29 September, 2024 – Professor Richard S Hamilton, Shaw Laureate in Mathematical Sciences 2011, Davies Professor of Mathematics at Columbia University, USA, passed away at the age of 81.

Professor Hamilton shared the Prize with Professor Demetrios Christodoulou and the pair were recognised for their highly innovative works on non-linear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.

Notably, Professor Hamilton introduced the Ricci flow in Riemannian geometry. This is a differential equation which evolves the geometry of a space according to how it is curved. He used it to establish striking results about the shape (topology) of positively curved three and four dimensional spaces. He developed a host of original and powerful techniques to study his flow; for example a technique called surgery allowing for the continuation of the evolution should singularities form. A primary goal of his theory was to classify all shapes in dimension three and in particular to resolve the Poincare Conjecture. Professor Hamilton’s program was completed in the brilliant work of Perelman. With his Ricci flow, Professor Hamilton provided one of the most powerful tools in modern geometry.

In the 2011 Shaw Prize Award Presentation Ceremony, Professor Hamilton reflected on his mathematics journey – “It’s hard for you to probably imagine how impossible and foolish this all seemed back when I started working on it in the mid-70s. But over the years, the techniques of non-linear partial differential equations have developed to be so powerful that now we can attack all kinds of problems and do all kinds of things that were only dreams back then.”

Professor Hamilton’s legacy will continue to inspire future generations of mathematicians. The Shaw Prize Foundation extends its sincerest condolences to his family, friends, and colleagues during this time of loss.

19 November 2024