Mark Mahowald

Mark Mahowald
Born	(1931-12-01)December 1, 1931 Albany, Minnesota
Died	July 20, 2013(2013-07-20) (aged 81) Illinois, United States
Nationality	United States
Fields	Mathematics
Institutions	Northwestern University
Alma mater	University of Minnesota
Doctoral advisor	Bernard Russell Gelbaum
Doctoral students	Michael J. Hopkins Gary I. Gutman
Known for	Homotopy groups of spheres

Michael J. Hopkins

Mark Edward Mahowald (December 1, 1931 – July 20, 2013) was an American mathematician known for work in algebraic topology.

Mahowald was born in Albany, Minnesota in 1931. He received his Ph.D. from University of Minnesota in 1955 under the direction of Bernard Russell Gelbaum with a thesis on Measure in Groups. In the sixties, he became professor at Syracuse University and around 1963 he went to Northwestern University in Chicago.

Much of Mahowald's most important works concerns the homotopy groups of spheres, especially using the Adams spectral sequence at the prime 2. He is known for constructing one of the first known infinite families of elements in the stable homotopy groups of spheres by showing that the classes ${\displaystyle h_{1}h_{j}}$ survive the Adams spectral sequence for ${\displaystyle j\geq 3}$. In addition, he made extensive computations of the structure of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Barratt, Tangora and Kochman. Using these computations, he could show that a manifold of Kervaire invariant 1 exists in dimension 62.

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