Dennis P. Sullivan, a professor of mathematics at Stony Brook University and the City University of New York Graduate Center, has won this year’s Abel Award. This is equivalent to the Nobel Prize in mathematics.
In the quote, the Norwegian Academy of Sciences and Literature, the organization that manages Abel, said Dr. Sullivan “made a breakthrough contribution to topology in the broadest sense, especially algebraic, geometric and dynamic aspects. “In response,” he said he was honored.
Topology is the study of space and shape, and most of Dr. Sullivan’s work involves what mathematicians call manifolds, a higher-dimensional version of a two-dimensional surface. His work is abstract, but some of his recent work on fluid flow and turbulence includes hurricane paths, air pollutant dispersal, and vortex swirls behind the wing of an airplane. May be added to your understanding.
There is no Nobel Prize in mathematics. For decades, the most prestigious award in mathematics was the Fields Medal, which is awarded every four years to the most skilled mathematicians under the age of 40.
Named after the Norwegian mathematician Niels Henrik Abel, Abel was founded like the Nobel. It has been given annually to highlight significant advances in mathematics since 2003. Previous winners include Andrew J. Wiles, who proved Fermat’s Last Theorem and is now enrolled at Oxford University. John F. Nash Jr., whose life was depicted in the movie “A Beautiful Mind”. Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin, became the first woman to receive Abel in 2019.
Ulrike Tillmann, a mathematician at Oxford University and a member of the Abel Commission, said, “It was a very easy decision,” given Dr. Sullivan’s “absolutely great work” in both algebraic topology and dynamical systems. Said.
Dr. Sullivan said he had a “good reaction” to the news.
“I’m 81 years old,” he said. “They remember me.”
The prize will be accompanied by 7.5 million Norwegian kroner, or about $ 850,000.
Dr. Sullivan was born in 1941 in Port Huron, Michigan. His family later moved to Houston.
In the Parallel Universe, Dr. Sullivan probably spent his career as a chemical engineer. It was his major at Rice University until his sophomore year. One day during a lecture on advanced calculus, the professor drew two shapes on the blackboard. One is a circle and the other is more fluffy like a kidney. Then he said you could stretch either to fit the other.
It wasn’t particularly surprising. However, the professor said that there is a way to stretch so that the stretch is the same in all directions, which is essentially one way.
“This has blown my heart,” recalled Dr. Sullivan. “This wasn’t like the math I had learned so far. It was a lot deeper.”
He switched from chemical engineering to mathematics and received his PhD in Princeton in 1966.
Dr. Sullivan early adopted a technique known as surgery theory. Using this method, you can make innovative mathematical studies such as making two round holes in the sphere and gluing one end of the tube to each hole on the outside of the sphere to create a kettleball-like shape. became.
This allowed mathematicians to study what kind of topology could be stitched together.
Dr. Sullivan used surgical theory to study how to divide a manifold into simpler parts. For example, a two-dimensional manifold, such as the surface of a sphere, can be approximated by a triangle and then glued.
All triangulations on a 2D surface are known to be equivalent, and the same is true for 3-manifolds.
It is speculated that this claim applies to manifolds of all dimensions, and Dr. Sullivan has shown that it almost always applies to the 5th and higher dimensions.
We can see that there are some exceptions where the two triangulations of a 5-manifold are not equivalent. Later, other mathematicians have shown that the speculation is not true for many 4-manifolds.
Dr. Sullivan then shifted his focus to dynamical systems, but those issues were still related to manifolds. “Dynamic systems happen inside manifolds,” he said. “It’s a way to get back to that geometric context.”
One of his lasting contributions is what is known as the “Sullivan Dictionary” that links dynamics and 3D geometry. It made it possible for him to prove mathematical inferences that had not been resolved since the 1920s.
The deep and unexpected connections between these disciplines also helped Dr. Sullivan understand the mathematical basis of the phenomenon known as periodic-doubling bifurcation, which was discovered and studied by physicists.
It wasn’t an easy problem. “You had to find a hypothesis that made it true,” said Dr. Sullivan. “It took eight years.”
“He led a whole new theory of complex dynamical systems,” said Harvard mathematician Curtis T. McMullen, who completed his graduate studies with Dr. Sullivan as an advisor. “The tools he used, and even the analogies he brought to the fore, have led the field ever since.”
Since then, Dr. Sullivan has also tackled the problem of fluid mechanics.
When Dr. Sullivan won the Fields Medal in 2014, he said he wanted to test whether the theoretical tools he developed could be applied to real problems such as hurricane prediction and air resistance of aircraft wings. rice field.
Dr. Sullivan said he could not yet show that he had come up with a better computer model. “But I think we’re heading in the right direction,” he said.