A Cambridge-based mathematics institute supports young mathematicians and has raised the profile of a poorly understood field.
Mason Inman
The road to the biggest prizes in mathematics begins at a small office tucked away on a side street off Massachusetts Avenue near Harvard Square. This is the home of the Clay Mathematics Institute, where a handful of mathematicians and other staff are working to bolster fundamental research in math. They also oversee a competition called the Millennium Problems that offers million-dollar prizes for solving the most vexing problems in the field.
The only institute of its kind—completely privately funded and dedicated solely to mathematics research—the Clay Mathematics Institute (CMI) has been instrumental in supporting a field that has struggled to keep funding flowing from federal sources.
It’s the brainchild of Landon Clay, a wealthy Boston businessman who doesn’t have much of a background in math. He majored in English at Harvard but has a long-standing interest in the subject. His main motivation was to fund mathematicians who look at problems the way climbers look at Mount Everest: they want to solve big problems for the sheer challenge of it.
Clay put in tens of millions of dollars to set up the institute in 1999. A year later, the institute announced the Millennium Problems. It arranged a committee of top mathematicians to pick seven of the toughest problems in math and offered a $1 million prize for each solution.
“The existence of these prizes raises the profile of these problems in the public consciousness, and also in the consciousness of the mathematical community,” says James Carlson, a mathematician and president of CMI. “I think it drives home a point that we shouldn’t just be content to solve the problems that are ready at hand and are sort of easy. We should try for the really, really big fish, for the really deep problems, the ones that have resisted solution for a long time.”
The winner is…
Ironically, the first person thought to have solved one of these problems may shun the prize. The math community has generally accepted that Grigory Perelman, a reclusive Russian mathematician, made the breakthroughs, published online in 2002 and 2003, that solved one of the Millennium Problems, the Poincaré Conjecture.
This hundred-year-old problem in the field of topology deals with the properties of the surfaces of objects in four dimensions. It turned out that properties that are intuitive for surfaces of three-dimensional objects were relatively easy to prove for five, six, and higher dimensions, but for four dimensions, they were especially difficult to pin down.
Once mathematicians have verified Perelman’s proof, CMI will make a judgment of whether the problem has been solved. Assuming Perelman’s proof holds up, he should be awarded the first Millennium Prize. But will he accept it? Last year, Perelman made headlines when he turned down the Fields Medal—math’s equivalent of the Nobel Prize.
“The Clay Institute will make its decision independently of any attempt at psychoanalysis of Perelman,” Carlson says. But if he does turn down the prize, “All I’ll say is that we’ll have a carefully thought-out plan B that I think will be good for mathematics and will recognize Perelman’s achievement,” he adds.
Nurture the young
Separate from the high-stakes Millennium Prizes, the institute also funds fellowships, annual prizes, and summer schools. The institute’s single biggest expense is for the Clay Research Fellowships, which support 10 top young mathematicians for two to five years.
Getting a Clay fellowship is “pretty much ideal,” says Ben Green, who is finishing up a two-year fellowship. Last year, he became a professor at the University of Cambridge at age 29. “You have few duties,” such as teaching, which frees up time for research, Green says. “There’s a generous allowance for travel to conferences and for inviting collaborators to visit.”
Green says that having CMI as a private source of funding helps mathematics. “The NSF can be very political about what it gives grants to,” he says.
Bob Devaney, a Boston University mathematician who is not funded by the CMI, agrees that having private funding is especially important for the field. “In mathematics, we’ve been very poorly funded by government agencies,” he says.
CMI also tries to cultivate young mathematicians at the high school level through summer programs. The institute works with Boston University to bring about 60 top high school math students each year from around the world to the BU campus to learn advanced math and do research projects.
“Most people don’t have any sense of the incredible things going on in mathematics,” and what students are usually taught in school—arithmetic, algebra, calculus—is centuries old, says Devaney, who’s given talks about his research to students at CMI. “So this is really a chance for them to see what’s happening in mathematics. This is something that’s desperately needed.”