Wu Wenjun

Wu Wenjun the Chinese mathematician (1919-2017) who made fundamental contributions to topology and later founded the field of mathematics mechanization, using algebraic methods to prove geometry theorems by computer and becoming one of the most honoured scientists of his country.

Early Life and Education

Wu Wenjun was born on 12 May 1919 in Shanghai and grew up in a family of modest means. As a boy he was interested in mathematics and in the puzzles of numbers and shapes, and he showed an early determination to pursue a scientific career despite the disruptions of the period in which he came of age.

He entered the fledgling National Southwest Associated University during the war years and studied mathematics, graduating in 1940. In the difficult conditions of the wartime campus he received a solid grounding in analysis, algebra and geometry, and he formed friendships with classmates who would also become leading mathematicians.

After the war he went to France in 1946 to study at the University of Strasbourg, where he worked under the topologist Charles Ehresmann. He received his doctorate in 1949, and his promise was such that he was soon recognised as one of the most original young mathematicians of his generation.

Contributions to Topology

Wu Wenjun's early work concerned algebraic topology, the study of the properties of spaces that are preserved under continuous deformation. He developed the theory of characteristic classes, quantities that measure the twisting of fibre bundles, and introduced a class now named after him together with several related invariants.

He proved important theorems on the topology of manifolds and on the classification of fibre bundles, and his results became standard tools in the field. With his collaborators he produced a series of papers that helped to clarify the relations among the characteristic classes and their applications in geometry and in the theory of differentiable manifolds.

His work of this period earned him an international reputation, and he was invited to address major conferences and to work at leading institutes abroad. For many years he taught at the Chinese Academy of Sciences, where he built up a strong school of topology and supervised a large number of students.

Mathematics Mechanization

In the 1970s Wu Wenjun turned to a new and ambitious problem, the mechanization of mathematical reasoning. He asked whether the process by which mathematicians prove theorems could itself be carried out by machine, at least for a well-defined and important class of problems, and he sought a method that was both rigorous and practical.

He developed what became known as the Wu method, or the characteristic set method, which reduces a system of polynomial equations to a simpler triangular form by eliminating variables successively. This algebraic procedure can be used to decide whether a given geometric statement follows from a set of hypotheses, and it turns large classes of geometry problems into mechanical computations.

The method proved to be powerful and widely applicable. It has been used to prove and to discover many theorems in elementary and differential geometry, and it has found applications in robotics, computer-aided design and the verification of geometric constraints. The field of mathematics mechanization that he founded attracted researchers around the world.

The History of Chinese Mathematics

Wu Wenjun was also a distinguished historian of mathematics. He studied the classical Chinese mathematical texts and argued that the ancient tradition, with its emphasis on algorithms, constructive procedures and the solution of practical problems, followed a path distinct from the deductive style of Greek geometry.

He saw in the algebraic and algorithmic character of Chinese mathematics a kinship with his own mechanization programme, and he used historical insight to illuminate contemporary methods. His writings drew the attention of historians to the sophistication of Chinese work on equations, remainders and combinatorial problems.

He edited and annotated important sources and encouraged the study of the subject in China and abroad. His historical work helped to correct a tendency to treat the development of mathematics as an exclusively European story and to give the Chinese tradition its proper place in the wider account.

Honours and Legacy

Wu Wenjun was showered with honours. He was elected a member of the Chinese Academy of Sciences in 1957, received the first State Preeminent Science and Technology Award of China in 2000, and was awarded the Shaw Prize in mathematical sciences in 2006 for his work on topology and on the mechanization of mathematics.

An asteroid and several prizes and institutions bear his name, and his influence on Chinese mathematics was profound. He trained generations of students, many of whom became leaders in topology and in computer mathematics, and his institute became a centre for research on automated reasoning and symbolic computation.

He died on 7 May 2017 in Beijing at the age of ninety-seven. He is remembered as one of the great mathematicians of the twentieth century, a man who moved with equal ease between the most abstract problems of topology and the concrete task of teaching a machine to prove a theorem.

See also

• Mathematics mechanization
• Algebraic topology
• Characteristic class
• Chinese Academy of Sciences