The book covers Wu s papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel Whitney classes of sphere bundles or differential manifolds, established an imbedding theory with an application to the layout problem of integrated circuits, and introduced the I*-functors which turned the rational homotopy theory created by D Sullivan into algorithmic form. In computer mathematics, he discovered Wu s method of mechanical theorem proving by means of computers, which has been applied to prove and even discover on the computers hundreds of non-trivial theorems in various kinds of elementary and differential geometries. He also discovered a new effective method of polynomial equations solving, which has been used to solve problems raised from the fields of robotics and mechanisms, CAGD, computer vision, theoretic physics, celestial mechanics, and chemical equilibrium computation.
Contents: On the Product of Sphere Bundles and the Duality Theorem Modulo Two; On Universal Invariant Forms; The Out-In Complementary Principle; On Chern Numbers of Algebraic Varieties with Arbitrary Singularities; On the Foundation of Algebraic Differential Geometry; On a Finiteness Theorem About Optimization Problems; On Surface-Fitting Problem in CAGD; and other papers.