Perelman's Tryst with Unsolved Problems and the Big Prizes (which he rejects)

August 22, 2006 – Grigori Perelman is awarded the Fields Medal for his proof of the Poincaré conjecture in mathematics but refuses to accept the medal.

Who is Grigori Perelman?

Grigori Yakovlevich Perelman is a Russian mathematician. Grigori's mathematical talent became apparent at the age of ten, and he was enrolled in the Leningrad Secondary School #239, a specialized school with advanced mathematics and physics programs. Grigori excelled in all subjects except physical education.

In 1982, as a member of the Soviet Union team competing in the International Mathematical Olympiad, an international competition for high school students, he won a gold medal, achieving a perfect score.

What is the Poincaré conjecture?

Originally conjectured by Henri Poincaré, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. The analogous conjectures for all higher dimensions had already been proved.

The Poincaré conjecture was one of the most important open questions in topology. In 2000, it was named one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture. Perelman's work survived review and was confirmed in 2006.

What is the Fields Medal?

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.

The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the mathematician's "Nobel Prize.” The name of the award is in honor of Canadian mathematician John Charles Fields.

Perelman’s Tryst with the Awards

In August 2006, Perelman was offered the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

Perelman was awarded the Millennium Prize on March 18, 2010. He turned down the prize saying that he believed his contribution in proving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow with the aim of attacking the conjecture.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first time this honor was bestowed in the area of mathematics.

As of 2018, the Poincaré conjecture is the only solved Millennium problem.

Read an interesting article in The Guardian

x