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It was "the physicist who would win the race (as opposed to the mathematicians) to making discoveries about mathematical structures relevant to our universe" However, that trend seems to be changing. Are there any philosopher's of science who explain this this emerging trend?

Perhaps this list isn't exhaustive or the existence of the mathematical physicist obscures the analysis. But the main point I'm driving at is this the mathematicians seem to be playing a more direct role in physics. Where M stands mathematician and P stands for physicists "winning the race."

P - Maxwell versus Gauss (1873): Gauss was in the camp that electromagnetism could not be described by a wave and Maxwell proved him wrong and laid down the foundation of electromagnetism.

P - Einstein versus Gauss (1905): Einstein discovered special relativity first.

P - Einstein versus Hilbert (1915): Einstein discovered general relativity first.

P - Dirac versus Hilbert (1928): Hilbert did not believe the it was possible the Dirac equation could yield a solution which was both physically meaningful and mathematically consistent.

P - Dirac versus mathematicians (1930): Mathematicians were skeptical on the application of the Dirac Delta function. However, we now have a theory of distributions which justifies Dirac's work.

M - Hawking versus Penrose (1965): Penrose discovered blackholes first.

M - Alexander Grothendieck (& David Mumford) versus physicists (1966): David Mumford applied Grothendieck 's scheme theory in renormalization which was initially not well received by physicists.

P - Witten versus mathematicians (1990): Witten successfully discovered applications of Morse theory and knot theory's applications for QFT with formulas which even perplexed mathematicians.

M - Perelman vs physicists (2003): Perelman solved the Poincare conjecture. His proof was accepted by physicists in 2006.

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  • I just learned Ian Hacking makes a similar point. Gonna read up more. Commented Jul 8, 2023 at 8:49
  • I remember someone like Hacking say something like that. Can you post the quote for my sanity, please?
    – user66697
    Commented Jul 8, 2023 at 18:17

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I suspect there are at least two objections that could be made to your question. One is that your list of physicists and mathematicians beating each other in reaching some conclusion is almost certainly an unrepresentative subset- the other is that 'winning the race' supposes there is a single race to be won, whereas physics and mathematics advance on multiple fronts. However, leaving those squabbles aside, it would not surprise me if mathematicians came to play an increasingly influential role in the development of theoretical physics, if only because the subject has become so mathematical over the last fifty years that the physics significance of the equations has become harder and harder to conceptualise. It used to be the case that one could have a mental model of reality in terms of familiar objects such as tiny billiard balls and magnets, etc, so that it was possible to conceive of fundamental physics in everyday terms. However, those days are long gone, and mathematical, rather than physical, insights are likely to be what guides the future Einsteins and Dirac's to make breakthroughs in the development of theoretical physics.

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  • the examples I give are cases where there are common vested interests. Also I find the idea: "mathematical, rather than physical, insights are likely to be what guides the future" tragic (not that I'm disagreeing). Commented Jul 8, 2023 at 14:49
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    I agree wholeheartedly. Commented Jul 8, 2023 at 15:04

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