 Dr. Courtney Gibbons, an assistant professor of mathematics at Hamilton College, participating in the Park City Mathematics Institute undergraduate faculty program, which we lovingly call the UFP. Though I'm a mere epsilon compared to the giants on stage with me tonight, I have the distinct honor of having been chosen by the PCMI Steering Committee to moderate tonight's utterly fantastic PCMI debate. As you know, we live in unharmonic times bimodally distributed between two sides that can't even agree on the facts. Here in the United States, and indeed globally almost everywhere, our societies are in a state of convolution and extreme polarization. The goal of this afternoon's debate is to get us all in the same frequency and to reintegrate these warring factions. Today in this theater, we will sift through the lambdas, the moos, the news, the fake news to finally decide the question of which is more important, E or Pi. Given our venue, we'll be using a cutting edge method of modern science, the popular vote. Both of our debaters tonight are among my personal heroes. They truly believe in the mission of big tent mathematics as so literally embodied here at PCMI by the big tent outside. But befitting our theme of equity and inclusion, these two middle-aged white men could not be more different. To put it succinctly, their similarities form a set of measure zero. Professor Colin Adams earned his PhD in mathematics before pursuing postdoctoral research and then joining the faculty at Williams College in the 1980s. He's continued on at Williams to this day. He's a popular and award-winning teacher who embodies the rarest of pedagogical principles that learning math should be fun. He is also a serious scholar with many research papers and a number of successful books. He regularly lectures throughout the nation and in fact throughout the world. In addition to his uniquely successful career in mathematics, he's a valiant champion of equity and inclusion in mathematics. Indeed, he inspired me to pursue a career at a small liberal arts college. Professor Tom Garrity, on the other hand, earned his PhD in mathematics before pursuing postdoctoral research and then joining the faculty at Williams College in the 1980s. He's continued on at Williams to this day. He's a popular and award-winning teacher who embodies the rarest of pedagogical principles that learning math should be fun. He's also a serious scholar with many papers and a number of successful books. He regularly lectures throughout the nation and in fact throughout the world. In addition to his uniquely successful career in mathematics, he's a valiant champion of equity and inclusion in mathematics. Indeed, he inspired me to pursue a career at a small liberal arts college. Let's give them a big PCMI welcome. Professor Adams will argue on behalf of Pi and Professor Garrity will argue on behalf of E. Each will have seven minutes to present a formal argument on behalf of their constant followed by a short rebuttal period and finishing with concluding statements. The audience will then cast votes to decide once and for all which of these numbers is better. To determine which participant will start, professors Adams and Garrity race to construct a stellated icosahedron out of Zoom tools. Professor Adams, the floor is yours. Thank you. Thank you very much. So let me begin by saying how honored both Professor Garrity and I are to be chosen to participate in this momentous occasion. After thousands of years have passed in the history of mathematics, he and I will settle once and for all the question that has plagued human guide for generations and we will answer this question for all the future generations of humankind. Which is the greater number Pi or E? And the two of us are humbled, truly humbled to be chosen for this task from among all the incredible mathematicians in the world today. The Andrew Wiles, the Terry Tows, the Grisha Pearlmans of our age. Yes, they could have chosen any of them but in fact they chose us. When the representatives of the learned mathematical societies from around the globe held their conclave to decide who they should select for this debate. Representatives from the American Math Society, the Mathematical Association for America, the Institute for Advanced Study, the Park City Math Institute, the Banff International Research Institute, the Mathematical Sciences Research Institute and of course the Latvian Society of Actuaries. They chose us. And I can only hope that we live up to this amazing honor. Second, I just want to say what a privilege it is to share the stage with my learned colleague, Professor Tom Garrity. The incredible respect that I have for his voluminous knowledge and his intellectual acuity is exactly matched by my respect for the attitude that he engenders by his careful thought, his gentle wisdom and his dignified deportment as a faculty member. In fact, I know of no one who embodies more the essence of the teacher scholar who thinks carefully before he acts and who realizes at all times that he is a role model to his students and carries himself accordingly. He is someone who treats his students as disciples, the college as his pulpit and his very body as a temple which he maintains for all of us to worship. Be very clear on this. I have never put one iota of credit in the rumors about how the math department cookie funds disappeared when Professor Garrity was chair of the Williams math department. And I didn't doubt him for a moment when pets began to disappear from around his neighborhood and his family was looking particularly well fed. And I will not even consider legitimizing the rumors about him not having made childcare payments to the starving children that he denies are his own by stooping to utter them aloud. No, I want this debate to be about the issues. Not about the fact that he wears spider-man undergarments or that he often runs around the department with a pencil hanging out of his nose. So now that I've made that entirely clear let's get into the issue at hand. Which of these venerated numbers, pi or e, deserves to be held in the higher respect? Which of these numbers should be put on a pedestal to which we should bow every day as we pass by? Pi, dating back to the Greek antiquities together with the Venus de Milo and the Parthenon. I have a few digits shown there. Or e, pariah of the Renaissance, embarrassment to Euler, shunned by the neighboring numbers 2.7 and 2.8. And I guess you can't see that. There's actually an e on the bottom there. It says 2.72. Now Professor Garrity is gonna try to use facts and figures to confuse the issue. He'll have formulas and series and integrals and derivatives, but don't let that confuse you. I have facts and figures too. In fact, that briefcase, you can't see it right there, is filled with facts and figures. But this debate isn't about facts and figures. It's about, this debate is about what you feel in your gut. Which of these two numbers do you love more? Is it pi, pi which is simply defined as the circumference, oh there's my e, sorry. Pi which is simply defined as the circumference of a circle divided by, sorry, a circumference of a circle divided by its diameter. Now this is true for any circle at all. No matter how big or small, every circle in the universe has pi embedded in it as a fundamental part of its makeup. Every round frying pan, every DVD, every soda can, and even what is arguably the greatest invention of all time, the wheel has pi embedded in it as part of its basic makeup. Look around you in this room. If you look back at the back of the room, pi is everywhere. Those clocks that you see right there, non-digital clocks, there's pi sitting right there. It's in the face of that person sitting next to you with a particularly round head. It's everywhere in this room. But where's e, okay? That's a good question, so let's talk about the elusive e. The fact e was in fact invented about 1,500 years ago, sorry, was invented 1,500 years after the ever-present pi. Where did e come from? The first time someone investigated e was Jacob Bernoulli in about 1683. Now I wanna be very clear on this. How did he stumble across e? He was interested in compound interest. He wasn't investigating fascinating geometric properties, relationships that hold for every circle that has ever existed and will ever exist. He was not looking for great truths of the universe. Oh no, he was probably strapped for cash. After all, it was the Renaissance and the price of turnips was going up fast. So perhaps he went to a money lender, a loan shark if you will. Let's give the loan shark a name, shall we? Why don't we call this loan shark Tom, okay? And this loan shark Tom said, I will give you a Kroner now but at an interest rate of 100% per year. So Jacob B calculates and realizes that he will have to pay the loan shark back to Kroner at the end of the year, but his family starving. So Jacob B signs the contract, gets his Kroner and buys turnips for his family. But this loan shark, this Tom, is a clever fellow, much like our Tom here, a devious fellow. And he says to Jacob B, oh by the way, I forgot to say that I decide how often the interest is compounded. Now Jacob B figures, okay, well that can't be so bad. I mean after all, if it's compounded twice over the year, then ultimately what is gonna cost me is one plus one half times one plus one half, which is just equal to 2.25. So 2.25 Kroners, that's not so bad. But then he thinks about it some morning, he says well what if it's compounded three times in the year? If it's compounded three times, that'll be equal to one plus one third cube, that's 2.37, that's a little bit more. What if it's four times 2.44? What if it's five times 2.48? He's getting more nervous now, it's going up. What if it's six times 2.52? And then he realizes well no matter how many times it's compounded, you can figure out what it's gonna cost. It'll be one times one plus one over n to the n. And if you take the limit of that, as n goes to infinity, that'll be an upper bound for how much he will have to pay. And that is this number E, 2.718. So it will cost him no more than 2.72. But this is where E comes from, the loan sharks of our world. Now of these two numbers, which is intuitively the more obvious, which is the more natural, you could fool around with limits of lifetime and not come up with E, but pi you're gonna come up with. Let's take a look at the formula for pi. Pi equals C over D, that's a grand total of five symbols, okay? Let's take a look at the formula for E. That's a total of 16 symbols, that's more than three times as many symbols just to define it. Now when my son was three years old, I said to him, I said, Colton, what words start with E? And he looked at me blankly. And then he said, Colton starts with C. And I said, very good Colton. And I said, do you like Tom Garrity? And he said, he's scary dad. Yes, Tom Garrity is scary. And so is his number, E is scary too. It is cold and calculating. It is a tool of the capitalist machine that grinds all the starving academics under its heel. Pi is comforting, mom's apple pie comforting. I said to my son, that same son Colton, do you like pie? He said, yeah dad, I like pie. Can I have pie? And almost everyone likes pie. You ask them, do you like pie? The answer is universal. Yes, I like pie. Now I'm not gonna bore you with a bunch of details about how much better pie is than E. Details like the fact that discovery of pie predated the discovery of E by thousands of years, or the fact that pie appears in the Bible incorrectly, but it's there, okay? Or that in 1897, the Indiana legislature tried to legislate the value of pie as 3.2, and it passed the House, although it did not pass the Senate, good thing, okay? Or the fact that if you take an ideal triangle in hyperbolic space, it has an area of exactly pie, or that dropping needles on a lined sheet of paper will give an approximation to pie, and tell you absolutely nothing about E. Why should I? Those aren't the relevant issue. The relevant issue is that pie represents everything that is good about humanity. It came out of the search for truth and beauty which the Greeks held as the highest ideal. E on the other hand is the bastard child of a corrupted European culture, reeking of inequities and suffering. It is the sibling of one of the most despicable functions in history, dreaded by millions of students worldwide. Yes, I can only be speaking of the natural log function. E represents all the misery and pestilence humankind has ever suffered through. It is the rat carrying plague-infested fleas. It is the hand reaching out of the sewer grate and grabbing you by the ankle. The answer to the question, what word starts with E, is an answer, thank God, that my three-year-old son didn't know. Yes, the answer is embitter. The answer is infeable. The answer is extort, extinguish, eliminate, and trap. And of course, ultimately, the answer is evil. Yes, that is the word that best encapsulates this number. It is evil incarnate when you choose which number it is that you should celebrate. You are choosing between good and evil. Make the right choice. Thank you. It's kind of hard to see people from up here. And at first, I thought that would be bad. But I'm glad I'm not looking at your faces right now. We all here at PCMI. We all love mathematics. It's one of the great loves of my life. And if I could see your faces, I'd see the shame and the embarrassment at what Colin just did. E and Pi are just numbers. They're great numbers. I like both. I thought, when Rafe asked me, I thought this was gonna be like a discussion of E and Pi. And I come here and find out that it's a debate and that disturbs me. And not just a debate, something that, you know, an attack or, and it filled with just cheap jokes. And for those of you who know me, know that cheap jokes is just not my style. I came here to discuss mathematics. Mathematics is the ultimate search for truth. It's what's important. It's what makes the world go. It doesn't matter what's going on in the world. It doesn't matter how chaotic the world is. It doesn't matter who you are or what you are. When we come together and do mathematics, it's a blessing. That's what I came dressed as a mathematician. Sensible shoes, jeans and an LL being shirt. A coat and tie. I can dress up if I need to to go to a wedding and funeral and not bear as my family. But when it comes to mathematics, it does not matter what you look like. It just matters watching your show when you prove films. Sorry. I'm still a little upset. Pi's a great number. I like Pi. Colin no doubt likes Pi. As far as I can tell, everyone likes Pi. Who doesn't like Loves Pi? Even small children love Pi. Pi is popular. If you have the popularity contest on the world logo, Pi, Pi, Pi, it is popular. But if we were interested in doing what is popular, we'd all be in a different line of work about what's important. We care about what's significant. We care about what really counts. But Pi is good. Absolutely correct about Pi. If you take any circle, measure its circumference, divide it by its diameter, you'll get Pi. And any circle, round and round, divide it by its amusing. It's not that hard to find. Of course, it was discovered in 500 B.C. It's one of the few looking at a circle. It's the obvious thing to do. It's the easy thing to do. And we're here to do what's easy. Well, it's comparing you to discover an electron. Doing an electron is sending a chair that means you can sit. Could have been a bad two. Look at E. Now, I have nothing against loan sharks. I have nothing against interest rates. But that's not why E is important. What's important about E is not the number E, but the function E to the... That's what counts. We all know that among all spectacular, it's its own derivative. That's what's critical. That's what's important. That's why it's at the heart of reality. Earth would like E to the X. And consider its graph. Consider the way it's just a circle going... I assume a lot of you are sort of dweebish. Just a guess. I certainly am. And some of you read science fiction and like science fiction. And you speculate what would be the mathematics of an alien society? What would they do? They certainly wouldn't necessarily have things of base 10. We all know that. They certainly... Some of the math we do is very contingent upon the human condition. But some things are intrinsic. I would claim that alien mathematicians, they know E to the X. They know this curve, even if they don't have arms to be able to go like that. Now, their mathematicians might know Pi, but Pi is only intrinsic if the natural geometry of that world is a flat space with a circle. Only if you have a flat plane is somehow privileged and you have a circle would you think Pi is important. Yes, alien civilizations, mathematicians, would know about the existence of Pi, but it wouldn't be intrinsic. If they were big creatures and they could see the planet they lived on this curve, Pi's not there, but it ain't flat. And they're living in a watery environment with a little back. No Pi, E to the X they have. Let's not consider that just as in the abstract. Let's think about a certain alien civilization, one that's near and dear to my heart. Let's consider Venusians, creatures from Venus. As we know, Venus is an extremely watery environment. They swim through with their three little fins instead of arms. They would not think about Pi as being important. Now, they know about Pi because they're trying to infiltrate us. I assume among here some people are Venusians with their three little flippers, the one in the back. The person next to you who's kind of squirming unusually because the flipper's not quite fitting right, don't stare. It's rude. So let's think about this, Venusians. I claim they would know about E to the X. They would not know about Pi. Now let's think. Let's go back to this compound interest, this thing that's supposedly evil. And let's see what the Venusians would say about it. The Venusians would be talking about it in their little pools. Their mathematicians would talk about E to the X and Pi. They'd be going... However, Venusians will actually know how Venusians go. They go... In fact, of course, that's how we know. You can discover who's a Venusian. Back tonight. Well, tonight's the potato bar, right? Tomorrow night, go to a restaurant in Park City, walk into it, go to the front and go... Anyone who stares is a Venusian. It's your fire test. So let's think about these Venusians. Let's think about compound interest. Now, those of you in this audience who are older, they're probably not... You're not thinking of compound interest as being evil, are you? You're thinking about your old age. You're thinking compound interest, retirement funds and pensions, which are based on compound interest. Because of the fact that you invest money when you're young, it'll be a lot more when you're older. You can retire in the dignity that you expect. Hardly evil. Think of a Venusian society. Right now, because of E to the X, Venus is a decent place to live. They treat their old people well. Without E to the X, this is what life in Venus would be like. They would be sitting there on the ground, this old Venusian, going... What's translation? Again! Venusian! Going... What's translation? Get a job, old man! That's cruel without E to the X. That's why E to the X is the very opposite of being evil. That's why E to the X is so important. Beyond is something that should inspire us all to greatness. We'll now turn to the rebuttals and we'll start with Professor Adams. I don't know what to tell you. It sure seems like Tom Garrity seems to be much more interested in the concerns of the Venusians than he does for humankind. I mean, funny that. Who here actually is a Venusian? Are you a Venusian? Are you a Venusian? I don't think so. No, we're not Venusians here, Tom. So why is it Tom Garrity is so interested in the needs of the Venusians? And why is it Tom that the math department at Williams was never able to confirm the details of your curriculum vita before the year 1990? Did you really, as you claim, spend eight years in a field in Kansas thinking about spectral sequences? Or perhaps you weren't in Kansas at all. And why is it Professor Garrity that you refuse to use the common toilet facilities? Has anyone here seen him use the toilet facilities? Are you worried that someone may see some plumbing that is a bit out of the ordinary? Perhaps some suction cups where they don't belong? And the name Garrity, kind of an unusual name. Certainly not Belgian, as you claim. Now, I didn't want to get into the formulas, but Tom, you leave me no choice. So here they are, the amazing formulas that look something like this. It's amazing formulas. For instance, at the top, pi over four equals one minus one-third plus one-fifth. It's just a spectacular fact. Pi equal to the sum. And in that sum there, you see the Riemann zeta function. Tom, are you familiar with the Riemann zeta function? As far as I know, it's one of the most famous functions in all of mathematics. But somehow it does not make an appearance in your book. Here are some more formulas. You see all kinds of things there. Tom, there's the golden mean up there. Not in your book. Let's see your formulas, Professor Garrity. Or were you too drunk last night to make up any slides? That's a lot of formulas. I said pi is important. Of course there's lots of formulas for pi. I dare say there's just as many free. If that's the ones for pi, now that kind of think about it, they're really not hard to come by. Let's create one right now. Paul, I would claim this is significant. Let's start with, oh, let's try. Let's put pi on this side equal to. Let's create a formula. A formula would look impressive. Let's try. Can everyone see this in the back? One plus two minus three plus four plus five minus nine. And now put in plus pi plus 11 minus 21. Ah, a new formula for a book! Isn't it beautiful? Yeah, I'm impressed by these formulas. That's all that's going on here. E is what's significant. Think of what the formula for E is. E is equal to one plus one plus one over two factor plus one over three factor plus one over four factor. That's a beautiful formula. That is stupid. All right, we have time for brief closing remarks before we take a vote. Tommy, Tommy, Tommy. How many times have I told you that illicit drugs would rot your brain? How many times? You don't know how many times do you? Because that part of your brain containing the information has rotted. And how many times did I tell you don't come to the debate drunk? But would you listen? Did you realize what this was going to do to your career? Did you realize that everyone in this room, all of the amazingly talented students and teachers and professors here will forever lose respect for you? They'll return your book to the publisher and demand a refund. The publisher will demand that you repay your advance. You'll have to sell your bong just to afford groceries. And what about Latvia? Where the Latvian Society of Actuaries went out on a limb for you choosing you over all the other talented candidates for this debate and overrode all of the other learned societies in order to support you for this opportunity. They're crying in Latvia right now. Yes, they're crying in Riga, in Jogava, in Dogoville Pulse. They're watching this debate live and there are tears in their eyes right now. I think all of you can see what happens when someone who thinks E is better than Pi. There is no hope for him, but for the rest of us, Pi is there to save our souls. Make the right choice. Thank you.