-
Chaos
While studying a three-body problem Henri discovered the chaotic deterministic system. He determined that any small change to the initial state of any three bodies would have radical changes later on in the system. -
Philosophy of Geometry
Henri was a big proponent of the discovery of non-Euclidean geometries. He proved several geometric properties by means of Lobachevsky geometry which was not possible in Euclidean geometries. He would states that "All geometric systems are equivalent and thus no system of axioms may claim that it is the true geometry". -
Mathematical Logic
Poincaré argued against the established notion that mathematics was a symbolic form of logic. As an intuitionist the implied that the human intuition was a fundamental aspect within mathematics. According to Henri, "a legitimate mathematical definition creates and justifies its object". -
Neglect
Poincaré's works we largely ignored until the 60's when a meteorologist, Edward Lorenz, also stumbled upon a chaotic system while studying the atmosphere. This was probably due to the fact that the scientific community was focused on the new theory of relativity rather than classical mechanics.