### David Mumford

Born 11 June 1937 in Worth, Sussex (England)

Fields Medal (1974) for his contributions to the question of the existence and structure of moduli spaces, i.e. algebraic varieties whose points parameterize the isomorphism classes of some type of geometric object; and for his work on algebraic surfaces (Algebraic Geometry)

David Mumford grew up in an internationally oriented household. His father had built an experimental school in Tanzania, Africa and had worked for the United Nations since its inception. Mumford spent his childhood in the U.S., where the family lived near New York City on Long Island Sound. As a young man his talent was soon discovered when in 1953 he reached the finals of the ‘Westinghouse Science Talent Search’ (now supported by Intel). At Harvard, Mumford took his bachelor’s degree (1957) and later wrote his doctoral thesis supervised by Oscar Zariski (Ph.D. in Mathematics, 1961). In 1962 he became assistant professor there, and during his first year also visited Princeton and the University of Tokyo. After his return, he became associate the same year, and later full professor (1967). Mumford visited several universities and institutes as a visiting professor, including the Tata Institute of Fundamental Research in India (1967-68 and 1978-79), the University of Warwick (1970-71) and the Institut des Hautes Etudes Scientifiques, Paris (1976-77). Between 1977 and 1997 he was Higgins Professor at Harvard University, and between 1996 and 2007 University Professor at Brown University in Providence, Rhode Island, today as emeritus.

David Mumford was President of the International Mathematical Union from 1995-1998, he is a member of the National Academy of Sciences (1975) and was MacArthur Foundation Fellow from 1987 to 1992. He has received numerous honorary degrees and awards, including the IEEE Longuet-Higgins Prize (2005), the Shaw (2006) and the Wolf Prize (2008). In 2010 he received the National Medal of Science.

“Moduli spaces are essentially maps. In an ordinary map, a point on a piece of paper corresponds to a location on the earth. Similarly, a point in a moduli space corresponds to an object of some kind, an algebraic variety (the locus of solutions of a set of polynomial equations inside projective space) or bundle or something more elaborate. All the objects are laid out for your inspection in this fine but rather intangible ‘map’ known as a moduli space.” That’s how David Mumford describes one of the main areas of his work. He used moduli spaces to classify curves, surfaces and Abelian varieties. An Abelian variety is just a variety that is also a ‘torus’, that is a complex vector space rolled up by gluing it to itself by a lattice of translations. Mumford’s work continued various aspects of the research program of Alexander Grothendieck.

In the 1980s, he shifted his interest to studying the mathematical approaches to modeling thinking and perception, specializing in the study of vision. He has developed the use of Bayesian inference with graphical models as the basic computation underlying cognitive processes.

Mumford married Erika Jentsch in 1959. She became a poet and they had four children. After her decease in 1988, he remarried to the artist Jenifer Gordon. With both families he has spent summers on the coast of Maine and sailed the Atlantic coast from Newfoundland to the Caribbean.