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June 7

Publishing an article on original research in Mathematics

Hello, I am not a mathematics professional , nor I have a university degree, however I have spent much of my time studying maths on my own; I am confident that I have discovered a new definition of an existing mathematical object that complies with set theory, arguably I'd say that it complies with Bourbaki's "style" and somehow relates to Kuratowski's notation. So my question is: how do I get this definition published? Which are the best paths that I can follow to get an acknowledgement of the validity of my work? Brian George Walsh (talk) 18:18, 7 June 2018 (UTC)[reply]

It's definitely challenging for amateurs to get their work noticed, for a variety of reasons:

First, modern mathematics is a full-time job. In most cases, to produce anything new and valuable, you need to know a huge amount of background material, and even then you will be passed by unless you are keeping constantly up-to-date. This may not apply if you find something genuinely novel, but this is rare.
On the other hand, there are lots of amateurs who think they've found something new and valuable, and try to get it noticed. They are usually wrong.
Putting the first two points together, the a priori probability that a new contribution by an amateur is new and valuable is low. So the people who have to judge whether it is new and valuable, not irrationally, don't want to spend a lot of time on it.
Could there also be rent-seeking by established players, and reluctance to consider the work of people not in the social in-group (not invented here)? Sure, why not? They're human. But I don't think it's the main explanation.

That said, when amateurs really are on to something, the story can really have "legs".

One thing you could try is to write your findings very clearly, and submit them to the arXiv. Anyone can submit papers to the arXiv. For that reason, amateur papers presumably don't usually get a lot of attention. But if your work really is correct and valuable, you would establish priority, and maybe someone will eventually notice. "Write very clearly" is important, because no one wants to put a lot of effort into reading something that is unlikely to pay off.

Alternatively, you could try to cultivate mathematicians in the field you have in mind. Many universities have colloquia open to the public, often with informal discussion afterwards. You could sound someone out.

One final point: You say that what you have done is "discover a new definition". In most cases, people aren't terribly interested in new definitions, by themselves. Why is your definition valuable? Does it lead to actual and interesting theorems? Or does it at least illuminate the underlying ideas better than existing definitions? --Trovatore (talk) 19:07, 7 June 2018 (UTC)[reply]

"Anyone can submit papers to the arXiv." This is not true. However, it may be true in (some sections of) the math arXiv that it is not required to have an academic e-mail address in order to submit a paper. If you have a local university, I might suggest sending a brief e-mail to the department chair saying that you are an amateur, briefly describing the area in which you are working, and asking whether he can recommend a member of the department who might be willing to give you feedback. (Attach a write-up! And don't be surprised if you don't hear back right away.) --JBL (talk) 02:46, 8 June 2018 (UTC)[reply]

Do you want recognition, fame, and fortune, or merely to do mathematics? In the former case I don't know what to do. In the latter case upload your paper to www.academia.edu. Take the time to make your paper perfect. Check words for spelling, sentences for grammar, phrases for logic, and sections for legibility. Then you are successful. Leave it to others to judge it. Bo Jacoby (talk) 12:57, 10 June 2018 (UTC).[reply]

Ah yes, the excitement, the glamour, the romance, the lucrative financial opportunities of mathematical research :) Pretty sure if you're looking for fame and fortune you'd be better off learning the guitar. --RDBury (talk) 22:38, 10 June 2018 (UTC)[reply]