Timeline for Less-known conjectures of significant influence and the contrary
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2010 at 18:56 | comment | added | John Stillwell | Thanks, Terry. It's nice to know that Hilbert's fifth problem has come back to life. | |
| Aug 20, 2010 at 1:30 | comment | added | Terry Tao | I should point out that the work on Hilbert's fifth problem was a major component in Gromov's proof of his famous theorem on groups of polynomial growth, and more recently was used by Hrushovski to obtain some deep results on finite sets of bounded doubling. My experience has been that any really deep piece of mathematics tends to find its uses eventually... | |
| Jun 15, 2010 at 2:46 | comment | added | John Stillwell | Thanks, Tim. I should have made it clear that Ramsey's "solution" was only partial (and it could not have been complete because, as you say, the problem is unsolvable). Perhaps logicians were not impressed because they were still hoping for a complete solution. | |
| Jun 15, 2010 at 1:50 | comment | added | Timothy Chow | Point of clarification: The "problem of formal logic" referred to in the title of Ramsey's paper was the decision problem for first-order logic. This problem was certainly famous (and eventually resolved negatively by Church). However, the most lasting contribution of Ramsey's paper was not his partial result on the decision problem, but a result he proved along the way that we now know as "Ramsey's theorem." Probably because of these circumstances, Ramsey's theorem was largely overlooked by combinatorialists for many years, even though Ramsey flagged it as having "independent interest." | |
| Jun 14, 2010 at 12:22 | vote | accept | CommunityBot | ||
| Jun 14, 2010 at 12:22 | history | bounty ended | Unknown | ||
| Jun 8, 2010 at 0:08 | comment | added | John Stillwell | Andres, I may be wrong, but I think there was very little reaction to Ramsey's theorems from logicians at the time. (Maybe they were too busy absorbing Gödel's theorems.) The first people to take an interest were Erdős and Szekeres in their 1935 paper in Compositio Math., "A combinatorial theorem in geometry". Among other things, Erdős and Szekeres gave a much simpler proof of the finite Ramsey theorem, and they noticed the connection between infinite and finite Ramsey theorems via the Kőnig infinity lemma. | |
| Jun 7, 2010 at 23:20 | comment | added | Andrés E. Caicedo | Hi John, Decidability problems were central to logic for a big part of last century. Why do you say that Ramsey's decidability result was on a problem that was not well-known? (I am not questioning your claim. I'm genuinely curious, so as not to claim something false when teaching Ramsey's theorem, for example.) | |
| Jun 7, 2010 at 23:08 | history | edited | John Stillwell | CC BY-SA 2.5 |
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| Jun 5, 2010 at 14:25 | vote | accept | Unknown | ||
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| Jun 5, 2010 at 11:00 | vote | accept | Unknown | ||
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| Jun 5, 2010 at 10:18 | vote | accept | Unknown | ||
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| Jun 5, 2010 at 7:43 | history | answered | John Stillwell | CC BY-SA 2.5 |