Will his shouts from the window attract a real superset of prime candidates?
How do you inspire young people to pursue mathematics? Karl Sabbagh meets an offbeat talent-spotter.
Charles Ryavec is a trim, grey-haired man in his 60s, teaching at a strange institution called the College of Creative Studies, part of the University of California, Santa Barbara. He is the only mathematician in this particular faculty and he has a lot of freedom. "They just give it to me, the freedom," he says. "Actually, I'll tell you the truth, most people don't give a damn. We're not on a big budget, it's small potatoes. I think the university sees this place as window-dressing. They think there's nothing serious going on here, that it's window-dressing and that's it."
But there is something serious going on - Ryavec's quest to find talented young mathematicians who might fall through the cracks. He waves an arm towards the window of his cramped office and tells me a story of one of his students, Bob, that shows the flexibility of his approach.
"Basically what I do is if I see him walking by I give him a maths problem through the window. 'Hey, Bob, have you heard of this problem?' And then he'll come by a day later and tell me the solution. That's all we can do. If I were to try to get him to go into a room, he would not do it. He's brilliant. The other day I gave him this problem where you have an integer, like 2001, and two people play a game - one person takes a divisor of the number and subtracts it from the number and that's the number he gives the next person. And he takes a divisor and subtracts it from the number and gives it back to you, and so the person who can do it and get a 1 wins. So anyway, the student went to lunch and he came back and said 'Yeah, I know how to do that, it's easy. You do this and do that.' Now if I'd given him some function theory problem, he wouldn't do it..."
I was visiting Ryavec because he's one of two or three dozen mathematicians around the world who are passionate about the Riemann hypothesis, the most important unsolved problem in mathematics. He doesn't think he'll solve it, but his passion for analytic number theory - the field of mathematics where most people think the solution will come from - could spur the next generation of mathematicians to tackle what is thought by many to be the Holy Grail of modern pure mathematics. One index of its importance is a $1 million prize for a proof, offered by the Clay Foundation in the US.
The Riemann hypothesis is a statement about prime numbers, those whole numbers that cannot be divided by any other whole number without leaving a remainder: 3, 5, 11, 31, 10,007 and so on. There is an infinite number of primes but no rule for generating them that we know of. If the Riemann hypothesis is true, we would understand much more about how the infinite number of primes is distributed among all the other numbers. All we know now with any degree of precision is that the distribution is neither wholly random nor wholly regular. Those who are serious about the problem think about it morning, noon and night because they find thinking about a difficult mathematical problem to be a more satisfying activity than any of the other pleasures the world has to offer. The mathematician Andre Weil once wrote: "Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously... Unlike sexual pleasure, this feeling may last for hours at a time, even for days."
Many mathematicians, even if they don't find a proof of the Riemann hypothesis themselves, would die happy if they knew that someone had proved it. Ryavec put this very strongly to me, in connection with the $1 million prize. "I would be happy to dig ditches to earn a million and give it to somebody else for the proof. I don't want the million. If I solved it, they could have the million. I would probably buy books for the students."
For non-mathematicians, it might be difficult to empathise with such an attitude. But mathematics seems to be at once the most satisfying and the most abstract of intellectual disciplines. And therein lies the problem for teachers - how can you demonstrate the almost addictive qualities of higher mathematics to those who know little or nothing about it? How can you persuade them that it is worth slogging away on the nursery slopes for the view from the summit?
That's the sort of thing Ryavec tries to answer, from his cramped office in a building that looks like a morgue, dirty beige with no obvious entrance, a few small windows and shabby interiors. It has clearly seen better days compared with some of the other gleaming structures on the campus. But the College of Creative Studies started with high ideals.
"There were people way back when," Ryavec says, "who figured that education was terrible in American universities and what we ought to do is skip kids ahead of these rigmarole courses and get them into exciting stuff. But they couldn't get it done. Universities are very conservative places.
"Anyway, the Vietnam war came along and the campuses came apart. So this guy, this literature professor here, [Marvin] Mudrick, and a couple of other people who for a long time had this idea that the educational system was lousy, suddenly said: 'Hey, we can get a College of Creative Studies started? This is our dream, this kind of idea we've always been thinking of.' And the university said: 'Fine do it, anything to keep the students quiet.' So underneath that idea of keeping the students quiet and getting them back excited by learning they got it started. The idea was that here you would jump students ahead to some kind of vague mix of what they're excited at learning - it's very hard to describe. It wasn't another arts college. There was going to be maths, physics and chemistry as wellI" Ryavec has a down-to-earth speaking style that belies the rarefied nature of the ideas he is passionate about. He uses words such as "goofy" and "stuff" a lot and is very self-deprecating about his talents. He makes it sound as if he's in maths only because he wasn't much good at anything else.
"At a very early age I fooled around with numbers, but it was on and off again. I had other interests. I love writing a lot - actually, I was going to be a novelist for a long time. I'm writing a novel. It's my other pastime, I write novels and burn the stuff when I'm done. Actually I've found a publisher online so I'm going to publish a novel. It's junk but they accept junk."
What Ryavec's remarks show is a wide-ranging and versatile mind that is capable of coming at maths problems from an unexpected direction and - maybe - surprising the hell out of them with a brilliant insight. He is an unconventional man in an unconventional setting, and he shows passion and tenacity in getting the best out of students who don't fit in the system. Although a more conventional maths faculty tries to attract and process batches of high-school students and turn them into competent mathematicians, Ryavec, the only mathematician in the college, has the freedom to select high-fliers who may need careful handling but, in his view, have the potential to be much better than competent.
"One kid came into the CCS. Before I knew it, he'd disappeared. I thought, 'What the hell happened to this guy?' He was over at this advanced course in set theory - a really tough graduate course." The student came to Ryavec saying the professor wouldn't let him do the course because he was an undergraduate. "I said, 'Just let him take it, OK?' So four weeks later I was going down in the elevator with the professor, and he said, 'You know, that kid you sent over, he's my grader.' That's how good he was, but all he loved was set theory."
And for those who might feel that inspiring passion and love for a subject is too airy fairy, Ryavec rounds off the story in a way that shows that a brilliant teacher who is given academic freedom can achieve hard-headed results that would satisfy any government bean-counter.
"Now, this guy is running some big thing for Sun Systems. Almost all the kids I recruited in the first five or six years went to Silicon Valley. They all live within about a 10-mile radius of each other. Some are retired now - millionaires."
Karl Sabbagh's Dr Riemann's Zeros , is published by Atlantic Books on November 21, £14.99.