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Firstly, I apologize in advance if this post in not suitable for MO, but in my personal circumstances, I have no other place where I could post it.

Suppose one is fairly convinced that they have found a short proof of some famous theorem. But the problem is, this individual has no connections to any specialist of the area (due to geographical location or otherwise), such that they have no one to discuss their wok with. This lack of professional connections would also mean that they are going to find it difficult to find endorsements to publish on arxiv, hence their only option would be a place like vixra, where one should really never post their work. And if they try to find some specialist of the field, they are most certainly going to be dismissed as a ''crank'', which may not necessarily be so.

So, considering the really difficult circumstances that this young aspiring and passionate mathematician is in, what is the best way for them to ask for comments on MathOverflow, bearing in mind that MO has a policy against such posts?

Maybe the individual in question could be given the option to post their proposed proof using a polite tone like ``the following proof must be certainly wrong, but where is the mistake?'' And as soon as any mistake is found, have their account banned definitely or indefinitely? Just a thought.

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    $\begingroup$ Don't. Just don't. MathOverflow is not meant for such a service. You are more likely to alienate the help you seek by doing what you propose. Gerhard "Better To Blog Your Result" Paseman, 2020.08.10. $\endgroup$ – Gerhard Paseman Aug 11 at 6:55
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    $\begingroup$ A new proof should be submitted to a professional journal for checking. MathOverflow and the arXiv do not serve this purpose. If the person does not have a decent publication record (containing several new and interesting theorems), then most likely his/her short proof of the famous theorem is incorrect. $\endgroup$ – GH from MO Aug 11 at 6:55
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    $\begingroup$ The person has no other chance than to submit to a journal and wait. That's what all of us do. And we all build up our knowledge and reputation from scratch, step by step. We all start our lives as infants. That's how the world is. If the person submits a fantastic paper, then it will be recognized. $\endgroup$ – GH from MO Aug 11 at 7:02
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    $\begingroup$ By the way, the person can start building his/her reputation here at MathOverflow. He/she could answer a few hundred questions here, and then he/she will be taken rather seriously. $\endgroup$ – GH from MO Aug 11 at 7:05
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    $\begingroup$ Yes, the person has to work 100 days for someone else's 10 minutes. BTW a decent paper takes several months to check, not 10 minutes. There are papers which appear 4 years after submission (not because it was rejected). $\endgroup$ – GH from MO Aug 11 at 7:10
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    $\begingroup$ It is possible to ask several specific questions about specific technical points. This should be enough for everyone willing to be a professional mathematician. $\endgroup$ – Francesco Polizzi Aug 11 at 7:15
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    $\begingroup$ This would have been better asked on meta.mathoverflow. $\endgroup$ – David Roberts Aug 11 at 7:16
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    $\begingroup$ How about instead you ask questions within the scope of the forum? Would you rather get five minutes of attention, be told your proof is wrong and then be banned forever, or instead learn how to use the services of the forum, and possibly learn how to check your own proof? Gerhard "MathOverflow Doesn't Do Referee Services" Paseman, 2020.08.11. $\endgroup$ – Gerhard Paseman Aug 11 at 7:16
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    $\begingroup$ About the point "And as soon as any mistake is found, have their account banned definitely or indefinitely ?": here I utterly disagree. Our purpose here is to learn and discuss Mathematics, not to punish someone else's mistakes. $\endgroup$ – Francesco Polizzi Aug 11 at 7:17
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    $\begingroup$ I am not a professional mathematician. If anyone reads my proofs, it is because they are interested in the results or the methods, definitely not because of my career status. Gerhard "Worked Hard To Avoid Working" Paseman, 2020.08.11. $\endgroup$ – Gerhard Paseman Aug 11 at 7:19
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    $\begingroup$ @Pres10: It would be an option that would change the nature of the site, in a sinister way. $\endgroup$ – Francesco Polizzi Aug 11 at 7:21
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    $\begingroup$ I suggest you read the advice on academia.se for this specific case. $\endgroup$ – Federico Poloni Aug 11 at 8:17
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    $\begingroup$ @GHfromMO as an aside, it turns out Heegner was not a high school teacher, but an independent scholar. The 'teacher' story seems to be an urban legend, that I once repeated, but Norbert Schappacher, a historian of mathematics, got in contact with me to correct me, so I could correct what I wrote. $\endgroup$ – David Roberts Aug 11 at 10:33
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    $\begingroup$ A genuine new proof of a theorem all of whose current proofs are very difficult very likely cannot be checked within 10 minutes. If the author of such a “proof” actually thinks it’s so easy that it can be understood by anyone in ten minutes, it is almost certainly wrong and indicates that the author does not understand the difficulties surrounding the theorem. $\endgroup$ – Stanley Yao Xiao Aug 12 at 9:47
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    $\begingroup$ Your latest comments paint a picture of your approach to this that puts you squarely in the same category as cranks to a lot of people. That is a good way to make sure nobody will take you seriously. $\endgroup$ – Tobias Kildetoft Aug 13 at 17:41
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There is no "best way".

MathOverflow is meant for a sometimes casual (and sometimes not) discussion of mathematics "near the frontier", meaning that the intent is to discover or invent new mathematical knowledge. In order to engage with the community, one needs to do so helpfully. This means meeting certain standards of behaviour.

Asking someone to vet a proof is against this standard. Asking someone to read something not in their area of interest is against this standard. Asking a professional to give up their time in a potentially fruitless (for them) endeavour is against this standard.

Providing meaningful and engaging and relevant content goes with the standard. Refining the area of difficulty of understanding into a precise and properly focussed question is with this standard. Using the terminology and methods that are familiar, or easily explained and replicated, go with the standard. In order to keep this community together and willing to provide the services it does for free (in its decade of existence, to my knowledge maybe one guy got paid for developing software related to MathOverflow, and he was outside the founding circle and may not even be a forum member; everyone else donates their time and energy), these standards have to be maintained; break them, and things erode and the community falls apart.

You might think your way is worth the risk. I don't.

Gerhard "Remember The Signature About Blogging" Paseman, 2020.08.11.

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