Abel Prize awarded for research into the randomness of the universe
A French mathematician has been awarded this year’s Abel Prize, the mathematical equivalent of the Nobel Prize, for advances in understanding the randomness in the universe – the heights of ocean waves crashing onto a beach, the weight of babies, the ups and downs of nature. market – work that has found use in mathematical physics and statistics.
The Norwegian Academy of Science and Letters, which administers the Abel Prize, announced Wednesday morning that the recipient was 72-year-old Michel Talagrand, a former researcher at the French National Center for Scientific Research.
“Talagrand is an exceptionally productive mathematician whose work has transformed probability theory, functional analysis and statistics,” the academy said in its award ceremony. “His research is characterized by a desire to understand interesting problems at their most fundamental level, and to build new mathematical theories along the way.”
Dr. Talagrand will receive 7.5 million Norwegian krone, or about $700,000. That money, along with money he won in 2019 for the Shaw Prize, another prestigious prize, will go toward a new prize “in my favorite areas of mathematics,” he said.
As a 15-year-old, a month in hospital helped boost his math skills. Ten years earlier, he had gone blind in his right eye after a detached retina, the result of a genetic condition. Then the retina in his left eye also detached. His father, a college math teacher, taught him math while his eyes were bandaged.
“This is how I learned the power of abstraction,” wrote Dr. Talagrand an autobiography for the Shaw Prize.
Until then he was an average student. “The trauma made me a different person, in ways that are still mysterious to me,” he wrote. “When I went back to school, I was an excellent student, at least in math and science.”
In an alternate universe, Dr. Talagrand might have ended up as a high school teacher and not done any research. But he also applied for a position at the National Center for Scientific Research that did not require a PhD.
He was hired in 1974 and remained with the center until his retirement in 2017. (He received his PhD from the University of Paris VI in 1977.)
The Abel Commission mentioned three areas of Dr. Talagrand.
One of these concerns so-called stochastic processes – temperatures, water level in a river, market fluctuations – where measurements fluctuate randomly. Dr. Talagrand investigated how to estimate the maximum of such random measurements. For example, someone who builds a house along a river would like to know what the risk of flooding is.
“You look at the river level as a stochastic process, and it evolves over time, and you want to find the maximum that this level can have over a 25-year period,” said Helge Holden, chairman of the awards committee.
An exact calculation is impossibly complex, but Dr.’s statistical methods. Talagrand were able to provide good estimates, better than he expected when he started the research.
“In this case, the universe turned out to be beautiful,” said Dr. Talagrand. “As simple as it can be.”
Assaf Naor, a professor of mathematics at Princeton University, said Dr. Talagrand could use ideas from geometry to analyze what could be said about arbitrary measurements.
“This is a very remarkable connection,” said Dr. Naor.
The technique has broad applicability, said Dr. Naor. “I’m not saying it’s easy to implement, but you know that if you follow his recipe, if you succeed, you will discover the truth.”
A second area highlighted by the Abel Commission concerned the way in which Dr. Talagrand helped demonstrate that there is a degree of predictability within random processes. A simple example is tossing a coin with a 50 percent chance of heads and 50 percent of tails. Flip the coin twice and the expected value of the number of heads is one. But half the time, the result will be as far away from the expected value as possible: zero or two.
Flip the coin 1000 times and the result will be much closer to the expected value. An essay for the earlier Shaw Prize pointed out that the probability that the number of heads will fall between 450 and 550 is approximately 99.7 percent; the chance that the number will exceed 600 is virtually negligible.
The same goes for other, more complex problems, such as the number of bins needed for items of different sizes or the shortest distance a traveling salesman can travel to a number of different cities.
Later, Dr. Talagrand is interested in a physics problem known as spin glasses, which involves complex interactions between individual magnets. An example of a spin glass is iron atoms randomly mixed in a lattice of copper atoms. Based on intuition, physicist Giorgio Parisi came up with a detailed description of how these disordered magnetic materials should behave.
“To a mathematician, this makes no sense,” said Dr. Talagrand on the rationale that Dr. Parisi used.
While mathematicians devise a mathematical proof for Dr. Parisi as an impossibly difficult problem, Dr. Talagrand to try it. “I say, ‘OK, I’m not going to fix it, but there’s nothing to lose if you try,’” he said.
After five years without success, he made a simple observation that led to solid evidence showing that Dr. Parisi was right.
“It turned out the solution wasn’t that difficult,” said Dr. Talagrand. “But of course you couldn’t get up in the morning and figure it out. There must be a lot of modest work.”
Dr. Parisi shared the 2019 Nobel Prize in Physics for his spin glass work.
For problems that Dr. Talagrand himself has not found out, he has offered money to anyone who can. On his website he proclaims, “Get RICH with my prizes,” listing five problems. One of them, known as the Bernoulli conjecture, was indeed solved in 2012, and Dr. Talagrand paid out the $5,000 prize to the two mathematicians who provided the proof.
“I worked on it continuously for over a decade, but I couldn’t solve it,” said Dr. Talagrand. “The most beautiful piece of mathematics I have ever seen. And I was very happy when they solved this, because I could never have done something so difficult.”
Unlike Nobel laureates who find out just before the prizes are announced publicly, Abel laureates get the news a few days in advance, usually from colleagues who have learned the secret before.
“The people who knew set up quite a trap,” Dr. Talagrand said, referring to a subterfuge of a telephone interview request to inform him of the Abel Prize news.
“My mind went completely blank for a good five seconds when I heard that,” said Dr. Talagrand in an interview. “I wouldn’t have been more surprised if I had seen the alien ship land in front of the White House.”