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I have heard of independent journalists, but are independent mathematics researchers a thing that exists?

I am asking because I am intensely interested and invested in a certain branch of maths and feel like I am capable of proving something new, however I am 23 with no formal education beyond highschool and with no interest in going to university.

I am not doing it for the money, I have a stable source of passive income, so I have a lot of free time.

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    $\begingroup$ Become a consultant. But for that you must be an expert, so with "no formal education beyond highschool" you might find convincing potential clients that you can solve their difficult problems. $\endgroup$ May 28 '19 at 19:57
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    $\begingroup$ Do you mean "independent from academia"? These do exist (e.g. themathcitadel.com), though (I believe) are mostly applied in industry sector. Apart from that, no one stops you from doing the research you like, and publishing it in e.g. arxiv.org. $\endgroup$
    – lisyarus
    May 28 '19 at 19:57
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    $\begingroup$ anyone can be an independent research of anything. This was the common way to do for many centuries. That you had "success" or not is a different question. $\endgroup$
    – Masacroso
    May 28 '19 at 20:03
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If money is not an issue, then you can absolutely be an independent researcher in mathematics. One of the main reasons of being affiliated with an organization like a university is that you need someone to pay you. In many areas of mathematics you don't need any special facilities or equipment to do your research, so if you don't need an outside source of money then you can by all means do research without affiliation.

However, without some degree of university education it's difficult to know whether your work is correct. In fact it's difficult even with a PhD. It's not technically required, and you could theoretically be a person where everything fits together just right so that you are able to know what you're doing without much guidance (think Ramanujan), but it's highly unlikely. So I would be very cautious if you decide not to get a degree and enlist extensive help from other mathematicians.

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    $\begingroup$ I believe it should be noted that there are also reasons not to get a math degree: it takes valuable time & money (not everywhere, though), and is often coupled with ridiculous amounts of irritating bureaucracy. $\endgroup$
    – lisyarus
    May 28 '19 at 20:20
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    $\begingroup$ @lisy Since money is not an issue and the OP is relatively young, I'd say that the reasons not to get it are not compelling in my opinion. $\endgroup$ May 28 '19 at 20:26
  • $\begingroup$ Not being in need of money and being able to spend large amounts of money are entirely different things. $\endgroup$
    – lisyarus
    May 29 '19 at 11:11

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