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Automorphic Functions
It took Poincare extra work and dedication in order to excel in mathematics. He was internationally recognized when he then contributed to the scientific community by discovering automorphic functions: Fuchsian and Kleinian functions in mathematics. In math, automorphic functions is a function on a quotient space.
Fuchsian equation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Fuchsian_equation&oldid=24 -
Algebraic Topology
Wrote a paper called Analysis Situs in which he presents his algebraic topology work. Algebraic topology investigates topological space using abstract algebra. The purpose of this form of mathematics is to find "invariants that classify topological spaces up to homotopy eqivalence." https://en.wikipedia.org/wiki/Algebraic_topology -
Science and Hypothesis
He wrote Science and Hypothesis ( 'La Science et l'Hypothes') which is one of his most famous writings. In it, he talks about math, physics, space and nature. He also made clear his point of view that "absolute truth is unattainable and many scientific beliefs are nothing but conventions." https://www.thefamouspeople.com/profiles/henri-poincare-448.php -
Poincare Conjecture
This theorem "concerns a space that locally looks like ordinary 3-dimensional space but is connected, finite in size, and lacks any boundary". This conjecture states that if a "three dimensional space has the additional property that each loop in the space can be continuously tightened to a point then it is necessarily a 3-D sphere." https://youtu.be/YPuOt0JUZBY
