Poincare conjecture. This problem was posed by the French mathematician Henri Poincare (1854-1912) in a paper published in 1904 on topology. The artwork shows a loop being continuously tightened to a point on a 2-sphere (the surface of a sphere). This surface property is known as simple-connectedness. Poincare's conjecture was that the same property characterises the 3-sphere (the surface of a hypersphere). This conjecture is one of the Millennium Prize Problems. The solution, building on earlier work by US mathematician Richard Hamilton, was published in 2002 and 2003 by Russian mathematician Grigori Perelman.