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 suggesting the research program that ultimately led to the proof, by Grigori Perelman, of the Thurston geometrization conjecture and the solution of the Poincaré conjecture.
Hamilton was awarded the Oswald Veblen Prize in Geometry in 1996 and the Clay Research Award in 2003. He was elected to the National Academy of Sciences in 1999 and the American Academy of Arts and Sciences in 2003. He also received the AMS Leroy P. Steele Prize for a Seminal Contribution to Research in 2009.
- Hamilton, Richard S. (1982), "Three-manifolds with positive Ricci curvature", Journal of Differential Geometry 17 (2): 255–306, MR664497, ISSN 0022-040X, http://projecteuclid.org/getRecord?id=euclid.jdg/1214436922 The paper that introduced Ricci flow.
- Cao, Huai-Dong (2003), Collected Papers on Ricci Flow, Boston: International Press, ISBN 1571461108 .