He received his PhD from Northwestern University in 1984 under the direction of Mark Mahowald, with thesis Stable Decompositions of Certain Loop Spaces.

For example, the nilpotence conjecture states that some suspension of some iteration of a map between finite CW-complexes is null-homotopic iff it is zero in complex cobordism.

[3] Another result in this spirit proven by Hopkins and Douglas Ravenel is the chromatic convergence theorem, which states that one can recover a finite CW-complex from its localizations with respect to wedges of Morava K-theories.

-ring spectra – this allowed to take homotopy fixed points of finite subgroups of the Morava stabilizer groups, which led to higher real K-theories.

[6][7] On April 21, 2009, Hopkins announced the solution of the Kervaire invariant problem, in joint work with Mike Hill and Douglas Ravenel.

[9] This includes papers on smooth and twisted K-theory and its relationship to loop groups[10] and also work about (extended) topological field theories,[11] joint with Daniel Freed, Jacob Lurie, and Constantin Teleman.