Fields Medal was never meant for ‘the greatest mathematical genius'

The most famous prize in mathematics, the Fields Medal, is often described as the Nobel Prize for math. Now, confidential correspondence from the 1950s provides a first window into the deliberations of early Fields Medal committees. The letters suggest the award was never intended to honor the most important discoveries in the field, but was meant to recognize promising up-and-coming talents. "It's basically exactly the opposite of how the Fields works today," says Michael Barany, a historian of mathematics at Dartmouth College, who reported the discovery last week at the Joint Mathematics Meeting in San Diego, California.

Beginning in 1936, the International Congress of Mathematicians awarded two Fields Medals every 4 years to recognize outstanding mathematical promise and achievement. In 1966, the organization (now run by the International Mathematics Union) bumped it up to four medals every 4 years and stipulated that recipients must be younger than 40. Yet the award committee's criteria for selecting the winners are notoriously enigmatic. Nowadays, deliberations are sealed for a period of 75 years, whereas records from earlier years weren't kept in any organized way.

But Barany had a hunch that there might be clues to the secret deliberations at Harvard University, which in 1950 hosted the International Congress of Mathematicians. Last year, he got access to the mathematics department's archives. There, sandwiched between the everyday minutiae of hiring records and course assignments, he found a folder labeled "International Mathematical Congress" from 1949–50.

The folder held letters from Fields committee chair Harald Bohr, a mathematician at the University of Copenhagen and a noted champion of promoting mathematics to the public. Bohr collected opinions from the seven-person committee and summarized them for the group. Everyone agreed the medals should go to relatively young mathematicians, but debate raged over the definition of "young." The committee also disagreed on whether the prizes should simply go to the most talented young mathematicians or to those who were comparatively unrecognized.

Four nominees rose to the top: The Russian-American Oscar Zariski, the Norwegian-American Atle Selberg, and two Frenchmen, Laurent Schwartz and André Weil. Bohr favored Schwartz, who shared the elder mathematician's penchant for promoting math to the public. Weil was considered the most accomplished mathematician, but at 43, he was relatively old in the eyes of committee. He also had served prison time in 1940 for skirting military service during World War II.

Bohr, Barany suggests, used his influence to steer consideration away from Weil and Zariski—also "old" at 51—and toward the younger Schwartz and Selberg. He argued against picking "the greatest mathematical genius" in favor of choosing younger winners whose careers would benefit from the recognition. And he got his way: Schwartz and Selberg received the Fields Medals in 1950.

A few months after Barany found the 1950 letters, he came across another trove from 1958 belonging to Zariski, then a Harvard mathematician. History repeated itself: Committee chair Heinz Hopf at the Swiss Federal Institute of Technology in Zurich ruled out two nominees because they were already thriving professionally.

Eventually, the 1958 medals went to Klaus Roth of the United Kingdom and René Thom of France. The U.S. mathematician John Nash, whose life was dramatized in the movie A Beautiful Mind, came in third place in votes. Years later, Nash openly wondered why he hadn't won for his brilliant contributions to solving partial differential equations. In the minds of the committee members, Barany says, Nash didn't need the Fields Medal to be successful, and they preferred recognizing the comparatively lesser known Roth and Thom.

"I was fascinated by the way in which the personal agendas of committee members were clothed in seemingly reasonable attempts to place restrictions on the prize," says Christopher Hollings, a historian of mathematics at the University of Oxford in the United Kingdom, who attended Barany's talk. "It is a nice and interesting reminder that mathematicians are people, too."

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