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Through their correspondence in 1654, Fermat and [[Blaise Pascal]] helped lay the foundation for the theory of probability. From this brief but productive collaboration on the [[problem of points]], they are now regarded as joint founders of [[probability theory]].<ref name=mactutor>{{cite web | last1 = O'Connor | first1 = J. J. | last2 = Robertson | first2 = E. F. | title=The MacTutor History of Mathematics archive: Pierre de Fermat | url=http://mathshistory.st-andrews.ac.uk/Biographies/Fermat.html| access-date=2008-02-24 }}</ref> Fermat is credited with carrying out the first-ever rigorous probability calculation. In it, he was asked by a professional [[gambler]] why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two [[dice]] resulted in his losing. Fermat showed mathematically why this was the case.<ref>Eves, Howard. ''An Introduction to the History of Mathematics'', Saunders College Publishing, Fort Worth, Texas, 1990.</ref>
The first [[History of variational principles in physics|variational principle]] in [[physics]] was articulated by [[Euclid]] in his ''Catoptrica''. It says that, for the path of light reflecting from a mirror, the [[angle of incidence (optics)|angle of incidence]] equals the [[angle of reflection]]. [[Hero of Alexandria]] later showed that this path gave the shortest length and the least time.<ref>{{cite book |last=Kline |first=Morris |title=Mathematical Thought from Ancient to Modern Times |publisher=[[Oxford University Press]] |location=New York |year=1972 |isbn=978-0-19-501496-9 |url=https://archive.org/details/mathematicalthou0000unse/page/n7/mode/2up |access-date=2024-10-09 |chapter=The Greek Rationalization of Nature |chapter-url=https://archive.org/details/mathematicalthou0000unse/page/
===Death===
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