  The question of when the Kervaire invariant is nontrivial was the only
question left unresolved by Kervaire and Milnor in their 1963 study of the
relationship between groups of homotopy spheres and stable homotopy groups. In
2009, Mike Hill, Mike Hopkins, and Doug Ravenel resolved this question except
in one dimension, by a highly innovative attack using large amounts of
equivariant stable homotopy theory and small amounts of computation. The
present paper is a Seminaire Bourbaki report on this work.
