Weekly Bulletin
November 15, 1999
Vol. 89, No. 9
[<] [>] [archive]


Thinking about math
Real-world problems
Randall manages musical banquet
In print
Nassau Notes
Page one
In the news

Thinking About Math


John Conway (Photo by Peter Murphy)

Public lecture series draws students, professors, professionals, highschoolers

By Steven Schultz

It's Wednesday night, and A10 Jadwin is filling up fast.Well before the speaker is scheduled to start, there's not a seat to be had; nearly 200 students, professors, professionals and even local highschool students cram themselves into every bit of floor space.

A large man with a wiry gray beard and a T-shirt printed with a design by M.C. Escher walks to the front of the hall: John Conway, John Von Neumann Professor in Applied and Computational Mathematics. With a brief quip about how he wasn't sure he'd have an audience, he begins to discuss the ancient Greek mathematician Archimedes.

The sole surviving record of Archimedes' work in the original Greek is a palimpsest, a papyrus document that was written on, erased, then turned and used again. Modern technology enables scholars to puzzle out the bottom layer of text underneath the later writing.

Conway has made a career of finding new layers of meaning in physical things. His fascination with games and puzzles has led him to important discoveries in areas of mathematics from number theory to geometry. He has broken new ground with theories about knots and sphere packing, and discovered one of the largest finite groups of numbers (known as the Conway group).

"Thinking about Math (and Many Other Things)"
On mathematicians in history: "As mathematicians we are unique among the sciences (with the slight exception of physics) because our history goes back so far. Those Greek geometers were doing amazing stuff 2,500 years ago." Conway hired an artist he met in a café to paint a frieze around his office depicting mathematicians through history. In talking with students, he likes to gesture to the paintings. "It adds something to see the man looking down at you."
    On discovering the surreal numbers: "For about six weeks, I went around in a permanent sense of daydream." During a recent trip to Australia, he began to think the sensation was something like "what the famous explorers felt when they stood on the edge of a vast new landscape. In a way, discovering the surreal numbers is like discovering a whole new continent. There's a world that no one has seen before. Of course, it's not the same. The surreal numbers are not a physical thing. On the other hand you can carry the concept around in your head, which you can't do with Australia."
    On the future of the surreal numbers: "One thing that worries me is that there aren't any questions about the real numbers that remain to be solved. The best math usually turns out to have applications in mathematics or physics. My numbers haven't found any application at all yet, and that disappoints me. But in respect to the surreal numbers, I am very proud. They may just be a footnote to mathematics, but they are a real, permanent footnote. And in 2000 years, it will be possible for people to look them up and think about them. There is eternality about math questions, a feeling that you're really getting to bottom of something."


His interest in the game Go helped him to identify an entirely new class of numbers, called the surreal numbers. In the nonacademic world he is known as the inventor of the game Life, in which checker-like objects replicate themselves and form patterns on a grid. The game, in turn, has spawned a field of research called cellular automata.

Conway is passionate about connecting people to math, which is one reason he's doing the public lecture series in Jadwin Hall.

"I really love my subject, and I want to spread it as widely as I can, to spread the gospel," he says.

The series of eight lectures is titled "Thinking about Math (and Many Other Things)."

The series has drawn students and faculty not only from the math, physics and engineering departments, but also from such areas as philosophy, linguistics, history and Hellenic studies.

Conway is "a great lecturer," said Dimitri Gondicas, executive director of the Program in Hellenic Studies. "He brings math alive and makes it relevant, and also puts it in its historical and philosophical context."

"He seems to know just how far to go into technical details and still keep his audience interested, and also convey the mathematical truths. That's a very delicate balance," said philosophy professor John Burgess, who attended with his son Fokion, a freshman at Princeton High School.

Proofs, historical tidbits, asides

In his lecture on Archimedes, Conway wove together the nuances of the ancient Greek's mathematical proofs with historical tidbits and asides about his own favorite books. He explained that he has been enamored of Archimedes ever since he read his proof of the formula for the perimeter of a circle.

"When I saw these theorems," he said, "my feeling was 'How is he going to fudge it?' I knew it was impossible, absolutely impossible, to prove this from Euclid's postulates. So I turned a few pages and got a spinetingling feelingbecause Archimedes didn't fudge it, not one little bit."

The palimpsest, which contains six books by Archimedes, was originally written in the 12th century. (Religious texts were written over the math a century later.) It is the only text of Archimedes in Greek, which is especially important, Conway noted, because the extant Latin translations were done by scholars who lacked a profound understanding of math.

When Conway found out that the palimpsest was going to be sold at Christie's Auction House last fall, he lobbied for Princeton to buy it. He convinced the University to put in a bid for $1.2 million, but the document sold for more than $2 million to a private collector. Fortunately, Conway said, the new owner has pledged to make the document available for study.

Despite the emphasis on history in his public lectures, Conway's real goal is to convey the most fascinating aspects of the math itself. His second lecture addressed the work of Kurt Gödel and the concept of uncertainty; the third focused on the set theory and infinite numbers of Georg Cantor; and the fourth turned to Conway's own surreal numbers. The topic of the next lecture, at 8:00 pm on November 17, is "Geometry, Logic and Physics."

"Syracuse was the math capital of the Greek world; Princeton is the math capital of the modern world," quipped physics professor Kirk McDonald at one lecture. "I grew up in Arizona, and you'd hear about these great mathematicians on the East Coast, and occasionally you'd hear about this guy John Conway. And now here we are actually hearing him."