Richard Streit Hamilton (January 10, 1943 – September 29, 2024) was an American mathematician who served as the Davies Professor of Mathematics at Columbia University. Hamilton is known for contributions to geometric analysis and partial differential equations, and particularly for developing the theory of Ricci flow. Hamilton introduced the Ricci flow in 1982 and, over the next decades, he developed a network of results and ideas for using it to prove the Poincaré conjecture and geometrization conjecture from the field of geometric topology. Hamilton's work on the Ricci flow was recognized with an Oswald Veblen Prize, a Clay Research Award, a Leroy P. Steele Prize for Seminal Contribution to Research and a Shaw Prize. Grigori Perelman built upon Hamilton's research program, proving the Poincaré and geometrization conjectures in 2003. Perelman was awarded a Millennium Prize for resolving the Poincaré conjecture but declined it, regarding his contribution as no greater than Hamilton's.
Life Hamilton was born in Cincinnati, Ohio, on January 10, 1943. He received his B.A. in 1963 from Yale University and PhD in 1966 from Princeton University. Robert Gunning supervised his thesis. Hamilton's first permanent position was at Cornell University. There, he interacted with James Eells, who with Joseph Sampson had recently published a paper introducing harmonic map heat flow. Hamilton was inspired to formulate a version of Eells and Sampson's work dealing with deformation of Riemannian metrics. This developed into the Ricci flow. After publishing his first paper on the topic, Hamilton moved to University of California, San Diego in the mid-1980s, joining Richard Schoen and Shing-Tung Yau in the group working on geometric analysis. In 1998, Hamilton became the Davies Professor of Mathematics at Columbia University, where he remained for the rest of his career. In 2022, Hamilton additionally joined University of Hawaiʻi at Mānoa as an adjunct professor. Hamilton's mathematical contributions are primarily in the field of differential geometry and more specifically geometric analysis. He is best known for having discovered the Ricci flow and developing a research program aimed at the proof of William Thurston's geometrization conjecture, which contains the well-known Poincaré conjecture as a special case. In 2003, Grigori Perelman introduced new ideas into Hamilton's research program and completed a proof of the geometrization conjecture. In March 2010, the Clay Mathematics Institute, having listed the Poincaré conjecture among their Millennium Prize Problems, awarded Perelman with one million USD for his 2003 proof of the conjecture. In July 2010, Perelman turned down the award and prize money, saying that he believed his contribution in proving the Poincaré conjecture was no greater than that of Hamilton. In 1996, Hamilton was awarded the Oswald Veblen Prize in Geometry "in recognition of his recent and continuing work to uncover the geometric and analytic properties of singularities of the Ricci flow equation and related systems of differential equations." In 2003 he received the Clay Research Award for "his introduction of the Ricci flow equation and his development of it into one of the most powerful tools in geometry and topology". He was elected to the National Academy of Sciences in 1999 and the American Academy of Arts and Sciences in 2003. In 2009, he received the Leroy P. Steele Prize for Seminal Contribution to Research of the American Mathematical Society for his "profoundly original" breakthrough article Three-manifolds with positive Ricci curvature, in which he first introduced and analyzed the Ricci flow.[H82b] In 2011, the million-dollar Shaw Prize was split equally between Hamilton and Demetrios Christodoulou "for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology." In 2024, he and Andrew Wiles received the Basic Science Lifetime Award in Mathematics at the International Congress of Basic Science. Hamilton died at a hospital in Manhattan, New York City on September 29, 2024, at the age of 81.
Mathematical work Hamilton was the author of forty-six research articles, the majority of which were in the field of geometric flows.
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