David Mumford and Wu Wentsun both started their careers in pure mathematics but then each made a substantial move towards applied mathematics in the direction of computer science.

Mumford worked on computer aspects of vision and Wu on computer proofs in the field of geometry. In both cases their pioneering contributions to research and to the development of the field were outstanding. Many leading scientists in these areas were trained by them or followed in their footsteps.

**David Mumford **was for many years a professor at Harvard and his early work, for which he received the Fields Medal in 1974, was in the study of algebraic curves. This is an old and central subject with contributions from many of the great names of the past. Mumford’s work revitalized this field and has been widely influential even, surprisingly, in modern physics.

After two decades in this area Mumford made a drastic switch to computer vision, moving also to Brown University, where he used his mathematical abilities and insight to make original and fundamental contributions. His 1985 paper with Shah on signal processing was recently awarded a prize by the Institute of Electrical and Electronics Engineers (IEEE).

**Wentsun Wu** was born in Shanghai in 1919 and studied at Shanghai Jiaotong University and then in Paris. He was one of the geometers strongly influenced by Chern Shiing-Shen (Shaw Laureate in 2004), and did pioneering work in topology. This is the branch of geometry typified by the study of knots which has dominated the field in the past fifty years. Wu returned to China in 1951 but his career was seriously affected by the Cultural Revolution, as a result of which he turned his attention to the questions of computation, in particular the search for effective methods of automatic machine proofs in geometry. In 1977 Wu introduced a powerful mechanical method that transforms a problem in elementary geometry into an algebraic statement which lends itself to effective computation. This method of Wu completely revolutionized the field, effectively provoking a paradigm shift.

Although the mathematical careers of Mumford and Wu have been parallel rather than contiguous they have much in common. Beginning with the traditional mathematical field of geometry, contributing to its modern development and then moving into the new areas and opportunities which the advent of the computer has opened up, they demonstrate the breadth of mathematics. Together they represent a new role model for mathematicians of the future and are deserved winners of the Shaw Prize.

Mathematical Sciences Selection Committee

The Shaw Prize

21 June 2006, Hong Kong