Grigori Perelman was awarded the Fields Medal for his proof of the Poincaré conjecture in mathematics but refused to accept the medal.

Grigori Yakovlevich Perelman is a Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg and has declined requests for interviews since 2006.

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 name of the award honours the Canadian mathematician John Charles Fields.

In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.