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David Bryant Mumford

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11 June 1937

Worth, Sussex, England

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David Mumford's father, William Mumford, was English and :

... a visionary with an international perspective, who started an experimental school in Tasmania based on the idea of appropriate technology...

Mumford's father worked for the United Nations from its foundations in 1945 and this was his job while Mumford was growing up. Mumford's mother was American and the family lived on Long Island Sound in the United States, a semi-enclosed arm of the North Atlantic Ocean with the New York- Connecticut shore on the north and Long Island to the south.

After attending Exeter School, Mumford entered Harvard University. It was at Harvard that Mumford first became interested in algebraic varieties. He relates in :

... a classmate said "Come with me to hear Professor Zariski 's first lecture, even though we won't understand a word" and Oscar Zariski bewitched me. When he spoke the words "algebraic variety", there was a certain resonance in his voice that said distinctly that he was looking into a secret garden. I immediately wanted to be able to do this too. It led me to 25 years of struggling to make this world tangible and visible.

After graduating from Harvard, Mumford was appointed to the staff there. He was appointed professor of mathematics in 1967 and, ten years later, he became Higgins Professor. He was chairman of the Mathematics Department at Harvard from 1981 to 1984 and MacArthur Fellow from 1987 to 1992.

Mumford's greatest honour was being awarded a Fields Medal at the International Congress in Vancouver in 1974. Tate describes the work that Mumford was awarded the Fields Medal for in . He writes:

Mumford's major work has been a tremendously successful multi-pronged attack on problems of the existence and structure of varieties of moduli, that is, varieties whose points parameterise isomorphism classes of some type of geometric object. Besides this he has made several important contributions to the theory of algebraic surfaces. ... Mumford has carried forward, after Zariski , the project of making algebraic and rigorous the work of the Italian school on algebraic surfaces. He has done much to extend Enriques ' theory of classification to characteristic p > 0, where many new difficulties appear.

Tate goes on to explain in more technical terms Mumford's work in and it is also described in . In the 1980s however, the direction of Mumford's work changed dramatically. He writes in that, after his first wife Erika died:

... I turned from algebraic geometry to an old love - is there a mathematical approach to understanding thought and the brain? This is applied mathematics and I have to say that I don't think theorems are very important here. I met remarkable people who showed me the crucial role played by statistics, Grenander, Geman and Diaconis.

The article is a survey of this new area that Mumford has worked on. It makes fascinating reading and we quote here some comments from the introduction which give an idea of the scope of the ideas covered:

The term "Pattern Theory" was introduced by Ulf Grenander in the 70's as a name for a field of applied mathematics which gave a theoretical setting for a large number of related ideas, techniques and results from fields such as computer vision, speech recognition, image and acoustic signal processing, pattern recognition and its statistical side, neural nets and parts of artificial intelligence. ... The problem that "Pattern Theory" aims to solve ... may be described as follows "the analysis of the patterns generated by the world in any modularity, with all their naturally occurring complexity and ambiguity, with the goal of reconstructing the processes, objects and events that produced them and of predicting these patterns when they reoccur".

Mumford has received many honours in addition to the Fields Medal. He received an honorary D.Sc. from the University of Warwick in 1983 and he is a member of the National Academy of Sciences . He was elected President of the International Mathematical Union in 1995, a position he will hold until 1999.

Source:School of Mathematics and Statistics University of St Andrews, Scotland