Beating the clock

French mathematician Evariste Galois documented his findings on group theory at age 20 on the night before his death. Norwegian math prodigy Niels Abel perfected his revolutionary theorem when he was still in his early 20s.

Princeton's own math department chair Charles Fefferman earned his B.S.E. at age 19 and his Ph.D. at 20, before being granted tenure at the University of Chicago at 22 and going on to win the Fields Medal — one of the highest honors a mathematician can receive — by age 29.

An outsider might consider these men early bloomers. But according to those in the math profession, they were right on schedule.

In his 1940 autobiography, "A Mathematician's Apology," G.H. Hardy called math a "young man's game," in which most players reach their prime before they turn 35.

Today, University professors and graduate students acknowledge that there is more truth to the idea than many would care to admit.

"You do have prodigies in math that you don't have in other fields," said University math professor John Stalker.

University graduate student Tom Watson, 25, also agreed that "mathematical talent tends to show itself early in a person's life."

"It is easy for a young person to reach a relatively advanced level because there isn't much needed in the way of equipment or special experience to do math," Watson said, echoing one popular explanation for the trend.

University graduate student Jose Luis Rodrigo, 23, offered another hypothesis.

"It's possible . . . that before 40, the way you look at mathematical objects can make you come out with different approaches and new ideas," he wrote in an e-mail.

Stalker agreed that — unlike in most other academic professions — a lack of experience can be an asset in math. "Sometimes not knowing too much is an advantage," he said, explaining that a young mathematician might be less "tempted to apply standard techniques" in problem solving.

The belief that mathematicians must achieve at a young age, however, seems to come from within the field itself.

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In most academic fields, experience is seen as central to a researcher's success, and math seems to be a rare exception to this rule.

Stalker credits this phenomenon to the "objectivity of math" in comparison with the humanities or social sciences — fields where "your reputation has a lot to do with how people respond to your work."

But in math, "you can be regarded as spectacular even at a young age," he said.

While crops of younger mathematicians often thrive early in their careers, some in the profession say one-time math whiz kids tend to become less productive as years go by, and myriad explanations are offered to explain this trend. Nevertheless, few contend that one's mathematical abilities actually diminish with age.

"It might be simple laziness," Stalker said, describing many mathematicians who are still capable of doing exceptional research yet no longer feel the pressure to do so, after they have been granted tenured jobs.

Others say some older mathematicians refrain from publishing their later research for fear that it will be judged against outstanding work they conducted at an earlier age.

And some contend that well-known math masterminds are more likely to pursue more unorthodox research topics as they grow older — and less likely to pursue publication.

"Once you're an established mathematician, you don't care as much about what [the public] finds interesting, but about what you find interesting," Stalker said.

The famed Fields Medal — viewed as the Nobel Prize of mathematics — actively emphasizes the image of math as a youth-dominated profession.

Unlike Nobel Prizes, which are given to recognize lifetime achievement, the Fields Medal is awarded based not only on past accomplishments, but also on perceived potential for future success in math.

In fact, it is widely believed among mathematicians that the group that selects Fields Medal recipients sets a virtual "cut-off age" of 40.

And while the tradition of achieving early fame is viewed as essential to finding success in the math field, the graduate students interviewed said they did not feel pressured while still in their youths.

"It's just something you're aware of. It's there," 19-year-old University graduate student Aakshay Venkatesh said, to which fellow graduate student Emma Carberry, 26, added, "No one actively worries about it."

Even the prospect of winning a Fields Medal is hardly a relevant concern "unless you're extremely, extremely ambitious," according to graduate student Vadim Kaloshin, 28.

Some members of the math department said they are often suspicious about the claim that math is young people's turf.

"Like many gross generalizations this one is true in a statistical sense, but often false in individual cases," Stalker said, adding that many "prominent counterexamples" seem to disprove the theory.

Famous 19th-century mathematicians Leopold Kronecker and Leonhard Euler continued their significant work well past the traditional retirement age. Ilya Piatetski-Shapiro — who, in his 80s recently helped prove the Converse Theorem — is still active in the math community today, as is Fefferman, who is 51.

Most mathematicians emphasize that, though the "youth myth" contains more than a grain of truth, it is often exaggerated. Age and experience play as important a role in mathematical success as they do in any other field.

"With experience you become more flexible with using different tools," Karoshin said.

And Stalker agreed that "acquired knowledge of [mathematical] literature" is essential to gain respect and status as a mathematician.

In short, most mathematicians firmly believe success in their career field is ultimately determined on an individual basis — that trends relating age and achievement have little effect on one's own career outlook.

"If you're a good mathematician," Watson said, "you'll be doing good work all your life."