AWE

COLBY COSH ON A VENERABLE CANADIAN MATH WHIZ.

Robert Langlands, a Canadian giant of contemporary mathematics, has been declared this year’s winner of the Abel Prize endowed by the government of Norway. There is a weird rule of journalism that any major monetary prize for mathematical accomplishment must immediately be compared to a Nobel Prize. If there were a math Nobel, reporters could use it as a way to understand and easily convey a person’s importance and prestige. We might even occasionally turn Nobel-laureate mathematicians into celebrity sages, as we sometimes do to unfortunate physicists.

Mathematicians, who tend to live up to stereotype when it comes to unworldliness, are mostly comfortable with this situation. It saves them a lot of crank letters. But it is a nuisance to journalists, who are forced to resort to “It’s as if so-and-so had won the Nobel!” talk. The Abel Prize was actually founded in 2002 specifically as a sort of paraNobel; the Norwegians have a lot of cash lying around, and they understand that the real Nobels have provided amazing PR for themselves and the Swedes.

Well, let us be brutal and mercenary about this. The most famous math prize is still probably the Fields Medal (named for another Canadian, who helped organize and pay for it), but that is restricted to mathematicians under 40 and comes with just C$15,000. You can still win the Abel Prize for a life’s work at age 81, as the great Langlands just has, and the accompanying cheque is for six million Norwegian kroner. This is almost exactly a million bucks, Canadian, at today’s rates.

The name of Robert Langlands, who has Einstein’s old office at the Institute for Advanced Study in Princeton, appears in the newspaper almost exclusively when he is given some such prize. It has never, if my search-fu is any good, hitherto appeared in the pages of the National Post. Yet he is on a short list of Canadians who could be said to have universal and permanent, or at least very enduring and certain, historical significance — people whose names might appear in a big printed encyclopedia in the year 2200, if we had not already mostly done away with printed encyclopedias. (If we have gone back to them in the meantime, I prefer not to think about what might have gone wrong.)

But Langlands, as I think he would be the first to admit or even insist upon, is of no merely social importance whatsoever. When journalists want to transform a physicist into a celebrity, we have recourse to romantic poster images of the farflung cosmos or the infinitesimal building blocks of reality. Physics delivered the Bomb: it will be a long time before anyone starts asking what it has done for us lately. But pure mathematics is abstraction explored or created (yes, I am papering over a philosophical abyss) for its own sake.

As it happens, the name of Robert Langlands is known wherever math is done professionally because his work, exemplified by the so-called “Langlands Program,” involves abstraction at an especially high level. Langlands works with complicated, rigorous concepts that have a spooky power of uniting areas of math that developed, and that are initially taught to young people, separately.

To take the most obvious example, they connect number theory — the behaviour of the integers, particularly the primes — with geometry and topology. Maybe you have heard of Fermat’s Last Theorem, which is simple enough for almost any yutz to understand. The theorem was cracked ultimately because of the Langlands research program — which was itself the product of certain speculative insights Langlands had in 1967, and set down in a hesitant, presumptuous letter to a respected senior scholar, Andre Weil.

The Fermat solution was almost, one might say, an attention-getting side effect of the real work: it fell out of it like a tooth. It turned out that to confirm the theorem, Big Math had to go many levels “up” from naive number theory to a world of unrecognizable — and not instinctively related — “modular forms” and “l-adic representations.”

I have met people who claim to understand this material. But not often. The “Langlands program” really is a research program, an ongoing one that keeps hundreds of people employed pursuing conjectures and filling in gaps: the name is not just jargon. And Langlands is not just the architect of this cathedral: he has helped push particular inferential stones into place over the years. He is someone of whom Canada ought to be proud, and will someday have a statue or other grand monument on the campus of UBC, where the New Westminster native earned his first two degrees.

I fear I cannot help adding that UBC’s chief contribution to his career may have been slightly inglorious. According to biographical notes by Langlands himself, his master’s thesis was “not well-written and could be understood by no one” at the university. “Moreover,” he says, “I myself discovered, very soon after submission, an error in the arguments.”

But Langlands already had an offer in hand from Yale, so the hapless UBC math department, in a spirit of frontier generosity, stamped his credential and bundled him off. He remains grateful, and so shall be many generations of mathematicians to come.