David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory.

Mumford was born in Worth, West Sussex in England, of an English father and American mother.

His father William started an experimental school in Tanzania and worked for the then newly created United Nations.

[3] He attended Phillips Exeter Academy, where he received a Westinghouse Science Talent Search prize for his relay-based computer project.

He married Erika Mumford (1935-1988), an author and poet, in 1959 and they had four children, Stephen, Peter, Jeremy, and Suchitra.

Mumford's work in geometry combined traditional geometric insights with the latest algebraic techniques.

His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique, the only accessible introduction.

Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and a study of Goro Shimura's papers from the 1960s.

Mumford's philosophy in characteristic p was as follows: A nonsingular characteristic p variety is analogous to a general non-Kähler complex manifold; in particular, a projective embedding of such a variety is not as strong as a Kähler metric on a complex manifold, and the Hodge–Lefschetz–Dolbeault theorems on sheaf cohomology break down in every possible way.In the first Pathologies paper, Mumford finds an everywhere regular differential form on a smooth projective surface that is not closed, and shows that Hodge symmetry fails for classical Enriques surfaces in characteristic two.

Worse pathologies related to p-torsion in crystalline cohomology were explored by Luc Illusie (Ann.

In the second Pathologies paper, Mumford gives a simple example of a surface in characteristic p where the geometric genus is non-zero, but the second Betti number is equal to the rank of the Néron–Severi group.

In the second Pathologies paper, Mumford finds that the Hilbert scheme parametrizing space curves of degree 14 and genus 24 has a multiple component.

[10] There is a long list of awards and honors besides the above, including He was elected President of the International Mathematical Union in 1995 and served from 1995 to 1999.