Timeline for Proposals for polymath projects
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2017 at 15:42 | comment | added | Gerhard Paseman | Let me argue by analogy. In the determinant spectrum problem I proposed, one approach which might be successful is to add the predicate "and the row sums for a matrix are either k or k+1 for k near n/3". This makes the approach more specific, and allows independent searches (maybe someone uses n/4 instead) in which individual discoveries might inform and influence the search efforts of the others. The Syracuse problem by itself may not be as easily modified, but some other arithmetic dynamic may be. Gerhard "A Problem Of Many Names" Paseman, 2017.10.06. | |
| Oct 6, 2017 at 15:19 | comment | added | Robert Frost | @GerhardPaseman It's sad to discover I overestimated the ambition of polymath. Could an approach to Collatz based upon a single predicate be appropriate? What sort of parallelisation is possible? | |
| Oct 5, 2017 at 15:06 | comment | added | Gerhard Paseman | Oh, and don't worry about ego injuring. Most mathematicians (of my acquaintance, and probably outside of it too) are more concerned with time misspent on studying worthless claims than on priority claims. Gerhard "And This Is My Claim" Paseman, 2017.10.05. | |
| Oct 5, 2017 at 14:00 | comment | added | Gerhard Paseman | Yes. These are all excellent reasons for it not to be a Polymath project. Such projects are sufficiently narrow in scope and arranged so as to allow a coordinated effort by an easily managed team, producing some insights. Your comments suggest something much broader in scope, possibly providing person-decades of work and yielding several dissertations. Gerhard "It's Too Big To Polymath" Paseman, 2017.10.05. | |
| Oct 5, 2017 at 10:34 | comment | added | Robert Frost | transcendental number theory, the application of Prufer groups, distilled into certain polynomials, expressed as the existence of Power series of certain forms as well as approached by rudimentary modular arithmetic. A realistic parallelisation of this problem would involve a survey of the many approaches to it, and a skilful distillation into a set of the strongest prospective leads in each field of maths and then for experts in each field to attack each formulation. I think it's even possible this approach would yield connections between disparate fields which are not yet understood. | |
| Oct 5, 2017 at 10:34 | comment | added | Robert Frost | b) it seems to injure the egos of more experienced mathematicians that the less experienced should dare to claim they might solve it. I think these are bad reasons for mathematicians to be biased against collaborating on it. It is actually VERY suitable for parallelisation, and the reason is this: It is very unclear by what method, and in what field of maths, the problem will ultimately be solved. The problem can be extended to 2-adics, it can be made a metric space problem, a discrete calculus problem, a continuous calculus problem in 2-adic space, | |
| Oct 5, 2017 at 10:34 | comment | added | Robert Frost | @GerhardPaseman Terrence Tao gives some arguments in his blog for why this problem is SO hard and argues that its solution will either lean upon existing transcendence theory or will involve some potentially important leap in transcendence theory. Having studied this in some depth I think it's potentially an exceptionally important problem. However it's also an exceptionally unfashionable one among advanced mathematicians, and not for good reasons. Unlike most exceptionally hard problems, it's accessible to lesser mathematicians and as such it a) attracts poor quality attempts and | |
| S Aug 19, 2017 at 9:20 | comment | added | Falken | Calling the pairs (4a+1, 8a+3) where a is odd "buds", and having established that their solving solves Syracuse, it is important to observe that some of them "solve themselves", and I can demonstrate why. As some buds point one to another (are redundant), it is relevant to ask which proportion of the set of all buds must be solved to solve Syracuse, typically the sort of question one might ask in Ramsey theory. In any case, the systematic attacking of buds can be parallelised, and is one way to parallelise the solving of Syracuse. | |
| S Aug 19, 2017 at 9:20 | comment | added | Falken | Regarding the question of parallelising the efforts, here are the three most important theorems that the paper demonstrates: 1) for any odd number a, whoever can prove that 4a+1 and 8a+3 have a common number in their orbit (anywhere, backward or forward) solves Syracuse 2) for any odd number a, either the orbits of 8a+1 and 16a+1 will merge, or 8a+1 will merge with 64a+17 and 16a+1 will merge with 2a-1. 3) theorem 2) will occur at least once in any odd number's forward orbit, because any odd number will have either a number 8a+1 or 16a+1 where a is odd, at least once in its forward orbit. | |
| Aug 16, 2017 at 7:49 | review | Suggested edits | |||
| Aug 16, 2017 at 10:33 | |||||
| Aug 16, 2017 at 3:00 | comment | added | Fred Daniel Kline | +1, nice paper. We're making progress. Still don't know how to parallelize. | |
| S Aug 15, 2017 at 20:11 | history | suggested | Falken | CC BY-SA 3.0 |
autocorrect: fight-->fulfil
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| Aug 15, 2017 at 19:29 | review | Suggested edits | |||
| S Aug 15, 2017 at 20:11 | |||||
| S Aug 15, 2017 at 13:31 | history | suggested | Falken | CC BY-SA 3.0 |
adding a source that might fit the comment below
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| Aug 15, 2017 at 12:50 | review | Suggested edits | |||
| S Aug 15, 2017 at 13:31 | |||||
| Jan 7, 2017 at 21:13 | comment | added | Gerhard Paseman | As stated, this would be unsuitable, as it is unclear how to "parallelize" in a fashion desirable for Polymath. If you were to provide, say, an additional predicate P(n) such that P(n) and the Collatz dynamic terminates upon input n, that might be suitable. Many of the other examples provided are sufficiently restricted that the leap to parallelize is not so great. Please edit this to find a restriction that suits the conditions of the post. Gerhard "Polymath Is Not Group Mathematics" Paseman, 2017.01.07. | |
| Jan 7, 2017 at 18:35 | review | Late answers | |||
| Jan 7, 2017 at 18:49 | |||||
| S Jan 7, 2017 at 18:20 | history | answered | akm | CC BY-SA 3.0 | |
| S Jan 7, 2017 at 18:20 | history | made wiki | Post Made Community Wiki by akm |