What should an amateur do with a proof of an open problem?

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for verification or send to some authorities? Is there a high risk that nobody will treat it seriously?

Answer

I’m no expert on this subject, but the impression that I have comes down to this: your work may be very worthwhile, but it’s hard to be taken seriously if you cannot communicate your discoveries.

A particular difficulty in getting published in mathematics is that the subject is very technical — to use a shaky metaphor, mathematicians speak their own language; and, within the field, each subject has its own dialect. If you’re working without formal training or regular interaction with other mathematicians, it’s naturally going to be difficult to gain the knowledge of terminology, notation, conventions, etc., that is needed to write research-level mathematics.

The problem is that lack of mastery of “the language” is often construed as a lack of understanding of concepts themselves. A professor of mine once mentioned that he receives many papers from amateurs, and in these there are often give-aways (like misuse of terminology and unintelligible symbolic manipulations) which indicate that reading the paper will simply be a waste of time.

With this in mind, put effort into writing your results clearly and carefully. Strive to use the vernacular of the field in which you have made a discovery. Read/skim papers on subjects close to yours to get an idea how to do this. Post on MSE with terminology questions. If you have trustworthy friends with experience in mathematics, try to get them to read over your proof and give you their candid opinions (both about your exposition and about the validity of your arguments).

Probably far more helpful than my rambling, here is a webpage with extensive advice for amateurs, including suggestions for how to go about publishing. You might also find this MSE thread helpful.

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Source : Link , Question Author : Ztalloc , Answer Author : Community

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