Describes major advances made in algebraic topology in recent years, focusing on the nilpotence and periodicity theorems, which were conjectured by the author i... » 

Describes major advances made in algebraic topology in recent years, focusing on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins and Smith in 1985. A number of significant developments in homotopy theory are addressed. «