- by Sylvia Nasar - Simon and Shuster - 1998

This one page excerpt (from Chapter 31) mentions Kurt O. Friedrichs multiple times. Jürgen Moser and Peter Lax are also

mentioned in this same excerpt.

The next Fields Medal would be awarded in August 1958, and as everyone knew, the deliberations had long been under way.

To understand how deep the disappointment was, one must know that the Fields Medal is the Nobel Prize of mathematics,

the ultimate distinction that a mathematician can be granted by his peers, the trophy of trophies. There is no Nobel in

mathematics, and mathematical discoveries, no matter how vital to Nobel disciplines such as physics or economics, do not in

themselves qualify for a Nobel. The Fields is, if anything, rarer than the Nobel. In the fifties and early sixties, it was awarded

once every four years and usually to just two recipients at a time. Nobels, by contrast, are awarded annually, with as many

as three winners sharing each prize. Tradition demands that recipients of the Fields be under forty years of age, a practice

designed to honor the spirit of the prize charter, which stipulates that the purpose of the honor is “to encourage young

mathematicians” and “future work.” The incentive, incidentally, is of an intangible variety, as the cash involved, in contrast

to the Nobel, is negligible, a few hundred dollars. Yet since the Fields is an instant ticket in midcareer to endowed chairs at

top universities, ample research funds, and star salaries, this seeming disadvantage is more apparent than real.

The prize is administered by the International Mathematical Union, the same organization that organizes the quadrennial

world mathematical congresses, and the selection of Fields medalists is, as one recent president of the organization put it,

“one of the most important tasks, one of the most taxing responsibilities.” Like the Nobel deliberations, the Fields selection

process is shrouded in greatest secrecy.

The seven-member prize committee for the 1958 Fields awards was headed by Heinz Hopf, the dapper, genial, cigar-

smoking geometer from Zurich who showed so much interest in Nash’s embedding theorem, and included another prominent

German mathematician, Kurt Friedrichs, formerly of Göttingen, and then at Courant. The deliberations got under way in late

1955 and were concluded early in 1958. (The medalists were informed, in strictest secrecy, in May 1958 and actually

awarded their medals at the Edinburgh congress the following August.)

All prize deliberations involve elements of accident, the biggest one being the composition of the committee. As one

mathematician who took part in a subsequent. committee said, “People aren’t universalists. They’re horse trading.” In 1958,

there were a total of thirty-six nominees, as Hopf was to say in his award ceremony speech, but the hot contenders

numbered no more than five or six. That year the deliberations were unusually contentious and the prizes, which ultimately

went to Rent Thom, a topologist, and Klaus F. Roth, a number theorist, were awarded on a four-three vote. “There were lots

of politics in that prize,” one person close to the deliberations said recently. Roth was a shoo-in; he had solved a fundamental

problem in number theory that the most senior committee member, Carl Ludwig Siegel, had worked on early in his career.

“It was a question of Thom versus Nash,” said Moser, who heard reports of the deliberations from several of the

participants. “Friedrichs fought very hard for Nash, but he didn’t succeed,” recalled Lax, who had been Friedrichs’s student

and who heard Friedrichs’s account of the deliberations. “He was upset. As I look back, he should have insisted that a third

prize be given.”

Chances are that Nash did not make the final round. His work on partial differential equations, of which Friedrichs would

have/been aware, was not yet published or properly vetted. He was an outsider, which one person close to the deliberations

thought “might have hurt him.” Moser said, “Nash was somebody who didn’t learn the stuff. He didn’t care. He wasn’t

afraid of moving in and working on his own. That doesn’t get looked at so positively by other people.” Besides, there was no

great urgency to recognize him at this juncture; he was just twenty-nine.

No one could know, of course, that 1958 would be Nash’s last chance. “By 1962, a Fields for Nash would have been out of

the question,” Moser said recently. “It would never have happened. I’m sure nobody even thought about him anymore.”

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