Henri Poincaré

Jules Henri Poincaré^[1] (UK: /ˈpwæ̃kɑːreɪ/, US: /ˌpwæ̃kɑːˈreɪ/; French: [ɑ̃ʁi pwɛ̃kaʁe] ^ⓘ;^[2] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist",^[3] since he excelled in all fields of the discipline as it existed during his lifetime. He has further been called "the Gauss of modern mathematics".^[4] Due to his success in science, along with his influence and philosophy, he has further been called "the philosopher par excellence of modern science".^[5]

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.^[6] In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. Poincaré is regarded as the creator of the field of algebraic topology, and is further credited with introducing automorphic forms. He also made important contributions to algebraic geometry, number theory, complex analysis and Lie theory.^[7] He famously introduced the concept of the Poincaré recurrence theorem, which states that a state will eventually return arbitrarily close to its initial state after a sufficiently long time, which has far-reaching consequences.^[8] Early in the 20th century he formulated the Poincaré conjecture, which became, over time, one of the famous unsolved problems in mathematics. It was eventually solved in 2002–2003 by Grigori Perelman. Poincaré popularized the use of non-Euclidean geometry in mathematics as well.^[9]

Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity, for which he is also credited with laying down the foundations,^[10] further writing foundational papers in 1905.^[11] He first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations, doing so in 1905.^[12] In 1912, he wrote an influential paper which provided a mathematical argument for quantum mechanics.^[13][14] Poincaré also laid the seeds of the discovery of radioactivity through his interest and study of X-rays, which influenced physicist Henri Becquerel, who then discovered the phenomena.^[15] The Poincaré group used in physics and mathematics was named after him, after he introduced the notion of the group.^[16]

Poincaré was considered the dominant figure in mathematics and theoretical physics during his time, and was the most respected mathematician of his time, being described as "the living brain of the rational sciences" by mathematician Paul Painlevé.^[17] Philosopher Karl Popper regarded Poincaré as the greatest philosopher of science of all time,^[18] with Poincaré also originating the conventionalist view in science.^[19] Poincaré was a public intellectual in his time, and personally, he believed in political equality for all, while wary of the influence of anti-intellectual positions that the Catholic Church held at the time.^[20] He served as the president of the French Academy of Sciences (1906), the president of Société astronomique de France (1901–1903), and twice the president of Société mathématique de France (1886, 1900).