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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 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>Poincaré, Henri (1902). ''La science et l'hypothèse'' (Paris: E. Flamarion). [https://web.archive.org/web/20040212235637/http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_toc.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>Poincaré, Henri (1902). ''La science et l'hypothèse'' (Paris: E. Flamarion). [https://web.archive.org/web/20040212235637/http://spartan.ac.brocku.ca/~lward/Poincare/Poincare_1905_toc.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 contributed to the understanding of the difficult three-body problem in celestial physics. He demonstrated that series expansions previously used in studying the 3-body problem were convergent, but not generally uniformly.  This added skepticism to the stability proofs of [[Joseph-Louis Lagrange|Lagrange]] and [[Pierre Simon Laplace|Laplace]].  

Poincaré contributed to the understanding of the difficult three-body problem in celestial physics. He demonstrated that series expansions previously used in studying the 3-body problem were convergent, but not generally uniformly.  This added skepticism to the stability proofs of [[Joseph-Louis Lagrange|Lagrange]] and [[Pierre Simon Laplace|Laplace]].