Virtuoso Mathematician Who Reshaped Topology Wins Abel Prize

One of the most prestigious awards in mathematics is given to a US mathematician named Dennis Sullivan.

Sullivan has changed the landscape of topology by introducing new concepts, proving landmark theorems, answering old conjectures, and formulating new problems that have driven the field forwards, according to the citation for the 2022. Sullivan has moved from one area of mathematics to another and solved problems using a wide variety of tools, according to the citation. The prize is worth over a million dollars.

Hans Munthe-Kaas is a mathematician at the University of Bergen and chair of the prize committee. Sullivan is one of the mathematicians who did their most renowned work in the mid-to-late twentieth century. Karen Uhlenbeck, a mathematician at the University of Texas at Austin, is the only one so far who has been a woman.

Manifold maths

Sullivan was born in Michigan and grew up in Texas. He started his mathematical career in the 1960s. Efforts to classify all possible manifolds were the focus of the field of topology at that time. There are manifolds that appear indistinguishable from the plane or higher-dimensional space. The global shape of a manifold can be different from that of flat space, just like the surface of a sphere is different from a 2D sheet.

In the late 19th century, mathematicians realized that the manifolds had vastly different behavior depending on the number of dimensions of the object. The study of manifolds of up to four dimensions had a very geometrical flavour, and techniques used to investigate these manifolds by cutting them apart and putting them back together got scientists only so far. For objects with a higher number of dimensions, such techniques enabled researchers to get further. Sullivan and others were able to achieve a nearly complete classification of manifolds by breaking down the problem into one that could be solved with algebra calculations, according to a mathematician at the Norwegian University of Science and Technology. Sullivan says that the result he obtained in 1977 is the proudest of him. This was one of his most popular works.

Sullivan's interests moved to dynamical systems in the 1980s. These are systems that evolve over time and can be more abstract. Munthe-Kaas says that Sullivan made contributions here. Sullivan gave a proof of a fact that had been discovered through computer simulations. Sullivan's work explained why certain numbers appeared to be popping up across many types of dynamical system. Sullivan had to find new ideas after other mathematicians tried the proof with existing tools.

Sullivan has become interested in the turbulent behavior of fluids over the years. He wants to discover patterns that will make motion predictable on a large scale.

The article was first published on March 23.