Influential Mathematician Wins Honor Akin to Nobel

In 1967, Robert P. Langlands set out a road map to prove a “grand unified theory” that would tie together disparate areas of mathematics.

The conjectures of Langlands, now 81 and an emeritus professor at the Institute for Advanced Study in Princeton, New Jersey, have proved fertile ground for mathematical advances in the past half-century. And although his suppositions remain far from fully proven, the Norwegian Academy of Science and Letters announced Tuesday that Langlands was this year’s winner of the Abel Prize, which many view as a Nobel Prize of mathematics.

“He’s a visionary,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee. The panel reviewed more than 100 candidates before selecting Langlands, Chang said.

There is no Nobel Prize in mathematics. (Contrary to myth, that is not because of an affair between a mathematician and Alfred Nobel’s wife. For one, Nobel never married.)

For decades, the most prestigious math awards were the Fields Medals, but they are limited to mathematicians 40 years or younger, to recognize the promise of future discoveries as well as work already accomplished. The Fields medals are also only given out every four years.

The Abel Prize, first awarded in 2003, honors a lifetime of mathematical work and influence. It is named after Niels Hendrik Abel, a Norwegian mathematician. Previous winners include Andrew J. Wiles, a mathematician now at the University of Oxford who proved Fermat’s Last Theorem; Peter D. Lax of New York University; and John F. Nash Jr., whose life was portrayed in the movie “A Beautiful Mind.”

In an interview in 2010, Langlands, who was born in New Westminster, Canada, near Vancouver, recalled that even though he skipped a grade, he had no intention of going to college until a teacher “took up an hour of class time to explain to me, in the presence of all the other students, that it would be a betrayal of God-given talents for me not to attend university.”

At the age of 16, he enrolled at the University of British Columbia, and he later pursued his doctoral studies at Yale.

As a professor at Princeton, Langlands started investigating ideas that connected the mathematics of integers with a generalization of the theory of periodic functions. Periodic functions are repeating patterns like the undulations of a sine wave in trigonometry. More than two centuries ago, mathematicians developed a method called Fourier analysis for describing, for example, the vibrations of a guitar string as the combination of multiple sine waves.

Langlands made use of this type of analysis in curved spaces of higher dimensions (that is, more than the three dimensions of the world we live in) to address fundamental problems in the theory of numbers.

In 1967, Langlands spoke with André Weil, a prominent French mathematician then at the nearby Institute for Advanced Study, who told him to put his thoughts in writing.

The result was 17 pages, handwritten. “After I wrote it I realized there was hardly a statement in it of which I was certain,” Langlands wrote apologetically. “If you are willing to read it as pure speculation I would appreciate that; if not — I am sure you have a wastebasket handy.”

Weil had the letter typed up, and it circulated among other mathematicians, becoming what was known as the “Langlands program.” Langlands proved a few pieces of it; others have solved additional special cases.

“He never got a Fields medal,” said Peter C. Sarnak, a mathematician at the institute said of Langlands. “But many people have got Fields Medals for settling special cases of his conjectures, relying on his tools to start off.” The Abel committee contacted Sarnak a few days ago as a sort of spy to check that Langlands would be around to receive the news on Monday morning, a day before the official announcement. “It seems like they do this kind of detective work, I guess,” Sarnak said.

Even though the conjectures have not been proven in general, Sarnak was sure they would be eventually. “There’s no question about the truth,” he said. “It’s so intellectually compelling, it cannot not be true. God would never make the world in which that was not true.”

King Harald V of Norway is to present the prize, accompanied by $764,000, to Langlands at a ceremony in Oslo on May 22.