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Acta Mathematical
His thinking of nature and the way we can not truly predict the inherently unpredictable just understand why it does what it does eventually lead Henri to give the first mathematical description of chaotic motion. This was to be published in the Acta Mathematical. Interestingly he actually made a minor error in the initial publication. This error eventually spawned what became known as Chaos Theory. A man so embroiled in math he was creating new ideas by accident. -
Algebraic Topology
Sometimes called "The Last Universalist" the life of Henri Poincare work in the most basic of arithmetic lead to him creating the basis of algebraic topology. In 1894 He published the first of six papers covering the topic. In this work he postulated as well that those who would attempt to define that natural world would eventually be doomed to failure. He also coined what was called Poincare Conjecture which showed what could be done with math.
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Foundations of Geometry by David Hilbert
Reviewing Hilberts work Henri wrote "The logical point of view alone appears to interest [Hilbert]. Being given a sequence of propositions, he finds that all follow logically from the first. With the foundations of this first proposition, with its psychological origin, he does not concern himself." Henri believed that logic was not the only tool to use and that by using intuition one would unlock further mysteries to solve. Logic alone was doomed to fail without intuition to guide it. -
Mathematical Definitions in Education
"By logic we improve, by intuition we invent." What was initially a book trying to simplify math for it to be easier to consume Henri showed a way of thinking that was not often seen. He believed that math even as it was a structured world was still guided by some innate guiding feel of the where it was leading. Best shown as he would clear his mind and not think of his task on purpose and let it come when it may. This being shown when he combined Fuchsian functions with non-euclidean geometry.
