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I am not a people person, and therefore I usually work alone. I'm quite content with this, and I have actually been able to achieve some wonderful results (to me, anyway) working this way. However I worry that nobody else will really care about my research.

Are there examples of modern day mathematicians who have been successful (as recognized by the mathematical community) working alone?

How can I get more people to be interested in the problems I'm interested in, without being able to connect on a personal level? Even if I'm not able to collaborate with anyone, I'd like to create some level of dialogue between other mathematicians and my publications. That is, I'd like for them to perhaps answer some of my questions, and for them to pose new ones that I could possibly answer. So far, I have failed to achieve this.

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    Please edit your question to clarify: 1) Do you aspire an academic career? 2) If yes, what have you achieved so far in that respect? 3) If no, do you care about publishing your work? 4) Did you publish any of your work so far and if yes, how? – Wrzlprmft May 2 '17 at 7:49
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    I know that it does not directly answer the question: however, one has to ask why one expects to get something out of others which one does not want to invest oneself. My experience is that people do not like such an imbalance of giving and taking; why should they be interested in dialogue if OP isn't. There are exceptions, either because the work is astonishingly brilliant or in cases such as Fermat, where one suspects his isolation was due to being a judge at the time of Richelieu; any undue social interaction could have cost him job, freedom or life. That being said, try a blog. – Captain Emacs May 2 '17 at 8:41
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    I am not in the field, so I can't give you real insight. Only that, yes, in specific cases like maybe Perelman (en.wikipedia.org/wiki/Grigori_Perelman), it is possible. But it is not likely to work. – skymningen May 2 '17 at 8:49
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    Do you at least give good talks? – Alexander Woo May 2 '17 at 17:17
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    Does your research build off of existing research? – Jacob Murray Wakem May 2 '17 at 22:39
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Plenty of mathematicians are introverted, quiet, and typically prefer to work alone. (Also, plenty of mathematicians are extroverted, boisterous, and prefer to work with others -- but I believe the profession does a reasonably good job of welcoming various personality types.)

All successful mathematicians whom I know spend some of their time and energy engaging with the mathematical community. Going to conferences or chatting with colleagues are good ways to do this. There are also ways such as MathOverflow to interact with mathematicians online. And simply reading the (contemporary) work of other mathematicians is also a form of engagement.

If you want your work to be appreciated by others, then I recommend taking the time and energy to appreciate others' work. For example, are there any questions asked by others, for which your work gives any insights? If you can help people answer questions they are interested in, then it is quite natural that they might take an interest in your own work as well.

Good luck!

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    I will try to follow the advice in your third paragraph! – Forever Mozart May 7 '17 at 1:45
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The questions in the body of your question are quite different from the one in the title. I will address the titular question

"Can I be successful as a lone wolf researcher in mathematics?"

by going out on a limb and predicting that the answer is, simply, No, you cannot.

It's true that there are people like Perelman, Wiles, Yitang Zhang and other notable (and less notable) examples of "lone wolf researchers" who have become very successful. But the fact remains that those examples are few and far between. My experience is that among ordinary, "mere mortal" working mathematicians, it is normal to see people producing the occasional solely authored paper, but one hardly ever encounters a researcher who has not had coauthors on at least, say, 50% of their papers (my own ratio is about 50% coauthored papers, and I've been told that that's an unusually high proportion of solely authored works).

What this suggests is that by limiting yourself to not collaborating at all with others, you are confining yourself to such a small group of people that most of us professional mathematicians here have trouble naming more than 2-3 people (all of whom are extremely famous) belonging to it. Unless you know something about yourself that we don't that leads you to believe you have a reasonable shot at being the next Wiles or Perelman, I don't think I'm taking too much of a chance by predicting that in fact you aren't (and that's not an insult in any sense since obviously I'm not either), and that your chances of making a successful collaboration-free career in math are very close to zero.

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  • +1 for being blunt. Being a successful researcher is hard and doubly so if you are doing it without help. – Thomas May 3 '17 at 21:30
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    Among the lone wolf researches we must not forget Victor Porton, who works in the field of the OP (general topology). Also, neither Wiles (who obtained essential help by R. Taylor and N. Katz) nor Perelman really are "lone wolf researchers" in the sense of the OP. These people worked on well-known problems, which by virtue of their importance are interesting to many people (the OP, like Porton, works on isolated problems which have no connections to main stream subjects like algebraic geometry or algebraic topology). – Rüdiger May 4 '17 at 9:24
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I think this is among the most philosophically troubling and challenging questions in mathematics research. I wish there was a clear answer one way or the other.

The majority of mathematicians are, I think, working very hard to achieve publications and collaborators. Many will say that networking at conferences is crucial. In fact, some will argue that the whole essence of a mathematical proof is that it is a social construct, and that the very best strategies are to work with others and explain it to others.

However, I can't help but recall a number of researchers in recent years who did work almost entirely alone for many years: Wiles, Perelman, Zhang. And in fact these are uniquely the figures who broke open the pinnacle, hard, long-standing, important problems: Fermat's Last Theorem, the Poincare Conjecture, and the Twin Prime Conjecture.

Personally I have an outstandingly hard time reconciling these observations. As far as how did those lone figures get attention: But working on, and solving, such incredibly hard and famous problems that no one could ignore their results.

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    One attempt to reconcile these observations involves the idea that some people have a talent for "wearing different hats", that is, switching between the perspectives of a creative problem-solver and a critical peer who aggressively tries to find the flaw in the solution. – lighthouse keeper May 3 '17 at 16:15
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    I think an important element of this issue is Survivorship bias - the most logical synthesis between the observations that 1) some solo figures are successful, and 2) most mathematicians try to collaborate is that success with the solo approach is so rare that only the most successful who solve the hardest problems are ever recognized. – Bryan Krause May 3 '17 at 17:02
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    @BryanKrause: Perhaps, but based on the existing sample, it seems equally valid to infer that the hardest problems are only solved by the solo approach. For example, are there any teams of mathematicians who have solved a Millennium Prize Problem? – Daniel R. Collins May 3 '17 at 20:37
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    @DanielR.Collins Only one of those problems has been solved (sort of an impossibly small sample size), and the person given credit, Perelman, who you mentioned, refused the prize on account of, in his opinion, an at least equal earlier contribution by Richard Hamilton. So, even if he primarily worked alone, his work was closely influenced by others in the community that he read. Of course don't know enough about the personal biography of Perelman to know to what extent he interacted with colleagues outside of reading the literature. – Bryan Krause May 3 '17 at 20:50
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    @BryanKrause: Of course I agree that reading literature is indispensable. Zhang has said the same. (Not that we need someone to tell us this.) – Daniel R. Collins May 3 '17 at 22:48
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I will take the following to be your question, rather than what appears in the title: "How can I get more people to be interested in the problems I'm interested in?"

I suspect that if you imagine some other mathematician working in a solitary fashion, but wishing for some professional interaction, you might surprise yourself, with your ability to find a solution for him or her.

Wouldn't you suggest that s/he make the first move? And not be discouraged if the first attempt doesn't get you anywhere?

Some ways to take the initiative to connect with other mathematicians:

  • Math SE

  • write to the author of a paper that interests you

  • you might need to compromise and branch out a bit from your own niche

  • go to talks, chat with others over cookies afterwards

  • go to conferences -- again, here, please don't limit yourself to your own niche

  • visit another university, and write to someone there ahead of time to say, "I'll be in your area in the month of x, may I give a talk about my work while I'm there?" followed by a very short description of your possible topics, along with links to publications

  • volunteer to tutor math undergrads who are having some trouble with a class -- this will help you get out of your shell, and help you improve your math communication skills; also, it will make you more visible and attractive to other mathematicians.

I recommend that you do some reading about how others with limited people skills have negotiated this in their lives.

Congratulations on taking the first step.

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To answer your first question, here is an example of a highly successful mathematician who never collaborated with anyone: http://www.ams.org/mathscinet/search/author.html?mrauthid=177585 (William Austin Veech).

It is worth noting though, that collaborations are just one aspect of participating in the mathematical community - one still needs to give talks, write papers, get hired to an academic job, be on committees, be chair of the dept, ....

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  • Louis De Branges is another well known mathematicians who works almost exclusively by himself. Of his more than 80 publications, only a handful are not solely-authored. – Dan Romik May 3 '17 at 18:55
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    The obvious downside being that he De Branges has annouced multiple wrong proofs. One could argue that this is happening since he is not open to collaboration. In fact he has claimed to have proven Riemann Hypothesis! – mystupid_acct May 3 '17 at 20:35
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    @mystupid_acct most mathematicians would be extremely happy to have authored a body of work equal in importance to that of De Branges. The fact that some of his claims are controversial is indeed interesting but does not invalidate his legitimate, important contributions, and indeed it's not even obvious to me that it should be considered a "downside". – Dan Romik May 3 '17 at 20:40
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    @Dan It is. His work is often not taken seriously, so achieving grants is almost impossible, as is publishing in decent venues or even having people believe in his results. – Andrés E. Caicedo May 4 '17 at 1:10

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