I’m pretty sure that I’ve solved a certain open problem in mathematics. My solution is currently in its third week of peer-review at some journal that is known for rejecting cranky papers within five days of submission.

I’m currently searching for the next relevant conferences where I can present my paper. The thing is I’m not yet a famous person in the math community, hence it might not be easy to convince the conference organisers. Can someone kindly advice me on how I can go about it?

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    Could you make your question more specific? What would you like to know about this process? As it is, I would simply answer "There's no need to do anything special, just submit your abstract, and keep fingers crossed." – Federico Poloni Nov 25 '18 at 19:54
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    Also, if you managed to convince an editor and two referees that you are not a complete crank, you have good chances to convince the conference organizers, too. In math, conferences do not automatically produce publications, and on average they are not as selective as in many other fields. – Federico Poloni Nov 25 '18 at 19:56
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    Do you have connections in the mathematics community at all? Do you have a successful publication record? Are you affiliated with an academic institution or other established research organization? These are not necessary, but if they apply to you, an answer could discuss how to take advantage of them. – Nate Eldredge Nov 25 '18 at 19:58
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    Why not just put up your manuscript on ArXiv and email it to specific experts. If the proof you have is solving an important open problem as you say, it's bound to get traction. – Spark Nov 26 '18 at 3:44
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    I think in recent years poster sessions have also become more common. This might be an option if you do not get a talk. A poster might not get you the same size of audience, but you are more likely to get into a direct conversation with people who are actually interested, which might be beneficial if you want to continue working on similar topics. But do try to spend some time designing a nice poster and preparing a short pitch, like you would spend time on preparing a talk. Some people just pin a printout of the paper on the wall and wonder why no one wants to talk with them... – mlk Nov 26 '18 at 11:43

I’ll assume the open problem you solved is in pure mathematics. What you should know is that in most areas of pure mathematics, conferences do not have a formal paper submission mechanism, nor do they publish a proceedings volume as they typically do in other areas. One does not go to a conference to “present a paper” but rather one will get invited to “give a talk”, whose contents may be somewhat correlated with the contents of one’s most recent paper, but could also be about a less recent paper or about a still unfinished work, or some combination of such things; that’s entirely up to the speaker.

My suggestion is that you try to find a conference in an area of math related to the open problem. Once you find one, you’ll have the option to register to attend (not to give a talk, which is by invitation only). Except for very large events, there is usually no registration fee, and although they may ask about your affiliation, it’s likely that most conferences will not use that as a basis for deciding whether to let you register, so don’t worry too much if you don’t work at a university.

Now, as I said in order to give a talk you’ll need to be invited to speak by the organizers. They usually select speakers with a proven record of publishing interesting results in the field of the conference. But one thing you could do is email them in parallel with registering, tell them about your paper with the solution of the open problem and ask if you could give a talk about it. I don’t think your chances are too high, but it’s worth a try. Your chances will be higher if your paper is available to download online from a place like arXiv, and if it’s written in a professional way that makes it clear it comes from a mathematician with a good level of experience and formal training. If you don’t want to make your paper publicly available just yet, you can send it to the organizers directly, but it will likely be viewed with suspicion and lower your chances of being invited to speak. (And if you don’t make the paper viewable at all, no one will take you seriously and the chances are essentially zero.)

Even if you are not invited to give a talk at the conference you found, it may still be a good idea to attend it, since there you will have a chance to talk to experts informally, tell them about your solution and get some valuable feedback about your approach.

Good luck!

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    If you do attend, you should work out and rehearse an elevator pitch. It should convey, in minimal time, what problem you are working on, and the key ideas that make your approach to it successful and different from previous failed attempts. – Patricia Shanahan Nov 25 '18 at 22:05
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    Depending on the topic of the paper, there are certainly conferences which support contributed talks, which require no invitation and do require some sort of application. – Santana Afton Nov 26 '18 at 1:06
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    @Mark I think the goal is to have a pitch that doesn't result in the other person thinking, "Oh god, I'm stuck in an elevator with a crank." – David Richerby Nov 26 '18 at 13:08
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    @Mark That pitch misses the really important, but difficult, part. It is essential to explain, clearly but succinctly, why the OP's approach works, and how it differs from failed attempts. The objective is to get an expert to want to hear more, not to have them walk away as soon as they can. – Patricia Shanahan Nov 26 '18 at 13:42
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    @Mark "I've got an elegant proof of Fermat's Last Theorem"...but this elevator ride is too short to describe it. – Ray Nov 26 '18 at 21:18

"My solution is currently in its third week of peer-review at some journal that is known for rejecting cranky papers within 5 days of submission"...

There is a lot of space between "cranky" and "acceptable right away"...not all papers that are not acceptable are cranky and not all papers that are not cranky, are acceptable.

The peer review outcome is not just about acceptance, but what you get is a good, professional feedback on your work, which could be very helpful. (No where else you will get this kind of feedback, certainly not for a conference talk).

Mathematics, especially at research level, should best be communicated, via well written papers than giving a talk. Talk only happens when your work is accepted after a peer review and it stood some test of time, and also has been read by people who are attending the talk. Otherwise you will probably be wasting valuable time of the audience of the talk.

So advice is : Wait for peer review report.

PS : I have not given any special consideration for the fact that the paper is about a famous problem. My answer is for all cases and not just about open problems.

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    +! For Wait for peer review report. To the OP, what's the point to present your solution to the open problem to a conference if solution is wrong? A problem is an open problem for reasons. The peer review report can convince people that your solution is for real. Then, and it is only then, you present it to the math community. Before then, what you can do is to upload it to arXiv and then wait for the peer review report. – scaaahu Nov 26 '18 at 9:24
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    @scaaahu Although, uploading to arXiv when you're not affiliated with a university might not be straightforward. – Misha Lavrov Nov 26 '18 at 18:03
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    Talk only happens when work is accepted after peer review? Tell that to all the "preliminary report" talks in AMS abstracts e.g. click on a few abstracts at ams.org/meetings/sectional/2259_progfull.html ... naturally in this special case waiting for peer review might be helpful to avoid egg on the face. But people give talks before being publication-ready all the time in math. – kcrisman Nov 27 '18 at 3:51
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    I suppose that may be your experience, and I don't have experience with 1., but all I can say is that this is not my experience in pure mathematics. In fact I think it is fairly typical for people extending other researchers' work, e.g. graduate students. – kcrisman Nov 27 '18 at 14:14
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    Plus (and this is an important point) mathematics publishing is very slow by other scientific standards. So to wait for publication would be pretty crippling! – kcrisman Nov 27 '18 at 14:15

The other answers already cover several issues.

One that has not been mentioned is that it would be slightly weird for someone who has never attended a math conference to give a talk. With few exceptions, people give their first talk after having attended many talks at their own university and at some conferences; and for their first talk they get significant help from their advisor and other PhD. students. Also, it would be very unusual to present mathematical work that you have never discussed with any other mathematician, at least informally.

Without the above, I find it unlikely that you can give an engaging talk. I would suggest that you wait on two things:

  • Wait for the referee report, to see what objections/issues/praise come back

  • Try to engage with experts informally, before standing in front of an audience to convey your ideas.

  • Try to attend talks/conferences in related topics to your work, to get acquainted with the people, the results, the presentation style.

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    I disagree, at least with respect to applied math. I gave a talk at the first math conference I attended and so did many people I know. I do agree that you should practice by giving a presentation to your advisor or research group beforehand. – David Ketcheson Nov 26 '18 at 6:08
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    If you had an advisor or a research group, you had at least attended many seminars. And you likely got advice on your presentation. – Martin Argerami Nov 26 '18 at 7:11
  • Yes, definitely. I was disagreeing with your second sentence. – David Ketcheson Nov 26 '18 at 7:19
  • I disagree in principle. If the OP has no experience giving technical talks, well, that is one thing. How else is one supposed to get experience? I do agree that it might be unwise to give a technical talk in a special session of a conference in that scenario, but I have definitely seen reasonable talks given by non-mathematicians in more general sessions. – kcrisman Nov 27 '18 at 3:28
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    I also disagree. You are assuming that OP’s goal is to give an “engaging” talk, but that’s hardly the point. I’ve seen famous, experienced mathematicians give talks about theirs solutions to important open problems, that were far less than engaging in their delivery. Did anybody in the audience care? No, we were very impressed anyway. – Dan Romik Nov 27 '18 at 5:19

This question is vague and has some loaded terminology ("not yet a famous person"?), but the question overall is good, so I will answer a closely related question, which is:

Where is a good place to present new mathematical results if I am unknown to the broader mathematical community?

I'll write about the US context, since that is what I know about.
In that context, I'm surprised that no one has suggested simply registering for the next AMS Sectional Meeting near you and submitting an abstract for the general contributed paper session. While it is not super likely that an "expert" in the result will attend your talk, it is a good chance to give a (short!) talk about your result in a low-stress environment. And the Sectionals are pretty cheap. My view is that simply gaining experience giving a concise talk is more valuable than trying to get big press for something. The publication, should things work out, would be how to get cognoscenti to pay attention. But writing a good paper and giving a good talk are quite different skills.

If you are fortunate and your area is one of several that often have people outside of "professional mathematics" contribute, you could also submit an abstract to one of their sessions at a Sectional (or the Joint Meetings), though here there is not always room. But there are certainly some subfields, especially some interdisciplinary ones, that encourage these submissions. Be aware that here the issues raised in the other answers will definitely come into play if it is clear you aren't fairly immersed in the literature.

Finally, in some areas (especially of "recreational math") the Math Association of America meetings will have sessions that are more research-focused and open to newcomers.

If you are not based in North America, I'm less sure whether there are similar events. Perhaps there might be joint meetings between 'advanced-high-school' and 'beginning postsecondary' studies folks? In any event, I would recommend the local equivalent of a regional conference that has at least one 'no-rules' generalist session and costs less than the PPP equivalent of $100 to attend.

Naturally, it's always caveat lector when it comes to "solving famous problems", so one has to be careful in the situation posed by the poster. Don't present a solution to the Goldbach Conjecture publicly without having someone who knows what they are doing vet it! Instead, give a talk about the GC and its history, and then in the second five minutes (yes, it could be that short) say, "here is a new approach that shows promise". Maybe someone in the talk will point out an obvious error. Or maybe it will turn out it really is a promising new approach. Or maybe you already solved it. But you won't have claimed to prove the GC and then have to retreat.

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    +1 for the last part. I think it's very unlikely that anyone could present a solution to any reasonably interesting unsolved problem in 10 or 15 minutes --- the eyes of all but two or three true experts on the topic will glaze over if too much technical detail is presented (and those experts likely might skip the talk anyway, thinking it's not worth their time), and I don't see how those watching are going to notice errors unless the errors are so glaring that the talk never should have happened. A talk comes AFTER the result has been mostly vetted, and would be an overview of the approach. – Dave L Renfro Nov 27 '18 at 9:51
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    I'm still mystified by how many people think a talk comes after a result is mostly refereed (in math). I've seen plenty of talks where people are pretty open about "here are some partial results, and I think the following argument works but it's not ready for publication yet". But yes, if the OP is really doing as claimed, it's quite unlikely that any experts at all will be there wherever a first talk is given; the goal would be to get enough experience to give a good talk once said experts recognize the validity of the approach (again, assuming said proof is more or less correct). – kcrisman Nov 27 '18 at 14:09
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    How would your answer translate to someone who isn't based in the USA, who doesn't have funds to travel, etc? – Yemon Choi Nov 27 '18 at 15:08
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    I'm still mystified by how many people think a talk comes after a result is mostly refereed (in math). --- I don't know whether this is thought of by a lot of people, but I've certainly heard many talks and have read even more talk abstracts that were well in advance of formal paper refereeing. I tried to soften my language by using "mostly vetted", but even that sounds a bit too strong when I look at it the next day, especially since the phrase was applied to "the result" rather than "the approach". Perhaps better stated, my point is that surely if the result is more than (continued) – Dave L Renfro Nov 28 '18 at 7:57
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    @DavidRicherby good point, I forget this because so many of the questions I read seem to have that implicit assumption. If I edit my response appropriately, hopefully you can rescind that :) – kcrisman Nov 29 '18 at 17:46

From your post, I'm assuming you are not affiliated with a university. I wouldn't read to much into how long accept/reject takes. Conferences change this process year to year based on feedback and how busy the editor is.

Here is the process your paper will go through

1) The editor will quickly review it (maybe) before sending it on to reviewers.

2) There will be several reviewers (5 seems to be a popular number). Each reviewer will give it a rating that will map to Reject/Accept with revisions/Accept.

3) You'll be informed of the decision at some point in the future.

Now to your question...

The thing is i'm not yet a famous person in the math community, hence it might not be easy to convince the conference organisers.

Lots of non-famous mathematicians publish regularly. I'm not sure what being famous has to do with it. You'll convince organizers of the paper's worthiness for inclusion by doing a rigorous proof and explaining your ideas clearly.

From your post, I'm guessing you're not affiliated with a research institute or university. This puts you at a serious disadvantage for several reasons.

1) You don't know the current state of the art in the field. Math has several sub-fields. In order to get published, you'll need to know which conferences cater to each sub field.

2) A university has faculty to guide your work and lots of great resources from classes you can audit to undergraduates you can hire for pay or grade to do grunt work.

3) Independent researchers don't have the best track record. "Famous" physicists/mathematicians regularly get contacted with some pretty wild (and wrong) ideas. This has happened enough there is a Crackpot Index online to help rate unsolicited papers.

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    Most conferences in pure math don’t have any paper submission mechanism like the one you’re describing. Your answer would apply for certain areas of applied math, and for computer science and lots of other disciplines of course, and for a very small number of pure math conferences. I’ve posted an answer covering the scenario of the typical pure math conference. – Dan Romik Nov 25 '18 at 21:55
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    From my experience this answer does neither fit to practices in pure mathematics and applied mathematics. – Christian Nov 26 '18 at 8:53
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    "There will be several reviewers (5 seems to be a popular number)" I'd say two or three is normal; more than three would be surprising. And this isn't how mathematics conferences work, anyway. "A university has faculty to guide your work and lots of great resources from classes you can audit to undergraduates you can hire for pay or grade to do grunt work." That has nothing to do with writing papers in mathematics. – David Richerby Nov 26 '18 at 13:09
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    In pure mathematics I have never seen more than two reports and most of the time it seems to be one report only. – Christian Nov 26 '18 at 15:41
  1. Try submitting your paper to a preprint site like arXiv.

  2. Solicit comments, preferably from experts of the field.

  3. Try to email some known professor working is currently active in the area of the problem. Note that most mathematicians regularly receive dozens of irretrievably flawed papers claiming to be proving some famous problem like the RH, Goldbach, FLT etc. It is your duty to convince this mathematician that your case is different. Chances are high that you're not going to receive any response, but this shouldn't discourage you.

  4. You might be finding it difficult to find endorsement for posting on arXiv. If so, then your very last option would probably to post on viXra. This is a site where anyone can post anything, so you're not likely going to gain much by posting there.

Note that my answer is suggesting that you strive to make your paper get public attention (by posting on public sites like arXiv and viXra, especially the former). If you do succeed in getting the attention, then probably it's the conference organisers that would be looking for you!

Anyway, good luck, it would be nice if you let us know the result of the review process!

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    I'd say that posting to Vixra is actively harmful. The quality there is so low that people are very likely to say, "Oh, it's on Vixra. It's garbage." without even looking at the text. – David Richerby Nov 26 '18 at 18:02

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