# American mathematician Dennis Sullivan wins prestigious Abel Prize

American mathematician Dennis Sullivan received the 2022 Abel Prize, one of the most prestigious prizes in mathematics, for his contributions to the fields of topology and dynamical systems.

According to a __declaration__ of the Norwegian Academy of Sciences and Letters (DNVA), which distributes the prize each year as well as a prize worth approximately $864,000 (7.5 million Norwegian kroner), Sullivan was recognized “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects.”

Topology is the study of the properties of objects and spaces that do not change when deformed. The field is sometimes referred to as “rubber sheet geometry”, because objects can be stretched into different shapes like rubber but cannot be broken, depending on the __University of Waterloo__ in Ontario. For example, a square can be deformed into a circle without breaking, but a donut shape cannot. Thus, a square is topologically equivalent to a circle, but a donut is not.

Sullivan, now a professor of __mathematics__ at Stony Brook University in New York, was born in Port Huron, Michigan on February 12, 1941. He began studying topology as a graduate student at Princeton University in the early 1960s. His thesis dissertation from 1966, titled “Triangulating Homotopy Equivalences”, helped revolutionize the study of manifolds, spaces that appear flat when viewed from any point on their surface but have a more complicated overall structure ( like the surface of a sphere), according to the DNVA.

Over the next few decades, Sullivan held fellowships at the University of Warwick, England; the University of California, Berkeley; and MIT.

“During this time, he gradually changed the way mathematicians thought about algebraic and geometric topology, introducing new ideas and building new vocabulary,” according to the DNVA. “In 1970 he wrote a set of unpublished notes which have been widely circulated and considered extremely influential, having a direct impact on the classification of smooth varieties and central problems in algebraic topology.” (These so-called MIT notes were finally published in 2006.)

In the late 1970s, Sullivan began studying the problems of dynamical systems, that is, the study of a point moving in geometric space and a fundamental part of __chaos theory__. His work united dynamical systems and algebraic topology in a way that had never been done. In 1985, Sullivan proved a 60-year-old conjecture that points moving through complex dynamic systems in fractal patterns eventually return to their starting point rather than wander endlessly, according to __Quanta Magazine__.

“Dennis P. Sullivan repeatedly changed the landscape of topology by introducing new concepts, proving historical theorems, answering old conjectures, and formulating new problems that moved the field forward,” said Hans Munthe-Kaas, chairman of the Abel committee. DNVA declaration. “I’m not sure he sees the boundaries between different areas of mathematics the way others see them.”

For more, read a full biography of Sullivan and career highlights, __courtesy of DNVA__.

*Originally posted on Live Science.*

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