John Milnor, the American mathematician known for his discovery of exotic hyperspheres, has been awarded the 2011 Abel Prize by the Norwegian Academy of Science and Letters. The Abel Prize, which is accompanied by a cash award of USD$1 million, is generally regarded as the equivalent of the Nobel Prize in the field of mathematics.

Milnor’s principal field of study is the field of differential topology. One of Milnor’s discoveries was an exotic hypersphere in seven dimensions. Milnor showed that the solution of a problem such the propagation of waves or heat on this manifold could not be smoothly translated to solutions on an ordinary Euclidean 7-dimensional sphere — the spheres are not equivalent from the viewpoint of differential topology.

The study of n-dimensional hyperspheres has been the center of a number of recent high-profile mathematical results, including the Poincare conjecture, which is that a n-dimensional sphere (in n+1-dimensional space) is essentially characterized by the property of simple connectivity. In 1966 Stephen Smale, another recipient of the Fields Medal, proved this conjecture in all dimensions greater than four. In 2004, Russian mathematician Grigory Perelman completed the proof for the 3-dimensional sphere (for which he was offered, but declined, a $1,000,000 “Millennium Prize” from the Clay Mathematics Institute). The 4-dimensional case remains open.

Some additional information is available in this article from the *Scientific American* website: SciAm article