12/12/2018

Millennium Problems: The Russian who refused Fields and $1 million

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

In 1998, American businessman London T. Clay (1926–2017) created the Clay Mathematics Institute to "increase and disseminate mathematical knowledge."

Two years later, the Institute launched its best-known initiative, the Millennium Problems: one million dollars for solving each of the seven mathematical problems. I've already talked here about the oldest one, the intriguing Riemann Hypothesis.

The only Millennium Problem ever solved is the Poincaré Conjecture, a statement about the three-dimensional sphere, a kind of "older sister" to the two-dimensional sphere we all know.

Formulated by the Frenchman Henri Poincaré (1854–1912) in 1904, it was proven in 2003 by the Russian Grigori Perelman (1966-).

For this achievement, in addition to being entitled to the million dollars, Perelman also received the Fields Medal, the most coveted mathematical distinction. But he shocked the international community by refusing both the money and the medal! Perelman reportedly said it would be unfair to receive the sum, since he had used the work of the American Richard Hamilton (1943-). Hamilton agreed, even demanding half the money.

The situation must have been disconcerting for the institute, especially since the prize was awarded for the first time. But they resolved it well: the money was used to fund the Poincaré Chair, a temporary position for young researchers at the Henri Poincaré Institute in Paris.

Some of the Millennium Problems involve advanced theories that are difficult to explain in simple language. This is the case with the Hodge Conjecture, proposed by the Scotsman William Hodge (1903–1975) at the 1950 International Congress of Mathematicians, which concerns the solutions of systems of algebraic equations.

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