Princeton University - Council of Science & Technology

POPE PRIZE

Essay 1
Disease of a Thousand Names
Laura Joy Grasso Fitzpatrick

Essay 2
Miracle Cell
Laura Joy Grasso Fitzpatrick

Essay 3
The Outsider with a Reputation
Howard G. Yu

Honorable Mention
Viola Huang

The Outsider with a Reputation

John Horton Conway spends almost no time in his office. It’s a “repository for toys,” says one of his students. It is filled with colorful polyhedrons dangling from the ceiling, board games strewn on the floor, and unstable mountains of paper. Dressed in a t-shirt and sneakers, Conway spends the majority of each day in the math lounge reclining on coffee-stained couches amid unfinished Go games and blackboards paved with zany shapes and floating numbers. Conway is the John von Neumann Distinguished Professor of Mathematics at Princeton University. His prominent title confirms who he is because he has made breathtaking discoveries in group theory, number theory, knot theory, game theory, and quantum mechanics. Yet Conway describes his job as “playing games.” “When I was a little kid, all the other kids called me the prof, very early on that was my nickname,” says Conway smiling. Young or old, Conway always seems to stand out from his peers. “My mother tells the story I could recite the powers of 2 when I was four [years old], it’s tempting to think I got to 210!” Born in Liverpool on the day after Christmas in 1937, he was bemused by science and gadgets as a boy, even helping to fix up an illegal telephone line between his house and the home of a friend. “I was very nearly top in everything,” Conway goes on. Eventually, he isn’t sure how or when, Conway became drawn towards numbers. “Some parts of mathematics came as a revelation. I was tempted by the abstract ideas.” He went to Cambridge to study but ended up playing a lot of backgammon there. Not interested by the traditional games of chess, Go, or bridge (which his father played), Conway pursued with a passion games that were seen as less serious. “I hated the idea of waiting several minutes for my partner to make the next move. I studied children’s games,” Conway elaborates, “I was always into them more than the formal ones.” And he is intensely into them. One time during a lecture, he challenged a young man in the audience to play ten games of dots-and-boxes; if Conway lost a single game, he would concede defeat. Conway won. As the inventor of a set of numbers, the Game of Life, and more recently, the co-discoverer of a proof that shows fundamental particles might have free will, the septuagenarian Conway is a grownup kid who possesses a joie de vivre—he loves to wonder about mathematics and has a ton of fun doing it in his own original, playful way. For Conway, mathematics is alive, and capable of fluttering the heart. “Most people think that mathematics is cold. But it’s not at all! For me the whole damn thing is sensual and exciting,” exclaims Conway. When he talks about math or anything else he is interested in, which is just about everything, you can see that feeling in the big smile on his face and you can hear it in his upbeat, curious, British accent. The math lounge is his office, where people—including some of the world’s greatest living mathematicians—walk in and out, some to grab coffee, others to chat. Like the free flow of people, Conway is open to the free flow of ideas and new possibility. “I do whatever I like, no matter how frivolous or deep.” With a twinkle in his eye, he says that he doesn’t know where the source of discovery is, so he works differently. For example, early in his career when he was watching people play a board game, he made a discovery: surreal numbers. During Conway’s time at Cambridge, where he eventually became a professor, England’s Go champion visited the math department. “I never understood Go. I used to look at the people playing and stare,” says Conway. Then, after spending hours observing, “I noticed on the board there were little games going on,” Conway says. He assigned numbers based on what the available moves were in the mini games. “I always intended to study sums of games,” Conway confesses, “so I decided to study them and I discovered surreal numbers!” Surreal numbers, despite their name, are numbers as real as the integers, except these numbers lie in out-of-the-way places. For example, one such surreal number is a number greater than zero but less than any decimal (called iota). It’s similar to a decimal point followed by an infinite number of zeros, and then followed by a one at the end. “What I do, I am a professor of mathematics,” Conway muses, “Most of my colleagues study much more difficult subjects. I study simple things that have been studied for centuries by clever people. I really have to find something new, some way of looking at it in a new and simple way.” One topic studied for centuries, and more recently by Conway, are quadratic forms. Imagine that x and y could be any positive integer: 0,1,2,3,4, … Then the linear equation x+y can take on, or generate, any number form zero to infinity based on what x and y are. However, when one considers equations with higher powers, like x2+y2, interesting possibilities arise. These equations with terms that contain two of the variables multiplied together (x2 or y2 or xy) are quadratic forms and have been researched for over 200 years. Yet, Conway found a new and simple way of visualizing them through tree-like like diagrams with the numbers the form generates arranged on the vertices. Conway used his notation to show how easy it is to prove some fundamental theorems on quadratic forms, just by looking at the tree. Simple and intuitive notation, making hard math accessible, is one of Conway’s trademarks. The tree-like structures appear in his book, The Sensual (quadratic) Form, which is aimed at the public and has a title written in a silky violet font. “Conway thinks very deeply about everything in a way that few good mathematicians understand on that level…it is a primordial understanding,” says Seth Blumberg, one of his students. “I’m good at discovering simple things,” Conway remarks in his usual understated manner. One reviewer complimented Conway’s book by saying that each page was “spilling with new ideas.” For a subject that has been studied longer than some scientific fields have been in existence, it is quite a compliment. And it’s a compliment that often rings true for Conway. While Conway has been a fixture in the Princeton University math lounge for as long as anyone can remember—the lounge is usually the first place people (the author included) go to find him—it was not always the case. “I was invited to dinner at Prospect House [in the late 1980s],” says Conway, referring to the exclusive club where Princeton faculty dine. “The math chair at the time…came up to me and asked, ‘What are you doing in the future?’ I whispered to my wife, ‘He’s going to offer me a job!’ And he did…I was quite conflicted about Princeton. I figured it was 50-50.” Conway approached the problem practically and rationally, but as usual, unconventionally. “So I wanted to invite friends over and then flip a coin to decide. My wife at the time, Lorissa, talked me out of doing it…If I was married to someone else I probably wouldn’t be here.” “Coming to Princeton woke me up a lot…I also didn’t realize how good Princeton is at mathematics. I realized all the really great American mathematicians were from Princeton or were bound to come here…It’s nice to be at the center of it anyway,” says Conway with a shrug. Yet, by coming, Conway has brought a bit of Cambridge’s culture to Princeton and made learning math here more spontaneous. “There was a culture of perpetual frivolity at Cambridge,” explains Conway, who fits in with his students here more than he does with his sometimes reclusive colleagues. In a lounge often overrun with undergraduates, does he wish more Princeton math professors spent time there? “Yes,” says Conway without hesitation. These days, Conway, who looks as though he’s in his fifties, with long brown hair absent of any grey, has visibly slowed down from ten years ago. Back then, he would often leap up from the couch at a moment’s notice to greet people or to tell an interesting anecdote. “I feel older. I didn’t feel it so much then but I am slowing down.” Conway gestured at his right knee, which has lost some movement, mentioning the stroke he had last year. But he’s fine with it: “In one sense I don’t care. I never did.” What cannot be seen are the fireworks still going on in his head. Conway has recently become enamored with quantum mechanics, the branch of physics dealing with the strange behavior of electrons and other subatomic particles. In 2004, he and another Princeton mathematician, Simon Kochen, proved a theorem on free will. If one starts with three axioms in physics, like the constancy of the speed of light, and if a human being has free will, free to decide whether to drop a pen or not, then fundamental particles in the universe also possess this indeterminacy. Just as the laws cannot predict whether we will drop the pen, the laws cannot predict what this particle will do. “In some sense I try to understand at a simple level what happens in the universe. We know we can’t understand certain things; I just sort of try,” beams Conway. "Any day I learn something, no matter how small, it is a good day. Today, talking with Prof Kochen, I learned two things, so today is a good day.” Joking, Conway says that one sign of senility is when a person who has done good work in one field decides to try his hand in a new one, referring to himself and quantum mechanics. But: “The clinching sign is that after he is told this, he still tries!” Changing gears, Conway says that his recipe for success is to “think about six different topics at once…I’d work on something trivial, and then the Riemann Hypothesis!” referring to the greatest unsolved math problem currently. “I make progress that way.” But, Conway, who does not usually attend math conferences or meetings and is still learning quantum mechanics, ponders for a moment and says, “One of the penalties of being interested in so many different subjects is you tend to be on the fringe.” “I feel I’m a bit of a fraud. I’m a little bit of an outsider, an outsider with a reputation,” says Conway, grinning In the eyes of John Conway, math is mysterious and true. “If you prove that A implies B, and that B implies C da da da all the way to Z, then A implies Z! That doesn’t usually occur in real life. I don’t fundamentally understand why math works. It’s something of a miracle. It is this quest to understand...that drives me. “People have negative opinions…because I play games. I don’t really care!” states Conway in a playful tone. “What I want to know is what happens in the world.” “[Conway realizes] many things aren’t that complicated. He enjoys himself at every stage,” says Blumberg. “Working with him…It’s an adventure.” And it is an adventure—all the time. As this friendly, humorous, distinguished professor of mathematics bids “farewell,” he reclines back on the couch in a now-peaceful math lounge, sneakers propped on the coffee table, eyebrows raised, pen gliding. Working, he is again at home, playing in a field of numbers.