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When Poincaré later enrolled in school he was a brilliant student, excelling in nearly every subject in the Lycée (now renamed after him) and winning first prizes in a competition among the top students from all the Lycées across France. He did not learn by rote memorization, however, but by linking ideas in a visual manner, an approach attributed to his poor eyesight that prevented him from seeing what was on the blackboard. He received a doctoral degree in mathematics based on a thesis in differential mathematics that some of his reviewers criticized. He then taught in a university, where he also had critics of his disorganized style, but in 1886 gained an appointment to a prestigious chair of mathematical physics and probability at the Sorbonne. He taught there until his death at age 58.  

When Poincaré later enrolled in school he was a brilliant student, excelling in nearly every subject in the Lycée (now renamed after him) and winning first prizes in a competition among the top students from all the Lycées across France. He did not learn by rote memorization, however, but by linking ideas in a visual manner, an approach attributed to his poor eyesight that prevented him from seeing what was on the blackboard. He received a doctoral degree in mathematics based on a thesis in differential mathematics that some of his reviewers criticized. He then taught in a university, where he also had critics of his disorganized style, but in 1886 gained an appointment to a prestigious chair of mathematical physics and probability at the Sorbonne. He taught there until his death at age 58.  

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 just recently.<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 f are rational numbers.