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Poincaré invented algebraic topology, and for 40 years afterwards virtually all work in this field were based on six papers written by him in the late 1890s. He proposed the [[Poincaré conjecture]] in 1904 and it remained unproven until 2003.<ref>http://mathworld.wolfram.com/PoincareConjecture.html</ref>
Poincaré invented algebraic topology, and for 40 years afterwards virtually all work in this field were based on six papers written by him in the late 1890s. He proposed the [[Poincaré conjecture]] in 1904 and it remained unproven until 2003.<ref>http://mathworld.wolfram.com/PoincareConjecture.html</ref>
Poincaré had a major contribution to number theory in 1901 in connection with the Diophantine problem of finding the points with rational coordinates on a curve ''ƒ''(''x'', ''y'') = 0, such that the coefficients of f are rational numbers.
Poincaré had a major contribution to number theory in 1901 in connection with the Diophantine problem of finding the points with rational coordinates on a curve ''ƒ''(''x'', ''y'') = 0, such that the coefficients of ''ƒ'' are rational numbers.
Poincaré was an originator of the special theory of relativity,<ref>Henri Poincaré: La science et l'hypothèse, E. Flamarion, Paris, 1902; [http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_07.html English translation]</ref> using ideas of [[Hendrik Lorentz]] and prior to [[Albert Einstein]]. Poincaré gave a lecture on his special theory of relativity at the 1904 World's Fair in St. Louis, a year before Einstein published his paper on the same theory. Poincaré published additional papers on his theory in 1905, prior to the publication of Einstein's paper.
Poincaré was an originator of the special theory of relativity,<ref>Henri Poincaré: La science et l'hypothèse, E. Flamarion, Paris, 1902; [http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_07.html English translation]</ref> using ideas of [[Hendrik Lorentz]] and prior to [[Albert Einstein]]. Poincaré gave a lecture on his special theory of relativity at the 1904 World's Fair in St. Louis, a year before Einstein published his paper on the same theory. Poincaré published additional papers on his theory in 1905, prior to the publication of Einstein's paper.