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Dennis P. Sullivan, a professor of arithmetic at Stony Brook College and the Metropolis College of New York Graduate Middle, is the winner of this yr’s Abel Prize — the equal of a Nobel in arithmetic.
In its quotation, the Norwegian Academy of Science and Letters, the group that administers the Abel, mentioned Dr. Sullivan was honored “for his groundbreaking contributions to topology in its broadest sense, and particularly its algebraic, geometric and dynamical points.”
Topology is the examine of house and shapes, and most of Dr. Sullivan’s work entails what mathematicians name manifolds — the higher-dimensional variations of two-dimensional surfaces. Whereas that work is summary, a few of his latest analysis in fluid flows and turbulence may add to the understanding of the paths of hurricanes, the dispersions of air pollution and the whorls of vortices behind airplane wings.
There is no such thing as a Nobel Prize in arithmetic, and for many years, essentially the most prestigious awards in math had been the Fields Medals, awarded in small batches each 4 years to essentially the most achieved mathematicians who’re 40 or youthful.
The Abel, named after Niels Henrik Abel, a Norwegian mathematician, is ready up extra just like the Nobels. Since 2003 it has been given yearly to focus on essential advances in arithmetic. Earlier laureates embrace Andrew J. Wiles, who proved Fermat’s final theorem and is now on the College of Oxford; John F. Nash Jr., whose life was portrayed within the film “A Lovely Thoughts”; and Karen Uhlenbeck, an emeritus professor on the College of Texas at Austin who in 2019 turned the primary lady to obtain an Abel.
Ulrike Tillmann, a mathematician on the College of Oxford who served on the Abel committee, mentioned that given Dr. Sullivan’s “completely incredible work” in each algebraic topology and dynamical programs, “it was an easy determination to make.”
Dr. Sullivan mentioned he had a “good response” to the information.
“I’m 81,” he mentioned. “They bear in mind me.”
The prize is accompanied by 7.5 million Norwegian kroner, or about $850,000.
Dr. Sullivan was born in Port Huron, Mich., in 1941; his household later moved to Houston.
In a parallel universe, Dr. Sullivan maybe spent his profession as a chemical engineer. That was his main at Rice College till his sophomore yr. At some point throughout a complicated calculus lecture, the professor drew two shapes on the blackboard — one a circle, the opposite extra blobby, like a kidney. He then mentioned you would stretch both one to suit on the opposite.
That was not significantly shocking. However then the professor mentioned there was a approach — and primarily only one approach — to do the stretching such that the stretching was the identical in all instructions.
“This blew my thoughts,” Dr. Sullivan recalled. “This was not like arithmetic I’d realized as much as that time. It was a lot deeper.”
He switched from chemical engineering to math, and he accomplished a doctorate at Princeton in 1966.
Dr. Sullivan was an early adopter of a way generally known as surgical procedure principle. Utilizing this technique allowed for modern mathematical explorations, reminiscent of chopping two spherical holes in a sphere after which gluing one finish of a tube to every of the holes on the surface of the sphere, producing a kettleball-like form.
That allowed mathematicians to check what sorts of topologies may very well be stitched collectively.
Dr. Sullivan used surgical procedure principle to check how manifolds may very well be divided into less complicated items: For instance, a two-dimensional manifold just like the floor of a sphere could be approximated by triangles which might be then glued again collectively.
It was recognized that each one triangulations of two-dimensional surfaces are equal, and the identical was true for three-dimensional manifolds.
It was conjectured that the assertion was true for manifolds of all dimensions, and Dr. Sullivan confirmed that it was nearly all the time true in 5 dimensions or extra.
It turns on the market are a couple of exceptions the place two triangulations of a five-dimensional manifold should not equal. Different mathematicians subsequently confirmed that the conjecture was not true for a lot of four-dimensional manifolds.
Later, Dr. Sullivan shifted his focus to dynamical programs, though these issues nonetheless concerned manifolds. “Dynamical programs occur inside manifolds,” he mentioned. “It’s a solution to return to that geometric context.”
One among his lasting contributions is what is called the “Sullivan dictionary,” which hyperlinks dynamics with three-dimensional geometry. That enabled him to show a mathematical conjecture that had been unsolved for the reason that Twenties.
The deep and surprising connections between these disciplines additionally helped Dr. Sullivan work out the mathematical underpinnings of a phenomenon generally known as interval doubling that had been found and studied by physicists.
It was not a simple downside. “You needed to discover the speculation that made it true,” Dr. Sullivan mentioned. “It took eight years.”
“He ushered in an entire new principle of complicated dynamical programs,” mentioned Curtis T. McMullen, a Harvard mathematician who accomplished his graduate research with Dr. Sullivan as his adviser. “The instruments that he used, and much more so the analogies that he put to the fore, have been guiding the sector ever since.”
Dr. Sullivan has since additionally tackled issues in fluid dynamics.
When Dr. Sullivan accepted the Balzan Prize for Arithmetic in 2014, he mentioned he hoped to check whether or not the theoretical instruments he had developed may very well be utilized to sensible issues like hurricane prediction and the air resistance of plane wings.
Dr. Sullivan mentioned he couldn’t but present that he had give you higher laptop fashions. “However I might say, we’re heading in the right direction,” he mentioned.
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