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May 21 at 12:30 comment added Alexandre Eremenko @Hollis Williams: This short citation of Fourier, is just a brief conclusion of what he actually says in the long introduction to his book.
May 21 at 11:46 comment added Todd Trimble I don't know, but I'll give you an upvote anyway.
May 21 at 11:30 comment added Mikhail Katz Does "mechanics" include "statistical mechanics"? If so, then Ruelle's comment provides an answer to your interpretation of the OP. @Todd
May 21 at 10:09 comment added Todd Trimble @MikhailKatz No, it's not clear. Titles, being short, cannot and should not be relied upon as to what an OP is truly asking; as experience shows, they are often an inaccurate indicator. Always go to the body of the text to find out what the OP is really asking. But, even if you happen to be right in this particular instance, then that would only make the question much poorer for MO (and I don't think there would be much to stop me from voting to close).
May 21 at 9:34 history edited muru CC BY-SA 4.0
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May 21 at 7:52 comment added Mikhail Katz @ToddTrimble, it is clear from the title the OP is about physics in general and mechanics is mentioned in the body of the question as an example.
May 20 at 18:47 comment added Todd Trimble @HollisWilliams Hardly specific enough for the purposes of the question, which is about how mechanics in particular informs geometry; to me it's along the very general lines of Andy Putman's "And as the answers we have gotten show, what this question is really going to attract are the usual “inspirational quotes” about how amazing physics is." (Also I find your assertion of specificity here at odds with your comment below Carlo Beenakker's answer.)
May 20 at 17:39 comment added Hollis Williams The quote by Fourier is specific imo: he is saying that the deepest mathematical insights always come from studying physical problems.
May 20 at 14:38 history made wiki Post Made Community Wiki by Todd Trimble
May 20 at 14:33 comment added Todd Trimble @Vincent Is it? The quote from Fourier sounds pretty generic and non-specific; cf. Andy Putman's comments under the question, and also the comment by Sam Hopkins under Trunk's answer (now converted to a comment).
May 20 at 14:06 comment added Joe Silverman These are great quotes. Why not paste them into your MathOverflow answer, rather than putting them on a separate linked webpage? More people will read them if they don't have to leave MO.
May 20 at 13:59 comment added Vincent The first of these statements, by Fourier, seems to be exactly what the OP is looking for!
May 20 at 13:04 history answered Alexandre Eremenko CC BY-SA 4.0