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.