Alex Wilkins
Dennis Sullivan has won the prize for his contributions to the study of how surfaces change.
Sullivan, who is based at New York's Stony brook University, has been studying topology for more than 50 years, often by making connections between areas of mathematics that were historically considered distinct.
Sullivan says that areas can be blocked in certain directions.
Sullivan's founding role in rational homotopy theory was one of the most important contributions to the field.
The chair of the prize committee says that Sullivan is a master in connecting diverse areas of mathematics.
Data science is one field where the mathematics of complex geometries can be used to analyse large data sets. Sullivan laid the foundations for many of the field's advances in the past couple of decades.
Sullivan has entered unrelated fields in order to connect with subjects he has already studied. He began to work on complex dynamical problems, which look at how mathematical functions change over time, often in chaotic ways. Sullivan used objects called Kleinian groups to translate the chaotic problems into simpler ones that are easier to solve.
Sullivan says that almost any place you start digging, you find good stuff. It didn't have to be that way. Mathematics is like that.
The prize is worth 7.5 million Norwegian kroner.
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