It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better — H.Poincaré, Science and Method (1908, Part II. Ch. 2, p. 129)
Henri Poincaré (1854-1912) was a French mathematician of extraordinary breadth, depth, and ability. He made original fundamental contributions to many fields, including celestial mechanics, differential equations, complex function theory, algebraic geometry, topology, number theory, celestial mechanics, electromagnetic theory, and the theory of relativity.
Poincaré was born in Nancy, France, and entered the Ecole Polytechnique in Paris in 1873, where he studied mathematics, publishing his first paper a year later. He went on to study at the School of Mines, where he graduated as an engineer in 1879. Upon graduation he was called to investigate a trafic mine accident in Magny. From 1881 on, Poincaré taught at the Sorbonne. He was a prolific writer and creative thinker who revolutionized the mathematics of his day. What is now known as the Poincaré conjecture was first posed as a question in a paper written in 1904:
If a three-dimensional shape (compact three-manifold) is simply-connected, is it homeomorphic to the three-sphere?
In the linked text to the right we will explain terms such as three-sphere, etc., that are part of a mathematician's working vocabulary and in which Poincaré expresses his conjecture. We will also say a few words about the conjecture itself.
Poincaré's influence reached beyond his distinguished career as a research mathematician. He was a gifted expositor, the author of several books intended for a general audience, including Science and Hypothesis, 1901; The Value of Science, 1904; and Science and Method, 1908. He also gave generously of his time for various governmental commissions concerned with education.