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Fellows Directory

David Mumford

Professor David Mumford ForMemRS

Foreign Member

Elected: 2008


David Mumford is a mathematician renowned for major contributions to two different fields. His development of geometric invariant theory in algebraic geometry is currently being applied to the quantum field theory of elementary particles. His later research in pattern theory and the related area of understanding vision from a mathematical perspective, has potential applications in computer vision.

In algebraic geometry, David’s name is associated with key results including Mumford’s compactness theorem and the Mumford vanishing theorem. With Jayant Shah, he applied variational calculus to the theory of vision. Optimisation of the Mumford–Shah functional is a crucial technique for identifying the key segments of an image.

David’s work in algebraic geometry earned him the Fields Medal in 1974. He was elected to the US National Academy of Sciences in 1975. David has also received the Shaw Prize in Mathematics, the Steele Prize, and the Wolf Prize in Mathematics. From 1995–98, he served as President of the International Mathematical Union.

Interests and expertise

Subject groups


  • Fields Medal

    Contributed to problems of the existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory of algebraic surfaces.

  • Shaw Prize

    For contributions to pattern theory and vision research.

  • Wolf Prize

    In the field of mathematics for his work on algebraic surfaces; on geometric invariant theory; and for laying the foundations of the modern algebraic theory of moduli of curves and theta functions.