What Can You Do with a Degree in Math?

January 24, 2011

Careers in the Math Sciences

What is it that makes autobiography such a compelling form? The chance to learn how an exceptional individual looks back on and interprets an exemplary life or career? The possibility that secret keys to success will be revealed? The hope that the individual might be a gifted storyteller?

The crowd that packed an auditorium at MIT on December 9 for a colloquium talk by James Simons, "Mathematics, Common Sense and Good Luck: My Life and Careers," had probably come for all those reasons. That no one could sensibly expect to hear secrets, especially related to the phenomenally profitable hedge funds of Renaissance Technologies, the quant firm that Simons founded and until recently ran, in no way detracted from the audience's receptiveness.

To return to the title of the talk, which was Is Singer's starting point in his introduction of his former prot�g�, the "s" on "careers" was not an error but rather the main point. Simons has had three careers: in mathematics (both at a government agency and at a large research university), in the finance industry, and in philanthropy. As all three touch on interests of the SIAM community, highlights of each are offered here.

Successful professionals often credit teachers or mentors for inspiring them to go into their fields. Speaking of his decision to study mathematics, Simons evoked late nights in a Cambridge coffee shop during his undergraduate years; there he would often see Singer and Warren Ambrose, also of the MIT math department, working well into the night on mathematics---surely a discipline worth studying! (Ambrose, who died in 1996, worked in differential geometry and was known for his political and social activism, especially concerning events in South America.)

Simons's extensive ties with MIT date back to his undergraduate years. He entered MIT at 17 and graduated in three years that featured, along with mathematics, a lot of late-night poker and ended with a motor scooter trip from Boston to Bogot� with classmates to celebrate their graduation. He found Colombia intriguing for the absence of business and thus for its seemingly limitless opportunities---of which he took advantage.

With a PhD from UC Berkeley (Bert Kostant, his thesis adviser and now a professor emeritus at MIT, was in the audience), Simons spent three years teaching at Harvard and at MIT, where he connected with Singer on questions about Lie groups. In recent years Simons's role has been to provide support for the math department, including three endowed chairs in mathematics.

From 1964 to 1968, Simons held a position at the Institute for Defense Analyses in Princeton, under the arrangement that half of his time would be devoted to IDA work and half to his own research. The work he did at IDA, in the area of minimal varieties, culminated in the solution of higher-dimensional versions of what is known as Plateau's problem. He received the AMS Veblen Prize in Geometry for that work.

Otherwise, the IDA experience was less than smooth. The problems were sparked by a cover story in The New York Times Magazine, in which Maxwell Taylor, head of IDA (who had been, under Kennedy, a chair of the Joint Chiefs of Staff), expressed optimism that the U.S. could win the Vietnam War. Simons wrote a letter to the editor denouncing that viewpoint, and the Times published the letter; worse yet was his admission to a reporter that his survival strategy was to stop working on IDA projects and spend all of his time on his own research, until the U.S. left Vietnam. Ultimately, for the first and only time in his life, Simons was fired.

The ignominious departure from government was followed by ten years (1968�78) in academia---as chair of the math department at the State University of New York at Stony Brook. Physics and the geometric side of mathematics, inextricably intertwined today, were then just in the process of connecting, he pointed out. In that atmosphere, he worked at Stony Brook with Shiing-Shen Chern, a collaboration notable for producing Chern�Simons invariants---which are apparently, Simons said, quite useful in modern physics.

In 1978, at 38, having reached both professional and personal turning points (and with the early South American investments finally beginning to pay off), Simons "knew that it was time for a change." He did some investing and "turned out to be good at it." He also began to collect data, increasingly persuaded that "there was something to be modeled." In founding Renaissance Technologies, he brought with him a former colleague from IDA, "the best modeler in the world," who built models that were "right a lot of the time." But for the first two years, they ignored the models and stuck with fundamental trading---and gave their clients a 12-fold return on their investments. That "incredibly lucky" run was followed by another eight years in which results were good but less spectacular. Other mathematicians joined the firm and built models, to which the firm subsequently switched entirely.

From 1988 on, Renaissance based its trading---of currencies, various financial instruments, eventually stocks---on models. Collection of data, such as histories of interest rates, continued. "We analyzed everything," Simons said. "The models got better; we got better." In 1988, he started the hedge fund Medallion, which by 2002 was closed to all but employees. Today, Renaissance has about 300 employees---among them many mathematicians and physicists, leading to Singer's reference to the quasi-tongue-in-cheek description of the firm as "the best math and physics department in the world." It's not the only quant firm, Simons said, but people always ask, What's the secret?

Here are the guiding principles that he identified as responsible for the success of Renaissance: Start with great scientists who do first-class work and who have good taste in choosing problems. Provide those scientists with a great infrastructure. Maintain an open atmosphere in which, to the extent possible, everyone knows what everyone else is doing, at the earliest possible time---an approach that stimulates innovation. Renaissance researchers meet once a week to discuss new ideas; people are paid on the basis of the firm's overall performance.

Adhering to those common-sense principles, the firm has made a lot of money---so much so that in 1994, Simons started a foundation. Since then, he said, it has grown in terms of both size (the amounts of money given out) and sophistication.

The Simons Foundation supports basic science; it's serious research, Simons said, including autism research from the ground up: neuroscience and biology, along with physics and the mathematical sciences. In one of the less understated remarks in the talk, he expressed doubt that any other private foundation of comparable size is devoted to basic science. The focus is on building bridges between the mathematical sciences, physics, and the biosciences. Projects include support for endowed chairs linking two departments and a competition for a computer science institute (which closed in October).

Simons retired from Renaissance at the end of 2009 and has "never been so busy." A current project is Math for America, which has as a goal the preparation of math teachers who know math. Explaining the need for such an activity, he pointed out that if high school teachers of math knew as much as they should, they could qualify for jobs at Google or Goldman Sachs; good teachers get pulled away to more lucrative jobs. Math for America pays teachers better and "makes them feel special; if you improve the career, people will stay."

Looking back over his own interconnected careers, he identified unifying guidelines:


Information about Simons Foundation programs in the mathematical sciences can be found at http://simonsfoundation.org/ and in an article that appeared in the October 2010 issue of SIAM News (http://www.siam.org/news/news.php?id=1829).

Sue Minkoff ([email protected]), of the University of Maryland Baltimore County, is the editor of the Careers in the Math Sciences column.

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