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Many great scientists have made important contributations to many related fields. Gauss, Euler and Newton each made many contributions to both math and physic.

One of the great scientists of last century is Albert Einstein and I wonder, did he make any contributations to math?

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    $\begingroup$ Einstein summation: $u^i v_i = \sum_i u^i v_i$ $\endgroup$ – BananaCats Category Theory App Apr 8 '14 at 19:34
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    $\begingroup$ The letters between Einstein and Elie Cartan are available in book form. amazon.com/Elie-Cartan-Albert-Einstein-Parallelism/dp/… It was the usual thing: Einstein had amzing physics intuition but did not know how to write everything mathematically, Cartan filled in some blanks but arrived, eventually, at a physical theory that disagreed with experiment. $\endgroup$ – Will Jagy Apr 8 '14 at 19:36
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    $\begingroup$ He seems to be the first one who explained mathematically Brownian motion, one of the most important notions in probability, $\endgroup$ – Petite Etincelle Apr 8 '14 at 19:48
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    $\begingroup$ I don't think that there is any exact boundary in both subjects- Physics and Mathematics. Yeah, some people are more inclined to physical phenomenon. His theories are written in mathematical way; though have much relevance to physics. Therefore, he knew mathematics and its application. So I feel that he contributed but from applied point of view; so called mathematical physics. $\endgroup$ – Mat He Mat Cian Apr 9 '14 at 0:32
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    $\begingroup$ @mesel google Brownian motion and Albert Einstein, there are many, for example: physik.uni-augsburg.de/theo1/hanggi/History/Gora.pdf $\endgroup$ – Petite Etincelle Apr 9 '14 at 14:26
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Einstein gave a tremendous impetus to the development of differential geometry as a tool in doing general relativity. His contribution went far beyond introducing the index notation that currently bears his name! To cite a quick example, he deserves the credit jointly with David Hilbert for proving that the differential equations describing space-time ("the Einstein equation") is the Euler-Lagrange equation of a suitable variational functional; see Einstein-Hilbert action.

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    $\begingroup$ That seems more like a contribution to physics or mathematical physics than to mathematics. $\endgroup$ – naslundx Aug 2 '14 at 14:38
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    $\begingroup$ @naslundx: Can you blame him? He was, after all, a physicist. If you think about it, Physics is Math roughly applied onto reality so as to explain and predict everything around us. In that sense, his entire life's work is a contribution to math. $\endgroup$ – Nick Aug 29 '14 at 8:35
  • $\begingroup$ @naslundx, are you referring to Einstein's variational functional? I think this can be thought of as a purely mathematical problem: you have a certain differential equation, and you look for a functional such that the equation is the Euler-Lagrange equation of the associated variational problem. Now it is true that Euler and Lagrange could also be described as physicists, so with a sufficiently narrow definition of "mathematics" this can be excluded as well, but it is not usually done :-) I am commenting because this question was recently bumped up for some reason. $\endgroup$ – Mikhail Katz Jun 7 '17 at 7:21

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