Mathematics For All

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David Mumford (born 11 June 1937) - The Fields Medalist of 1974

After attending Exeter School, Mumford enrolled at Harvard University, where he first developed an interest in algebraic varieties. He relates in [D. Mumford, Autobiography of David Mumford, in M Atiyah and D Iagolnitzer (eds.), Fields Medallists Lectures (Singapore, 1997), 225.] that

"... 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 joined the faculty there. He was appointed Professor of Mathematics in 1967 and, ten years later, became Higgins Professor. He served as Chair of the Mathematics Department at Harvard from 1981 to 1984 and was a MacArthur Fellow from 1987 to 1992.

Mumford’s greatest honour was the award of the Fields Medal at the International Congress of Mathematicians in Vancouver in 1974. In [J. Tate, The work of David Mumford, Proceedings of the International Congress of Mathematicians, Vancouver, 1974 1 (Montreal, Que., 1975), 11-15.], Tate describes the work for which Mumford received the Fields Medal, writing that

"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."

Mumford has received numerous honours in addition to the Fields Medal. He was awarded honorary D.Sc. degrees by the University of Warwick (1983), the Norwegian University of Science and Technology (2000), and Rockefeller University (2001). He was elected to the National Academy of Sciences in 1975 and became an Honorary Fellow of the Tata Institute of Fundamental Research in 1978. Further distinctions include election as a Foreign Member of the Accademia Nazionale dei Lincei, Rome (1991), Honorary Member of the London Mathematical Society (1995), and membership in the American Philosophical Society (1997), as well as election as a Foreign Member of the Royal Society in 2008.

In recognition of his contributions, Mumford received the Shaw Prize in 2006, the Steele Prize for Mathematical Exposition from the American Mathematical Society in 2007, and the Wolf Prize in 2008. He also served as President of the International Mathematical Union from 1995 to 1999.

Finally, we mention a lecture delivered by Mumford on 11 February 2008, which reflects his interests at that stage of his career. The lecture, entitled What’s an Infinite Dimensional Manifold and How Can It Be Useful in Hospitals?, was accompanied by the following abstract:

"Morphing faces has become a popular game but what is the math behind it? One way to view it is as the construction of geodesics on an infinite dimensional manifold of shapes. I will try to explain what this means, using simple examples and then go on show why it is proposed as a new tool in the diagnosis of medical conditions."

(Source: MacTutor)