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History of Science and Mathematics

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    $\begingroup$ I recall skimming through a paper on the history of Galois theory that had significant discussions of how research trends leading to its development (from the late 1700s through the mid-to-late 1800s) led to changes in the acceptance of certain types of existence proofs, including specifics about which mathematicians heavily criticized the new methods and which mathematicians advocated acceptance of the new methods. The paper might be The development of Galois Theory from Lagrange to Artin by Kiernan (1971), but I don't have access. $\endgroup$ Commented Jun 8, 2023 at 9:27
  • $\begingroup$ @DaveLRenfro I looked through the paper, and it does seem like what you describe. There is an irony in Gauss giving 'pure existence' proof of the fundamental theorem of algebra, but disregarding the idea when it came to the impossibility side of inscribing regular polygons, which implies, in particular, impossibility of trisection. Lützen says "there is little doubt that Gauss knew how to prove it", but he "did not attach much importance to it". Kiernan also names Lagrange as a precursor for "dimly" seeing ""known" as an existence property, and not necessarily a constructive property". $\endgroup$ Commented Jun 9, 2023 at 10:53
  • $\begingroup$ It turns out that I actually have a (appropriately magnified) photocopy of Kiernan's 1971 paper, made perhaps 15-20 years ago. In fact, it's in its own 3-ring binder (hole puncher used on the photocopied pages) on one of my bookshelves. $\endgroup$ Commented Jul 1, 2023 at 10:34