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David Mumford

Professor Emeritus of Applied Mathematics
Room 222, 182 George Street
Phone: +1 401 863 3441
David_MumfordBrown.edu


Ph.D., Harvard University, 1961

 

Interests

I work in the area of machine and natural intelligence, following the statistical approach pioneered by Ulf Grenander, which we call "Pattern Theory". In this approach, thinking is modeled as statistical inference rather than logic and learning results from the accumulation of massive data from interactions with the world. My work concentrates on visual perception which seems to be more approachable than high-level thinking, more complex than auditory and tactile perception yet has been solved by three distinct classes of animals (cephalopods, birds and mammals) so it can't be that hard!

The aspect of this research with which I have been most involved is the construction of probability models for the variables of vision: direct models of the raw images, the shapes of objects, the texture of their surfaces etc. A second question is how to sample and estimate with these models, e.g. compute conditional means and modes. Many approaches involve computing with one or more samples from the distribution which evolve deterministically or stochastically, smoothly or with jumps. Sampling from the distribution can be viewed as feedback, i.e. prior knowledge of high level structures guides the reconstruction of an image. A third set of questions concerns how such statistical estimation may be performed in cortex, in neural nets with feedback. A major open question here is whether the information being handled by neurons is contained only in their firing rates or in the precise timing and synchrony of their spikes in the full network. Another is how cortex handles ambiguity, the need for maintaining multiple hypotheses while waiting for more data.

Awards

1953 Westinghouse Science Talent Search, finalist


1958-1961 Society of Fellows, Harvard University, Junior Fellow


1974 Fields Medal, International Congress of Mathematics, Vancouver


1975 Elected to the National Academy of Sciences


1978 Honorary Fellow, Tata Institute of Fundamental Research


1983 Honorary Degree of Doctor of Science, University of Warwick


1987-1992 MacArthur Foundation Fellow


1991 Elected Foreign Member, Accademia Nazionale dei Lincei, Rome


1995 Elected Honorary Member, London Mathematical Society


1997 Elected American Philosophical Society


2000 Honorary Degree of DSc., Norwegian University of Science and Technology, Trondheim


2001 Honorary Degree of DSc., Rockefeller University


2004 Elected Foreign Member, Norwegian Academy of Science and Letters


2005 IEEE Longuet-Higgins Prize, CVPR 2005, (with Jayant Shah)


2006 The Shaw Prize in Mathematical Sciences, Hong Kong (shared with Wu Wentsun)


2007 Amer. Math. Society Steele Prize for Mathematical Exposition


2008 Wolf Prize in Mathematics (shared with Pierre Deligne and Phillip Griffiths)


2008 Elected Foreign Member of the Royal Society (UK)

2010 National Medal of Science