Refusal as a protest
One of the requirements for obtaining the Clay Institute prize is the publication of the problem in a specialised journal with a peer review process. But the Russian mathematician Grigori Perelman published his 2002 and 2003 works only on arXiv, the famous Cornell University website for scientific manuscripts. Those texts do not even mention the Poincaré conjecture, even though it would be a consequence of their results. When his papers were verified by the mathematical community and it was clear that they were correct, the International Mathematical Union awarded him a Fields Medal, which he should have received at the International Congress of Mathematicians held in Madrid in August 2006. But Perelman refused the prestigious award.
It is difficult to know why he rejected it. Perelman has always avoided the press, and few journalists have managed to meet and talk to him. Not even his biographer, Masha Gessen, was able to interview him about it. The most extensive and documented article about him might be the one published in The New Yorker in August 2006. The authors, Sylvia Nasar and David Gruber, explain the Poincaré conjecture, analyse different aspects of its solution (among them, an attempt to appropriate the solution), and describe an encounter with Perelman.
It seems that the keys to his refusal are fundamentally ethical. He said that the Fields Medal «was completely irrelevant to me. Everybody understood that if the proof is correct then no other recognition is needed.» But there is also a general reproach to the profession: Perelman stated that «there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.» He added that «it is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated.»
Perelman did not say at that time whether or not his objection to awards extended to the million dollar prize of the Clay Institute: «I’m not going to decide whether to accept the prize until it is offered.» However, when he was offered the prize in 2010, he rejected it as well.