Poincaré

Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer and philosopher of science. Born in Nancy, he studied at the École Polytechnique and held chairs at the University of Paris. His work spanned pure and applied disciplines and helped lay the foundations of several modern fields.

In mathematics, Poincaré made foundational contributions to topology and the qualitative theory of differential equations. He introduced the concept of the Poincaré map (return map) for studying dynamical systems, formulated recurrence theorems, and helped develop hyperbolic geometry, including the Poincaré disk model. He also proposed the conjecture now known as the Poincaré conjecture in 1904, a central problem in geometric topology concerning three-dimensional manifolds. In celestial mechanics, his New Methods of Celestial Mechanics (1892–99) shaped the modern qualitative approach to stability and orbital dynamics.

In physics, Poincaré contributed to the mathematical formulation of space, time and invariance, influencing ideas that would culminate in special relativity; the Poincaré group is the mathematical expression of space-time symmetries associated with Lorentz transformations. The breadth of his work gave him a lasting impact on mathematics and physics, and his name is attached to several concepts and models used in geometry, dynamical systems, and theoretical physics.