Hamilton s Principle of Least Action and its associated equations concept configuration space led revolution mathematical physics. Top Alexandre Grothendieck Germany France has done brilliant work in several areas of mathematics including number theory geometry topology functional analysis but especially fields algebraic category both which revolutionized. that n x y z has positiveinteger solutions for any . Although Gauss and Bolyai discovered nonEuclidean geometry independently about the same time as Lobachevsky it worth noting that both of them had strong praise for genius

Read More →Top Mikhael Leonidovich Gromov Russia France is considered one of the greatest geometers ever but has unique soft approach geometry which leads applications in other fields contributed group theory partial differential equations areas analysis and algebra even mathematical biology. as well the identity where is floor function and ceiling . He seems to have been much better mathematician than Chang but just as Newton might gotten nowhere without Kepler Vieta Huygens Fermat Wallis Cavalieri etc. Hadamard was also influential promoting others work is noted for his survey of Poincar staunch defense Axiom Choice led to acceptance Zermelo

Read More →Descartes has an extremely high reputation and would be ranked even higher by many list makers but whatever his historical importance mathematical skill was not in top . He worked in mathematical foundations formulated Axiom of Regularity and invented elegant definitions counting numbers . He was noted for his strong belief in determinism famously replying to Napoleon question about God with have need of that hypothesis

Read More →The axioms Dedekind invented allow integers and rational numbers to built his Cut then led rigorous useful definition of real . Ptolemy also wrote on trigonometry optics geography map projections and astrology but is most famous for his astronomy where perfected the geocentric model of planetary motions. More important than his work with Fermat Last Theorem was Unit considered one of most theorems algebraic number theory

Read More →Srinivasa Ramanujan. Along with Cayley and Sylvester he founded the important theory of invariants. He coined several mathematical terms including vector scalar associative and tensor. For a while Clebsch was one of the top mathematicians in Germany and founded important journal but died young

Read More →He had ideas similar to Pythagoras about numbers ruling the cosmos writing that purpose of studying world should discover rational order and harmony which has been imposed by God revealed us language mathematics . The theory of tides was later refined by Laplace. Soc. Retrieved

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Several ideas are named after him including DeligneLusztig theory DeligneMumford stacks FourierDeligne transform local constant cohomology and at least eight distinct conjectures. a model windmill powered by mouse on treadmill. Hamilton s friend John