Richard Hamilton, an inventive mathematician who devised the Ricci flow, a groundbreaking equation that helped advance understanding of the fundamental nature of three-dimensional space, died on Sept. 29 in Manhattan. He was 81.

The death, in a hospital, was confirmed by his son, Andrew. Dr. Hamilton had taught at Columbia University since 1998.

In 1982, Dr. Hamilton published “Three-manifolds with positive Ricci curvature” in The Journal of Differential Geometry. The article laid out his revolutionary theory: a kind of geometric analog to the heat equation in physics.