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7$\begingroup$ See mathoverflow.net/q/325571 for some discussion on "tides turning" more than once on this problem! $\endgroup$Joe Silverman– Joe Silverman2025-08-15 02:56:49 +00:00Commented Aug 15, 2025 at 2:56
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7$\begingroup$ As I commented on another answer: I don't think that the OP's original question is really about "open problems where there have been attempts for or against", but more about cases where two independently formulated conjectures turn out to be mutually exclusive $\endgroup$Yemon Choi– Yemon Choi2025-08-15 14:23:00 +00:00Commented Aug 15, 2025 at 14:23
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2$\begingroup$ @YemonChoi I had read the question as looking for "on the record" examples of "expressing different sentiments about which way a certain problem might finally be resolved". $\endgroup$John Doyle– John Doyle2025-08-15 15:26:16 +00:00Commented Aug 15, 2025 at 15:26
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$\begingroup$ Reposting a link mentioned in a previous comment so that it appears in the "Linked" questions list: Joe Silverman's answer to "Have the tides ever turned twice on any open problem?" $\endgroup$The Amplitwist– The Amplitwist2025-08-22 21:02:25 +00:00Commented Aug 22, 2025 at 21:02
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