[[File:Perelman, Grigori (1966).jpg|thumb|right|[[Grigori Perelman]]]]
On November 1311, 2002, Russian mathematician [[Grigori Perelman]] posted the first of a series of three [[E-print|eprints]] on [[arXiv]] outlining a solution of the Poincaré conjecture. Perelman's proof uses a modified version of a [[Ricci flow]] program developed by [[Richard S. Hamilton]]. In August 2006, Perelman was awarded, but declined, the [[Fields Medal]] (worth $15,000 CAD) for his work on the Ricci flow. On March 18, 2010, the [[Clay Mathematics Institute]] awarded Perelman the $1 million [[Millennium Prize Problems|Millennium Prize]] in recognition of his proof.<ref>{{cite web |url=http://www.claymath.org/poincare/ |date=March 18, 2010 |title=Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman |url-status=dead |archive-url=https://web.archive.org/web/20100322192115/http://www.claymath.org/poincare/ |archive-date=2010-03-22 |publisher=Clay Mathematics Institute }}</ref><ref>{{cite web |title=Poincaré Conjecture |url=http://www.claymath.org/millennium/poincare-conjecture/ |publisher=Clay Mathematics Institute |access-date=2018-10-04}}</ref> Perelman rejected that prize as well.<ref name="interfax" /><ref name="PhysOrg1">{{cite web |url=https://phys.org/news/2010-07-russian-mathematician-million-prize.html |title=Russian mathematician rejects $1 million prize |publisher=[[Phys.Org]] |author=Malcolm Ritter |date=2010-07-01 |access-date=2011-05-15}}</ref>
Perelman proved the conjecture by deforming the manifold using the Ricci flow (which behaves similarly to the [[heat equation]] that describes the diffusion of heat through an object). The Ricci flow usually deforms the manifold towards a rounder shape, except for some cases where it stretches the manifold apart from itself towards what are known as [[Mathematical singularity|singularities]]. Perelman and Hamilton then chop the manifold at the singularities (a process called "surgery"), causing the separate pieces to form into ball-like shapes. Major steps in the proof involve showing how manifolds behave when they are deformed by the Ricci flow, examining what sort of singularities develop, determining whether this surgery process can be completed, and establishing that the surgery need not be repeated infinitely many times.
