we ask on a homework in that class. In an instant. I hope if college students are listening to this, don't do that. If there's one college student who doesn't already know that fact? [laughs] I'm sorry, I spilled the beans. But I think they all do. We're already at that equilibrium, I think what we have found, maybe I'm going to throw my own son under the bus to say I slightly know this from watching him do his calculus.

I think there are some who just don't do their homework, who are really tricked out of the class. But by and large, I think the dominant way that kids use these devices is to try to do the problem and then check their work after the fact. Like they use it as an aid and as a boost, not as a thing to do their homework for them. My non-catastrophist view on this is that just as with calculators and just as with every single other cognitive tool we've developed from advances in computer science, it's going to be something we use to help us do our work, not something we use to do our work instead of us, most of the time and for most people. We'll see how it plays out, because we're at the very beginning. But certainly in terms of math. At this moment, we're not at a place where it looks like mathematical reasoning is going to be replaced. On the contrary, I think there's lots of exciting ways in which we can hope that mathematical reasoning is going to be boosted. Actually, your example of coding is a great example of that because I definitely use these tools routinely now because I'm just going to put this out there. I hope it doesn't diminish my status. I'm pretty crappy programmer, I can do it. I know python and I need to do it because I run experiments all the time for my research. My life as a Python code or is definitely, oh my God, what's the syntax for that? Oh my god, command for that, I don't remember. Is this a bracket or as a parentheses? You know what I mean? I don't do it every day and so I don't really have it in my fingers.

These tools are tremendously useful for that. I don't use it to write an entire program. For me, I'm like, OK, there's something and it's like three lines of Python, what, three lines of Python, and then I generate it and I paste it in. But I'm still in the driver's seat. I'm using it to eliminate the tedious part of the job, and that's what computational tools have always done. Detonize the more tedious part of the job. When I talk about this stuff with AI and math, there's a little chart I like to make where on every task we go from incompetent to mastery. There's those dots on it like incompetent, submediocre, mediocre, good, master. Then I draw a little line from submediocre to mediocre, that's where AI is. I think there's very few domains in which it actually is good at things. It doesn't produce a good essay. But if you were, let's say if English is your second language, it will definitely take an essay that's hard to read because there are certain idioms you don't know or certain pieces of syntax that you haven't mastered. I'm cleaning that up and bring it from submediocre to mediocre. Somehow if you're like an AI triumphalist, it's like that doesn't sound very exciting going from submediocre to mediocre. I would say the exact opposite because of all of us are submediocre at almost everything.

David Gardner: Well said.

Jordan Ellenberg: We're good at the things we're good at. But like taking people from submediocre to mediocre and lots of domains at the same time at scale, that is a massive boost.

David Gardner: It is incredible and I would also like just to add that so many times that boost takes less than a second. You hit the return key and bam. I mean, you've got a pretty good answer and it took no time at all, so the speed is crazy.

Jordan Ellenberg: I wanted to trademark the phrase artificial mediocrity. I think artificial mediocrity is worth trillions of dollars.

David Gardner: [laughs] Well, I'm fascinated by what you said about five minutes ago, which is that mathematicians are now able to articulate questions that they wouldn't have even known how to phrase or ask 12 months ago. My first thought is, is this the most fun time to be alive as a mathematician in human history? I would have to believe it is and you're getting to live that. But second, Jordan, I may regret asking you this, but could you give an example of a question that you're now able to ask that we couldn't have asked before? I realized it's going to be very high math and or so abstract that me and probably most of my listeners, although we're pretty on submediocre, some of us. Some of them will grasp it, but I would love to hear you articulate something like a question that you couldn't have asked a couple of years ago.

Jordan Ellenberg: Well, I'll answer both those questions. One, is it the most fun time to be a mathematician in human history or at least in my lifetime as a mathematician? I'm going to be honest with you, it's all fun. I mean, mathematics just constantly gets bigger, and faster, and better. Certainly my lifetime has been a pretty amazing time to be a mathematician and I don't see that changing. I think this is an interesting moment because exciting stuff that happens is a little more legible to people outside mathematics than these more technical developments that are pretty groundbreaking. If I say like, imagine being present in Paris in the '60s when Grothendieck was developing the theory of schemes, you'd just be like, "Okay, why should I care about that? I guess that was good begets or something." To me, I'm like, oh man, that would be like seeing the Beatles in the Cavern Club or something. But that's a little bit harder to sort of. You asked what kind of questions.

Actually, that is a pretty answerable question because the fundamental interesting scientific fact about the current wave of artificial intelligence, and I don't just mean like large language models. Those are very big right now. I mean, the whole world of deep learning, reinforcement learning, all these mechanisms. I'm just going to be honest with you, we don't really know why they work. In some sense, they work much better than they have any right to. That's like a vast theoretical question, and that question is a math question because it's mathematical algorithms that are driving all these things. We have no theoretical guarantees, by the way. There's not a single artificial intelligence algorithm that we can prove that it works, and there's hot debate over whether it's even possible or makes sense to talk about proving that an artificial intelligence algorithm works. But even questions like, can we give a definition of learning? Can we give a definition of what it means for the machine to be able to generalize from previous observations it's made? Basically it's an engineering achievement, which doesn't yet have a theory. Imagine, OK.

David Gardner: That is amazing work.

Jordan Ellenberg: I'm worried that anybody who knows anything about engineering or artificial intelligence is maybe going to start projectile vomiting right now, but let's try it. I mean, imagine if people figured out how to build a steam engine, but there was no physics, no theory of pressure. They were just like, wow, you light the coal on fire and it makes steam and for some reason this train just goes to London. We don't know why. It's kind of like that.

David Gardner: That is awesome. That's a great metaphor.

Jordan Ellenberg: If that were the case, it would be an exciting time to be a physicist. You'd be like we got to figure this out. What the hell is driving the train? All we did was set some coal on fire.

David Gardner: I had a conversation on this podcast in July with my friend, Mahan Tavakoli, who was rocking some of the work of AJ Agrawal in Canada and basically said that the real revolution here, I mean, there's a lot of them, and you're pointing out some of them are abstract and we're still trying to figure out what the revolution is. But at least one of the early conclusions that they have is that the cost of prediction of what will come next is being dramatically reduced in a way that is systemic for our society. Obviously, large language models are predicting what's going to come next, the one or the zero, the keys to the code, the keys to letters and numbers and thoughts. But that is predictive, but then it can lead to weather and, I don't know, markets and all kinds of possibilities, baseball.

Jordan Ellenberg: But here's the thing, David. This is a perfect example of I think on the one hand, that's true. On the other hand, as a theoretician, you come to this and they say, well, boy, prediction covers a lot of different things and there's a lot of different phenomena you might try to predict. For instance, I'll put my cards down. If you tell me, hey, is all this new stuff going to allow us to predict what the weather is going to be like three weeks from today instead of one week from today? I highly doubt it. [laughs] I think there's structural and physical reasons why that problem is not going to be touched by these habits. Is it going to be able to tell me what the stock market is going to be a month from now? I'm highly skeptical. I highly doubt it. Don't believe that's true. Now, the world may prove me wrong. What I'm saying is there's prediction and there's prediction. I think rather than asking, are these machines intelligent or can they predict, we should be asking, what can they predict and what can't they, what cognitive tasks can they do and what can't they, and there's going to be ample examples of both.

David Gardner: Well, it does seem as if large language models do a pretty good job at predicting what might come next that would be helpful or instructive to take enough of us from submediocre to mediocre. That seems like an amazing gain in just for a lot of us. I know the work's been happening for decades, but for a lot of us this popped up somewhere around last fall, even on the early side. Most Americans have not even tried ChatGPT yet, and that's America, let alone the rest of the world.

Jordan Ellenberg: Actually, I have no idea. Do we know what kind of penetration it's had?

David Gardner: Well, as of a couple of months ago, the figures that I was hearing quoted and I trumpeted them, so I'm assuming I hope I had it not totally wrong. 86% of us had not tried or signed on or try the large language model yet. I mean, it's amazing that one in seven of us actually have.

Jordan Ellenberg: It's still like OPS. It's still not like have been broken out into the mainstream.

David Gardner: Yeah, it is, on-base plus slugging. Occasionally on this podcast, Jordan, by the way, we're just having fun. Yes, this is a book interview, but really we're just all over the map and that is very Rule Breaker. That's what I do try to bring to listeners every week. Thank you so much for indulging us. Occasionally in interviews on this podcast, when I feel like I'm reading something fun or crazy on my guest's Wikipedia page, I'd like to conduct a Wikipedia fact check. Jordan, did you in fact teach yourself how to read at the age of two, watching Sesame Street. Assuming that's accurate, could you tell a little more of that story?

Jordan Ellenberg: That's a hard one to fact check because I obviously have no memory of being that young. That's what my parents say. They insist that they did not right that into Wikipedia, I did not know who did. 

David Gardner: [laughs] I do realize, as genius as you were at the age of two, you still don't have memories of that.

Jordan Ellenberg: No, I don't remember. I mean, I do. Look, this isn't always an interesting thing to talk about because there are a lot of different stories of working mathematicians, like a lot of ways into this profession. I think there's a stereotype that mathematics is something that gets done, that you're hit with the math stick at birth or shortly after and the kids who are maybe going to do math know that when they're a small children. Working in a math department and working around math positions all my life, I can tell you that that is anything but the case. I got a great student just last year, it was like an engineer and suddenly his senior year of college was like, "I just realized I really don't care about my engineering classes and only care about my math classes, and I think that's what I want to do." He certainly did not think of himself as like a math guy, thought of it as a tool to do what he was planning to do.

David Gardner: Great.

Jordan Ellenberg: I mean, and we have people who get great PhDs. Some of them were like, I can think of people who were video game designers, people who were high school teachers. People come to it all over. There is this stereotype that no, it's a thing that you're born into that you do for when you're a small child. That's all preface to saying that while that's the stereotype and it's not the universal story, it was my story. So that's why. I always have to preface it with that. For me, I was always very, very into math from the time I was a small child and I do remember that.

David Gardner: It seems like you entered a number of competitions. I don't know if you did it out of an internal motivation or you had amazing helicopter parents who were themselves statisticians and think, "We got to push this guy. He can win at all globally," which it seems that as if at different points in your youth, and no doubt as an adult as well, you are the opposite of sub-mediocre when we talk about competitions with other humans figuring out the answers.

Jordan Ellenberg: Well, again, first of all, I should say my parents were not like dance mom of math competitions, and I'm not even sure they're like is that concept [laughs] for as far as I know. Maybe more nowadays, but I don't think of it as an era. I think the kids who are like doing these competitions are pretty self-motivated.

David Gardner: Yeah.

Jordan Ellenberg: Now, I went through a long period of being ambivalent about that whole world of doing high school math competitions, which, again, if your listeners don't know about this, there's an entire circuit. Counties and school districts have leagues and there's national contests and this and that. Because in many ways, what you train yourself up to do to win those contests is very different from actual math. An actual research math, the stuff that I do for a living and I draw so much meaning from never once has anybody said you've got to do this problem in three hours. That doesn't exist in real math. My timescale is like, "This seems important, I'm really going to get to work on it and hope to do it in like three months," or maybe if it's hard, a year. You know what I mean? That's the timescale. These timed contests that rely more on cleverness than on depth. On the one hand, I'm like boy, that gives kids a false impression of what math actually is. On the other hand, as a grownup, I've come to see, you know what? Anything that brings kids into the subject is probably good. Remember how I said at the beginning kids are just different from each other, they have different needs. There are some kids who are going to get excited about being on the math team, and that's going to bring them into contact with really deep exciting ideas and they're going to get excited about. There's other kids who are going to see a movie like Hidden Figures or A Beautiful Mind. A Beautiful Mind is a terrible movie. Sorry, Academy Awards jury. I mean, it's an awful, awful movie. The book is great, by the way.

David Gardner: I haven't read the book, but why is the movie terrible? Just for the fun of it.

Jordan Ellenberg: Why did they choose to make a terrible movie or what's my take on what makes it terrible?

David Gardner: Why do you come down calling the best picture, I think, wasn't it?

Jordan Ellenberg: I think it did win the best picture.

David Gardner: Terrible, and I love that you do, by the way. As a contrarian, as a fellow Fool, I'm loving this. But what is terrible about A Beautiful Mind the movie?

Jordan Ellenberg: Let me think back because I saw it once, I rolled my eyes, and walked out and never really thought about it again.

David Gardner: But did you watch the whole thing or did you actually walk out?

Jordan Ellenberg: I watched the whole thing. I succumb to the sunk cost fallacy. Is that what economics call it? I paid my money for the ticket.

David Gardner: [laughs] You did. That is behavioral architecture.

Jordan Ellenberg: No, I think Russell Crowe is a great actor. I felt like I was a post-doc in Princeton. I mean, Nash was around. So I felt like OK, this guy has captured the mannerisms. He did a good job as an actor, but the movie was like fundamentally very corny and any mathematician, we just like, I don't know how to put it. I feel like the movie succumbed in the way that the book definitely did not to the idea that mathematical achievement and insanity are very close together. They are not in fact very close together; they are very far apart. Thinking about mathematics is a kind of extreme sanity.

David Gardner: It's funny because GK Chesterton said the same thing about poets. As a writer himself, he took umbrage, this notion that most of the poets are half mad and they're all about to die young and go crazy. Actually, in a fun essay, I don't know if you've come across this one, he said, "You know what's crazy, it's not the poets, it's the chess players because they think the world exists in an eight-by-eight grid and everything good, and they're the crazy ones." Anyway, I don't think necessarily any of these people are crazy. Generally, I admire poets and chess players, but it is funny hearing from somebody who is that steeped in mathematics and a love of math to hear you criticize it rightly, I hear you there. The idea that you just a half-step away from craziness because you have a beautiful mind.

Jordan Ellenberg: But the overall point I'm making is that even though I thought that movie sucked, the number of math majors at Princeton literally tripled in a year, the year it came out. At some point, you just got to except the trend factor and be like, hey, if it tells, look, I mean, I always say sometimes I'll go on TV or something, going to do an appearance and people are like, OK, that was very content-free. Like you were on for 30 seconds, what good does it do? I'm like most people literally don't know there's such a thing as a mathematician who was alive and is not like a dead individual in a robe from Greece or something like that. I think just the mere fact that that is a job you can have and that is a profession that you can do, broadcasting that at scale to me is a really important for bringing people in contact with what we do.

David Gardner: Great point. I can relate having done a lot of TV spots in my past and often with the jester cap on. Similarly, we would get like one line about how people sell stocks too frequently. They should just find great companies and hold them. Thirty seconds, we're done, morning TV, CNBC, whatever it is, and yet we had the full cap on and we're talking about things that everybody can be part of the stock market, be a part owner of Chipotle or Nike and get wealthy over time by being patient. Sure it was fluffy, it was 30 seconds, and yet yeah.

Jordan Ellenberg: One thing I've had to, and I talk to people about this a lot in my profession, about doing math for the public and publicizing math, is that I'll write something and somebody will say like, "But you know that article is written before or even you've written that article before." It's like yeah, but not everybody read it the first time I wrote it and I'm going to say the same thing again and still nobody's going to hear it. Silly is saying, why should I teach calculus this year? I taught it last year. Yeah, they're different people. [laughs] Why we spent thousands of years building up an apparatus of math or, for that matter, a financial literacy? People don't know it until you tell them and you got to say the same thing again and again. You hype your true things that you know and they are worth repeating.

David Gardner: Jordan, your book is peppered with great lines and concepts that can and should be of interest. To general readers, that's what we're talking about, general listeners, this is an investing and business podcast and we're talking some about math. But in a way that, as you write, that doesn't seem to many of us anyway math-y. Here's an example. I'm going to quote you, but I would just enjoy hearing you riff a bit more on this outside of just this line from your book, and I quote, "A basic rule of mathematical life, if the universe hands you a hard problem, try to solve an easier one instead and hope the simple version is close enough to their original problem that the universe doesn't object."

Jordan Ellenberg: Absolutely, and that is something that I've learned the hard way over my career as mathematician. The most problems, the actual problem you're trying to solve is quite hard, and I would say that certainly applies when thinking about the economy. I mean, good lord. Nobody can think about finance or the economy without oversimplifying.

David Gardner: We need fractals. Microeconomics exist underneath macroeconomics

Jordan Ellenberg: Right. But the point is if every time you tried to think about something macroeconomical, and please stop me if I use these words incorrectly because I'm over the skis here.

David Gardner: You're killing it.

Jordan Ellenberg: If every single time you try to think about macroeconomically, you're like, "But I don't know what each individual is doing, I don't have a model for their behavior," you would just descend into a slough of despond and just be like, "Well, I'm just in a absolute paralysis of knowledgelessness and I can't do anything about anything," and like, well, that's no good. That's not useful. You have to simplify, but then you also have to calibrate. You have to simplify, be like, well, let me solve this easier problem. Let me try to analyze this system that's much simpler than the real thing, and then go back and look at the predictions I made and see, do they match up with what's actually going on? Or if not, then you're like, "I simplified too much. I assume the spherical cow," as they like to say in a physics literature. [laughs] You guys use that phrase in economics?

David Gardner: No, I haven't. Explain.

Jordan Ellenberg: It's the story where they ask someone in the agriculture department, like asks a physicists to make a model for some kind of beef production, this many inputs, this many outputs, and the first line is assume a spherical cow. [laughs] But that might be OK, actually. There's certain kinds of questions about cows you might ask in which, as funny as that is, a perfectly reasonable way to start. By the way, I'm going to break in and say, you apologize a bit for not sticking to the book and that we're just going off in random directions, but roofing and going off in random directions, I'm going to be honest with you is actually how I write books. I would say, [laughs] if you like this stuff, even though we're not really covering the material in the book. I mean, you've read the book, David, would you agree this is basically the experience that I'm trying to reproduce on the page when I write.

David Gardner: I absolutely would. I know we're going to talk, I'm curious we are going a little later your writing process and how you right, I've got a fun question or two around that. I'm always interested in people's art.

Jordan Ellenberg: By the way, I interrupt you, I'm going to be teaching this, this fall. I've never done it before. So I'm super interested in talking about this because I have to figure out, I can only figured out what I think about something by talking about it and writing about it. I actually need over this month because I'm teaching in September to be better, articulating what I think about how to write about quantitative topics. I'm allegedly explaining the 18 year-old how do it.

David Gardner: How do we know what we think until we've actually written it down to understand through our hands and our minds and our keyboards, what we actually do think, I totally can relate to that. We do need to talk some about investing and we are going to go back to the book once again, because of prominent story you tell among many and how not to be wrong is that of the Baltimore stockbroker. Would you tell that again here?

Jordan Ellenberg: Sure. I mean, this is a story I actually really tried hard to figure out its origin and I've never fully succeeded.

David Gardner: It's iconic.

Jordan Ellenberg: Yeah. I mean, actually you may know more than me about even earlier precursors than I was able to find. I don't even know why I think of it as a story about Baltimore that was lodged in my mind somewhere and that's where I always thought of it and I was unable to find the reference for that. But the story is this, that you receive a mysterious stock tip in the mail from somebody in Baltimore. You don't know this person, you don't know why they send it to you. They're like, hey, this so-and-so stock, watch it. It's going to go up a lot over the next week and you think, OK, so a crazy person wrote me a letter, but then you do take the time to look a week later and you see that that tip was correct. The next week you get another letter, another tip. Now you're intrigued and so you wait and you look, once again, the Baltimore stockbroker nails the motion of the stock. Then an amazing thing happens, which is that every week, for 10 weeks, you get an anonymous tip in the mail. Every week the tip is correct. Then of course this ends with the person saying like, if you're interested, I'll manage your money, for a modest percentage, I'll be your guy. Of course at this point you're totally sold. Well, what's the punch-line of the story? The punch-line of the story is that the Baltimore stockbroker, that first week, he didn't just write you a letter. He wrote 1,000 people a letter. More precisely he wrote 1024 people, the real heads out in the audience now know how this is going to go just from what number he chose. Let's say 1,000, and of those 1,000 letters, actually, 500 of them were like the one you got, and 500 of them were about the same stock, but they made the exact opposite prediction. Those people didn't get a second letter. They were just people who got a weird letter from Baltimore that proposed the stock tip. They didn't pan out and they never heard from the person again. Now you can see how this is going to go. Like each week, half as many people get a letter because half as many people have gotten a string of correct productions. In the end, it's just you, the luckiest, or by some measure, the unluckiest, you frozen that'd be original thousands. You're a fish. You are on the line now. The reason I tell that story is because, to illustrate this basic statistical principle, which is that when we think of statistical inferences, this process we do where we make observations and then we say, what can we conclude based on what we observe. The sad and difficult fact about statistics is that that is not enough. You have to have some model for what you might have observed, but did not. Without that, you can't really do inference. When you're getting those letters, you have to know in order to know what to take from them. Who else is getting letters and what did they say? Like, what letters did you not get? Then of course you may say, but in real life, you can't know that. Yeah, well, life's tough. Well, it's up and down. We're often subject to an observational environment where we truly don't have what we need to make principled inferences or even principled guesses.

David Gardner: There are all kinds of biases in our psychology that cause us to, with recency, favors certain things or look for a certain color. All of a sudden because we decided it was read, we see red everywhere. Just because we were just looking for that thing. John Allen Paulos, who is a professor of math. I don't know if you've met him.

Jordan Ellenberg: I have.

David Gardner: But he simply distinguished himself a generation ago.

Jordan Ellenberg: He created a whole market category that I live in.

David Gardner: Writing books like A Mathematician Reads the Newspaper, and I know this is the same tradition that you are riding thin to get.

Jordan Ellenberg: What a title. One of the great titles.

David Gardner: So you're a fan?

Jordan Ellenberg: I'm a fan.

David Gardner: I really appreciate your work and his work and I can only imagine what it must be like, Jordan, for you to read the newspaper, the news, and some of the headlines, of course, are there to get clicks. But often we're reading about studies. I have to put my cards at the table here, I majored in English literature, but at least from my standpoint, they're not necessarily quoting the study or it's not clear what the premises of the studies are. Then even the numbers that they're pulling from the study seem very selective and questionable. Do you read the news?

Jordan Ellenberg: Yeah. I mean, I guess I read it filtered through Twitter like everybody else. No, actually, that's not true. I'm going to stand up myself. I get a paper, New York Times every day and a paper Wisconsin State journal on Sundays. Yes, I look at Twitter like everybody else, but I do actually have a soft spot with this mode of information transmission. I think it's important to have stuff put in front of your face that is not either what you chose to look at or what an algorithm based on what you did choose, decided you should look at, like the physical paper, newspaper. I'm just going to stick up for it. It just looks like lots of random stuff in it that you otherwise would not see and I take some value in that.

David Gardner: Wonderful, I'm glad to hear that and I just imagine you read it and see it differently and it's getting me now into a little bit more of your process of writing, which I wanted to talk some about Jordan. You've written a novel and number of essays. I'm curious about your approach to writing. We talked movies earlier. Let's go back to another old favorite. There's a great moment in the movie Terminator, where for the first time we see things from Arnold Schwarzenegger's characters point of view, the Terminator robot point of view. I'm pretty sure it comes before that iconic line. I'll be back. Anyway briefly, the audience gets in Arnold's head looking outward. It turns out the whole interface is like numbers. I haven't seen the movie in awhile. They're probably all ones and zeros, but it's just like numbers everywhere dominating his interface. I'm curious, Jordan Ellenberg, when you pick up a pen to write or maybe just ready your keyboard to type. How you might be writing differently from Wadsworth say or Flannery O'Connor. I mean, are you typing letters, words, or was it all just numbers?

Jordan Ellenberg: I'm a little scared now that we've been talking for 45 minutes and still your mental model of me is as the Terminator like.

David Gardner: [laughs] I'm trying to get into your head.

Jordan Ellenberg: Put him on screen here and there was like a little in my eyes, there was like a little red box over your head and was like mathematical illiterate, identified. [laughs] Probability of comprehension, 3%. Like no, come on. That's not how our minds work.

David Gardner: I think the amount of times that I'm laughing show how much fun I'm having. John Malkovich has made an entire industry about being in his head, but I'm actually more interested in yours.

Jordan Ellenberg: Okay. But to answer your questions seriously. As I said, I was interested in math more as a little kid, but I was also interested in writing. I took a ton of creative writing classes when I was in college and then even after college, before I went and got my doctorate in math, I went, and did the creative writing degree, wrote a novel which I later published, so you alluded to before and I would say, what I learned, doing that has been phenomenally valuable to me as a popular science writer and as a writer about math. I feel like, look, I know Flannery O'Connor, but definitely what I learned from reading Flannery O'Connor about how to put together sentences and how to put together a story, that is what we're doing when you were writing Popular Science, we're telling stories and just like Flannery O'Connor, we're telling stories about people. Because every single thing in mathematics was created by human beings to serve human purposes. And I find those story is super interesting. But who's trained to tell stories about people and their desires and their motivations and the crazy stuff they went through? We don't learn that in grad school math. It's like when you learn to ride fiction, that you'll learn how to tell those stories. I use those skills all the time and I feel like what I'm doing as a writer is much more like what I was doing when I was trying to be a novelist than it is what I'm trying to do when I'm working on math. Reserved for just a very different thing.

David Gardner: Is it hard for someone so ingenious mathematically to have written how not to be wrong? Why not have a journalist cranking out dummies book, somebody who does that for living talk about the power of mathematical thinking? Did you ever feel like, why am I writing this for these people?

Jordan Ellenberg: No, because, I'm not even sure I can identify with why you would ask that question. The phrase I like to use is outward-facing science. I feel like science in general is very inward facing. We talk to each other. But I can tell you that there is a hunger among working scientists to be able to tell our own stories. I think actually you really need both, so you absolutely need journalists who are not embedded in our profession, whether that's math or computer science AI or physics or engineering or biology or anything else. You need journalists who can look at things objectively and talk about things as an outsider. But you also need that view from the inside. To keep the baseball thing going, you need sports writers, but you also need Jim Bouton, right?

David Gardner: Love it.

Jordan Ellenberg: Who writes Ball Four. You got to have both of those perspectives. I'm not a journalist. I'm not writing objectively. I get excited about stuff and I want to tell you how I see it.

David Gardner: You've done that so evidently this week and I really appreciate that about you. I really didn't mean in any way I love the way you phrased it. I don't even know where that question would be [laughs] coming from you said. I think it's because before I got to know you during this hour, I was just imagining what it must be like. Without overplaying the terminator hand, I was just thinking, why would Jordan spend as somebody who is comfortable in the highest levels of math and abstraction and the pioneering spirit of where we are in asking questions we couldn't have articulated before. Why would you write something to popularize it? But you've already made it so evident in this hour. You love getting people turned on to this stuff.

Jordan Ellenberg: But you know what, almost all of us who are researched my positions the way the profession is set up in this country, almost all of us are professors, we're teachers. So you've got to remember, I'm in front of 18, 19, 20-year-olds, all the time talking about this stuff and trying to convey my excitement about this stuff. There's some bumps in my profession who are not that into that but a lot of us really like it.

David Gardner: Those are professors we love.

Jordan Ellenberg: There's something soul enriching about being around young people all the time who are sponges for knowledge and are just excited about stuff. I see the books is actually very close to my teaching and spirit, it's continuous. But I get to do it for many more people at a time with a book than I can in a classroom.

David Gardner: Absolutely. I invite you on an investing podcast and here we are talking about. I have not read Shape. That is your 2021 book. Can you give fans of your first book, aka me, who finally in 2023, got around to reading the book you'd written nine years ago. Can you give fans of your first book who haven't yet read your second, maybe a little more context and enticement as to why to pick up your 2021 release and give the full title here, Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else.

Jordan Ellenberg: I wanted to make sure all my bases were covered so nobody complained or something was in the book that wasn't advertised in the cover. Well, you know what? Rather than try to give a whole praisy for the book, let me talk about the investment angle in that book, since that's exactly for your audience. Because one thing I talk about is the fascinating realm of mysticism around a number called the golden ratio. It's funny that some particular number between one and two would have a whole mystic culture around it. I write about the Da Vinci Code and I write about a movie called Pi that I love and have complicated feelings about. But another thing I write about is there's a whole world of investing. I'm watching your eyes very carefully as I say this because I don't know your stance on this. But there are people who believe in this theory of longer and longer waves, who's ratios are in this so-called golden ratio to each other.

David Gardner: I think it might be the Elliott wave theory.

Jordan Ellenberg: I learned a lot about Elliott himself, but it's a crazy stories. I was like, who the hell is this guy? I wrote a lot about him, how he got into this theory and the fact that you can still get golden ratio lines on your Bloomberg terminal if you want to. But actually, you tell me how many people in 2023 years still into this?

David Gardner: I don't think that many and since you're saying you're watching my eyes, I'm going to do my eyes for you. This doesn't work on the audio, but certainly you and I are seeing each other and video and [laughs] you saw a cross eyes because I do not really follow the Elliott wave.

Jordan Ellenberg: I wish we could all have seen this eyes.

David Gardner: I think it's crazy stuff, but in the end it's too abstractly divorced from what really is happening, which is that businesses are being created to solve problems or create new possibilities and then we buy them and over the course of time, the overall market rises and falls and I realize maybe it's all dancing to the tune of unseen violin somewhere. But I don't really care very much about that. Not only that, but I would say most of all Jordan, strategies like that are often promising on jumping in and out of the market. At least for me, what I've lived, not just preached now in my late 50s, it's going to work, I hope for the rest of my life is just buy and keep holding and keep adding and keep holding and don't try to guess where the market's headed or think that large language models will predict the weather three weeks from now or the markets themselves. Anyway, that that's my stance.

Jordan Ellenberg: That's certainly what I do as an individual with my own savings and that seems to me the principal thing to do.

David Gardner: I want to say I'm always open-minded though, and that's really how not to be wrong. That's one of the cardinal, maybe the cardinal lesson of your book. It's, humility. The way not to be wrong is not to be arrogant or think that you're right, or you found this crazy thing that nobody else understands. It's actually just to, sit there and wonder and try to answer and show intellectual curiosity and ultimately listen and learn and test and all the things that lead to much better baseball.

Jordan Ellenberg: Absolutely. I think in the end, the title is a little bit cheeky. Because in the end, where do I wind up? The last chapter is called how to be right? As you can imagine and there I put my cards that and I'm like, come on, you got to have this humility. There isn't a recipe for being right every other time. Holding in mind always the idea that you could be wrong is part of strong thinking. By the way, there are totally people who give my book of bad review on Amazon because they're like, well, it said it was called [inaudible] [laughs] and there was this philosophy at the end and I was expecting an instruction manual. I was expecting to come away from this book always being right. I'm like, come on, for $28 really, [laughs] that's what you expected?

David Gardner: Well said, but then you followed up with Shape where you're talking about everything else. Actually, it almost reads like a Douglas Adams title. I assume you were a Douglas Adams fan at some point.

Jordan Ellenberg: You know, you're right. It's funny, I haven't thought about life, the universe, and I must have been subconsciously. You're the first person to bring that up. [laughs] Life, the Universe and Everything. That's the book, that's the Douglas Adams book I must have been subconsciously.

David Gardner: You might have been, and or that might still be ahead. After those two titles, I don't know what you could possibly do next, although there are other universes perhaps, besides this one.

Jordan Ellenberg: What do you think I should write a book about?

David Gardner: That's a great question. I would need to read Shape, which I have not yet, but I certainly am here promoting to Rule Breaker fans and fellow Fools everywhere, and listeners to start with Jordan's first book. If you haven't read that, you're going to love it. I don't care whether you think you like math or not, we all can think better, which is ultimately, and more humbly, which is ultimately the big lesson of a math-y supposed book. But then Shape, I don't know well enough yet, although I have read some about the golden ratio.

Jordan Ellenberg: There's a lot of random walks in it, including down Wall Street. [laughs] That's only one of the random walks I had. There's going to be a lot of that.

David Gardner: Well, we're getting near the end, Jordan, this has been so much fun. We're going to play buy, sell, or hold in just a minute or two. But before going there, there's a sad though prevalent tendency in our culture, I think, to paint the math talented into a corner. I hope I haven't done that during this interview. Maybe I did subconsciously, but paint the math talented into a corner and assume on the one hand they can run rings around us in so many contexts, but on the other, they're nerds who clearly don't have any interests outside higher math. Jordan, thoughts about this, and by the way, how do you spend time outside your professional work?

Jordan Ellenberg: I've got to give a corny answer to this question, which is that I am a dad of two adolescent kids, and so I do feel almost all of my time is hanging out with them and doing the stuff they like to do.

David Gardner: What a great dad.

Jordan Ellenberg: I'm a baseball fan. In particular, I'm a Baltimore Orioles fan, which for many years has not been a way to have fun.

David Gardner: Best record in the American League as we speak.

Jordan Ellenberg: But this year is extremely fun and my kids like baseball, too, so we'd go to games a lot. The thing about math as a profession is, I always wonder, you read these people arguing you people work too much or they work too many hours. People who do math, we do math because we really like math. I think about math all the time. I think about math when I'm lying in bed, and can't sleep or whatever, is that work? Should I count that as my work hours? I don't know. That's just what I like to think about. I went with my son to see Six. Do you know that musical?

David Gardner: I think I do, but just give the two-sentencer on it.

Jordan Ellenberg: All needless to say.

David Gardner: No spoilers.

Jordan Ellenberg: I do stuff with the kids, that's fun, hanging out with my kids. This musical was not my cup of tea, so I thought about math. I listened to the songs, thought about math. It was good. [laughs] Was I at work or was I doing something with my kids? It's an interesting work-life balance question.

David Gardner: Good example. Do you paint?

Jordan Ellenberg: No, I don't. I think not.

David Gardner: Play an instrument?

Jordan Ellenberg: No, it's funny. I think whatever artistic ambitions I have are solely directed to words on the page. I like to try to make a snappy tweet, too. So any kind of words in any kind of page. I think there's a lot of mathematicians actually were super into classical music and I don't know how to listen to that kind of music. I haven't quite learned to understand it.

David Gardner: I like that you like baseball. All I really care about is that you're a fantastic writer. I think it's wonderful to hear that you're teaching writing for the first time at Wisconsin this fall, I think that's so cool.

Jordan Ellenberg: It's going to be fun. I'm a little scared about it because it's a lot easier to teach the things that you have been teaching for years and know how to do, but we'll see how it goes.

David Gardner: Let's play buy, sell or hold. These are not stocks. These are things that if they were stocks, Jordan Ellenberg, would you be buying, selling, or holding and maybe a thought or two as to why. You're ready?

Jordan Ellenberg: Yes, I think.

David Gardner: First up, chess. Yeah. The board game, the classic game, the staying power of chess, going forward, if it were a stock, are you buying, selling, or holding?

Jordan Ellenberg: I personally hate chess.

David Gardner: I do, too.

Jordan Ellenberg: I'm going to say hold. [laughs] I'm going to say hold because I think people thought there was going to be a massive disruption once computers got better at it than people. I don't think people are like that. I think people still like playing chess anyway. It's just chugging along as it goes. A lot of young people, you guys should read Jennifer Shahade's book about what's going on in chess, it was super good. Even though for me, every time I play chess, I'm like, if I'm going to be thinking this way and this hard, I could be doing math right now instead of this. Why am I doing this instead? This is stupid. But that's just me not appreciating it, so hold.

David Gardner: Before we get to the next one, I love games. I obviously I'm talking to a fellow sports fan and, by the way, we're both DC area guys.

Jordan Ellenberg: I didn't know that. Wait, are you Orioles, too?

David Gardner: I'm not actually because before the Minnesota Twins were the Minnesota Twins, they were the Washington Senators, and our family had some affiliation there and I was simply raised as a Twins fan of all things. So I was a bat boy back in the day.

Jordan Ellenberg: Otherwise known as the 2023 ALCS possibly. [laughs]

David Gardner: Yeah, the Twins have this magical ability to be five games ahead and they would be in last in the AL East. It's really a neat trick if others could figure out that technology. But sticking with games just for a second, do you play games? Do you enjoy board games, card games? Are you a gamer?

Jordan Ellenberg: I would not say I'm a gamer. I don't play a lot. It's one of those things I have to remind myself exist. But there's certain games where every time I play them, I'm like, this is cool, I should do this more. I would say that about, oh my god, I'm losing my mind, what do they call it? Sinking island or something like this? It's in my house, I should be able to see it from where I'm sitting.

David Gardner: I know which game you mean. It's a 40-year classic that's been put out in new edition.

Jordan Ellenberg: Wingspan is another one. You admire the design. You're like, wow, this is a really elegantly put together thing, I should do it more, and then I never actually do. [laughs]

David Gardner: Wingspan is a fine game. Next one on the list, buy, sell, or hold, self-driving cars. Will this actually happen in the next 20 years? Buy, sell, or hold? Of course, I mean at scale, I realize it's already been out there, Waymo, for some time driving. You always here they've logged millions of miles in Silicon Valley, but I'm talking about for the rest of us.

Jordan Ellenberg: Depending on what you mean, I'm going to say buy because I literally did buy a new car which has a lot of self-driving features, a Ford Mustang Mach-E, if you need to know.

David Gardner: Very cool.

Jordan Ellenberg: Which supplements my existing car, which is a 2001 Subaru Forester. I have leaped many generations of automotive technology. The new car does not have a tape deck like my old car. I'm wrestling with that. I'm going to say buy I for the following, but maybe not in the way that you think. Because I think what you see is that people are developing lots of really great features which are not full autonomy. It's not the car just goes from your house to come pick you up entirely by itself, but which, like we were saying about AI generally, really do a lot to help the human operator. A super-hyped merchant might say, well, your car is not self-driving at all because you're still sitting there with your hands on the wheel, and I would say, no, the car's self-driving a lot. It's keeping me from side swiping someone, not that I do that a lot. I would say that assistive technology is clearly the coming thing. To me, it seems obviously it's going to be in new cars that people buy and it's just going to get better and keep helping people. I'm going to buy, if that's what we mean, which is different from Waymo, I know.

David Gardner: Sure. That's what we mean. That was good. Let's go to the next one. Buy, sell, or hold university lecture halls. The traditional picture that we all have in our minds, still being people 20 years from today.

Jordan Ellenberg: Hold. Somewhat controversial stance. But I'm going to say hold. I understand all the reasons people say this is an outmoded method of knowledge transmission that cannot possibly survive in the Internet world. But I've also been teaching in college long enough to know that that has been being said for one reason or another since the day I walked out of grad school with my PhD, and somehow it has not happened yet, so it might. But I feel everything that was supposed to replace university lecturing has failed to replace university lecturing, has in many ways supplemented it. I think we might have killed the textbook by the way, that might go. But I would say this. This again, maybe it's going to sound corny. But I think there is something irreplaceable about this fact of a bunch of people coming together in the same place, at the same time and joining their attention on one thing that creates attention that is hard to get. When you're watching something at home on your own time, when you choose to do it, maybe you stop it because you feel a snack and come back to it later. It is not the same. I think people who make movies would say the same thing about the movie theater, that they don't feel people are not doing the same thing when they're watching the movie on their phone while also texting, as they do when they are with a group of people in the theater. I would also say everything we've talked about is secretly about baseball. You can watch baseball on your TV at home, but you would agree that being at the stadium is actually a different thing. It is not the same thing. If you say, oh yeah, I saw that game, you don't mean you saw it on TV. You mean you were there with tens of thousands of other people supporting your team, exerting a communal attention that you could only get in that environment. I guess that seems like a grand way to describe what happens in a 500-person calculus lecture hall at 8:00 in the morning when people are in their pajamas, I'll admit. But I do think there's something of that there. I'm going to hold.

David Gardner: Well, it is. I'm glad you confronted it. I mean, it's a fun question to ask. Commercial real estate has some dogs in this fight. There are lots of aspects of our society that are paused and waiting and trying to figure out what the future feels like. Thank you for that. Two more for you. We've done some sports. Let's do it one more time. Let's jump sports though. If it were a stock over the next 25-years, buy sell or hold, NFL football.

Jordan Ellenberg: I'm going to say sell. Partly because I haven't said sell for anything yet and I feel I'm coming off as something of a Pollyanna who just likes everything. [laughs] I'm not sure that's right because football is really popular and I watch it, too. I like it. I get the joy of it, but people thought there would always be boxing. Yes, there still is boxing, but if you look back at what place boxing held in like the American Soul in the 1950s or even when I was a kid in the 80s, it's a shell of what it was. How much people care, is a shell of what it was and partly it's because people really did start to understand better what it was doing to people and they just were like there's other stuff we could be watching. I think bullfighting, it's the same. Maybe not with people, but it's something that was a huge part of Spanish culture and now it's much less because people have just started to be like, can we watch soccer instead? [laughs] You know what I mean? Do we need to be doing this. I think people are more and more uncomfortable with what football does to the people who take part in it and provide our entertainment. I don't think it's as popular with parents and for their kids to play it as it once was. If we were really doing so, I really think the NFL is going to evaporate the way boxing has. I guess I don't really think that's better than 50, 50, but it definitely could happen, probably more likely than people.

David Gardner: Do you go to UW football games?

Jordan Ellenberg: I do sometimes go. The last one I went to, we got stomped so bad that our coach was literally fired. I think within a half an hour after the end of the game, I couldn't believe what I was seeing. But we have a great team where I'd say it's a couple of things. One, if you're investing in future football math, definitely read John Ursula's book, he's incredible. I don't know if you know this guy, but he's the guy who was player for the Ravens, who dropped out of the NFL to go get his PhD in math. He writes unsparingly about how the people who play football are seen. We'll I have the multi-billion dollar corporations that employ them and if you read that, you'll be like, he loves football by the way. He loves football, but you really see a clear picture. One of the questions I write about in Shape is this wonderful geometric conundrum of how many holes are there in a straw. I love it. Think about this at home. I just saw actually the Wisconsin football Twitter feed just like posted a video of our players all wrestling with this question. I thought it was so great. I'm like it's so awesome and it's so in the spirit of the student athlete, which I like to think that it Wisconsin we hold to a lot better than certain other schools and certain other conferences that can name SEC. What they're putting on the Twitter feed is a video of our players like thinking about math, which is great.

David Gardner: You are loving that.

Jordan Ellenberg: Definitely watch that. It's cool.

David Gardner: Thank you for the John Herschel reference that sounds very cool. Last one for you, Jordan. If it were a stock, ChatGPT going the way of the Facebook, i.e., being the dominant winner years from now, versus the Myspace wrath. So ChatGPT, its survivability, its winning characteristics, buy, sell, or hold?

Jordan Ellenberg: So again, I'm going to choose to interpret it my way. I'm going to say buy if we mean large language models generally. If you mean the company OpenAI, that makes ChatGPT, then I have no idea because I'm not an expert in this, but my sense of it is this is not that hard to do once you know that it works. Everybody is going to build large language models. And I don't think there's going to be a massive first-mover advantage held by OpenAI. I think this is not tech that you can really hide how to do it. I could be wrong about this, but that's my impression that there's going to be like lots of other products that are as good and they're already being built. But I do think it works. It solves a certain problem that hasn't been solvable before. So I think it's here to stay and so I think the general LLM concept is a buy.

David Gardner: It's a perfect ending really for our time together Jordan, when the author of the book, How Not to Be Wrong, closes with the final line. I could be wrong about this. You said that. [laughs] That really is a perfect demonstration of your work not to be reductionistic or try to be too glib here at the end. But I really appreciate the work that you do. What happens in your head, which I couldn't really begin to understand, but what happens on paper or on the web I can, and you're a wonderful communicator and an advocate for understanding the world around us and we need more of that and I'm so glad that you've joined us this week on Rule Breaker Investing.

Jordan Ellenberg: Thanks for having me on this is extremely fun.

David Gardner: Well, for this Authors in August episode, I feel like I lost the author part at different points. I mean, we did start with and returned to Jordan's book at different points, but this was in off the rails hour together and what I hope proved enjoyable. Next week, just to reminder, novelist Immortals in his recent mega hit, The Lincoln Highway. I'll probably keep my nose a bit more consistently in the book next week. But a word or two before you go. What are my recurring themes on this podcast I'm put in mind of. Once again, it's my sermon at that starts, do you have a blank friend? As in, do you have a white friend? Do you have a black friend? Do you have an Indian friend? Do you have a gay friend? Do you have a republican friend? Do you have a democrat friend? Do you have a fill-in-the-blank friend? In a lot of ways. This goes back to Mr. Rogers, himself, a friend of the Fool. We've played that interview back a few times with me and my brother Tom and Fred Rogers. Mr. Rogers wasn't at all the only one, but prominently, he did remind the world consistently to make friends, not to judge too much or too harshly. I know for me that my life is enriched by making more and more friends and more indifferent, that's the key, different friends. People who live differently from me believe different things, do things I would never do. Sometimes really amazing things like winning gold medals in International Mathematical Olympiad. We are enriched by every new and different friend we make. I feel like today here at the end of this week's podcast, you and I can now say in answer to the question, do you have a math friend? Yes, we do. Thanks for listening. Fool on.

As always, people on this program may have interest in the stocks they talk about and the Motley Fool may have formal recommendations for or against, so don't buy or sell stocks based solely on what you hear. Learn more about Rule Breaker Investing at rbi.fool.com.