If you were to discover a new math relation, to whom do you submit your findings? It cannot be patented. Is there some Secret Academy of Math Wizards that could assess your finding?
You would write a paper explaining it and submit it to one of the many scholarly journals of mathematics. You might also give a paper at a conference, but getting published in a maths journal is the best way to get permanent recognition.
(And before you do that, you’d better do a search of the journal literature to see if any one else discovered it before you did.)
Giles is right. I’ll add that the scholarly journal would have a couple academic mathematicians carefully look over you paper before it was published, to make sure it really was correct, new and interesting.
Interestingly, there is no Nobel Prize in mathematics. So, no trip to Stockholm.
There are two approximate equivalents in the mathematical world for the Nobel Prize:
The Fields Medal has been around longer, but it’s only given to those who are 40 or younger. It’s for achievements among younger mathematicians.
Incidentally, the chances that someone could make a useful addition to modern mathematics without having read a lot of higher-level mathematics are vanishingly small. The bizarre notion that a lot of people have that there are untutored geniuses who can create great mathematics without exposure to the current structure of mathematics is silly. No, the counterexamples you’re about to give are wrong. Ramanujan was not a poor Indian boy with no training when he wrote Hardy with his ideas. He grew up in a middle-class Indian family and entered college at 16. He knew many mathematicians, and he’d already published one paper when he wrote Hardy. No, Galois did not create the fundamental ideas of modern algebra the night before he died in a duel. He had been studying higher-level mathematics for six years, and he had worked on his ideas over that period. And those two are probably the closest anyone has ever come to being a relatively isolated mathematician, and those were one hundred and two hundred years ago (approximately). It’s even harder to do cutting-edge mathematics today, since it’s necessary to absorb much more background before one can reach the areas of math where breakthroughs are possible.
BrotherCadfael writes:
> Interestingly, there is no Nobel Prize in mathematics. So, no trip to Stockholm.
I’m not quite sure what you’re saying here, but let me say something about this. If your point is that in other sciences there is a general agreement that a discovery that has won a Nobel Prize is a great one, while one that hasn’t won a Nobel Prize is a lesser one, that’s not true. Scientists generally recognize that the awarding of Nobel Prize is more random than one would hope. There are great discoveries that didn’t get Nobel Prizes, and there are not so great discoveries that did get Nobel Prizes.
Why should there be any secrecy? Why would you want to patent it? What good would that do you?
If you were to genuinely discover a new math relation, and you wanted to let people know about it, you would just tell them about it. Professional mathematicians traditionally do this most significantly through writing and publishing papers in mathematical journals, and that still very much is the status quo. In ancient times, there were other ways of getting the word out there, and in modern times, there are other ways of getting the word out there, but submission to and acceptance by a suitable mathematical journal is the most straightforward way of gathering interested eyes.
That having been said, if you are proposing that you have made an important mathematical discovery without any significant mathematical background, well, as you no doubt know, that is very unlikely. But you may as well start telling us what it is now anyway.
The honor of knowing that people all over the world are jinxifying their numbers should surely be enough reward.
Well, it’s that secret formula to pick the winning lottery numbers. 
I’ve got a surefire method, but it takes several million tries before it works.
I’m sure your basic point is correct, but you may be underestimating prodigies like Ramanujan and Galois, who each demonstrated great talent many years before their famous publications. Even today, one sometimes reads of novel theorems by people in their early teens.
And, although they may be more like “engineering” than “mathematics,” there are many problems in recreational mathematics which are quite accessible. As just one example, consider Minimal Oblivious Sorts, a fun problem with possible real hardware applications.
Well, there’s Marjorie Rice, who discovered four of the 14 known pentagonal tilings, despite having received no more than a highschool education in mathematics…
That said, I do agree with your larger point. Very many very clever people have been doing mathematics for a very long time, so the chances to find something genuinely new (and interesting; one can of course always conjur up some new stuff and some rules for it, but chances are they won’t matter much to anybody) without being intimately familiar with the body of work thus built are tiny. But then again, there also is a lot of mathematics to explore!
When I was in high school, I discovered that the following set of rules creates a pentagon which can be tesselated:
- We have a pentagon ABCDE.
- Sides AB, BC, CD, and DE are all the same length.
- B and D are 90 degree angles.
- C is greater than 90 degrees and less than 180 degrees.
I sent off an email to the Wolfram MathWorld, asking if this was something new, as it didn’t appear to me to fit any of the types of pentagons which could be tesselated that I could find listed.
Something like 2 or 3 YEARS later, I got an email back from them saying that no, it was considered to be a subset of one of the known types.
I have no idea what went on during those years, but I did get an answer back!
Sounds like the Cairo Pentagonal Tiling. In yours, are the other three angles all 120, or can they differ?
They can differ, adjusting the length of side EA while maintaining a convex shape.
It is conceivable (not likely, but conceivable) that someone solve the Collatz (or hailstone) conjecture (q.g.) or the P=NP question. It is conceivable that someone might find an elementary proof of the 4-color problem or Fermat.
The thing about Ramanujan was not that he was untrained, but his training was unsystematic and he really didn’t know how to prove any of his odd-looking formulas. The case of Galois was utterly different. He created, to all intents and purposes, modern algebra. It took a long time before other mathematicians really came to understand what he did. Where would he have gone if he hadn’t gotten involved in nasty political games? His achievement was staggering.
A mathematical journal? Heck, post it here. Word will get around. It wouldn’t be that hard to prove later you are “Jinx”. I mean, you’d be outing yourself to some professor someplace, sure, but unless you take mathematicians to the Pit, is that such a big deal?
How is somebody who doesn’t already have a contact in the Secret Academy of Math Wizards going to get published in one of the math journals???
Well, by submitting to them, of course.
But I actually agree with you that you might as well just post it online somewhere for interested parties to read. I think journals are somewhat an archaicism* from a time when access to the means to distribute information widely was a scarce resource.
For the time being, a professional mathematician must, for career reasons, seek the prestige which continues to be conflated exclusively with journal publication, but for a non-professional mathematician, there may be less reason to seek traditional journal publication (though if one can convince at least one reputable journal to accept one’s paper, it will be quite helpful in convincing others not to dismiss it offhand, a hurdle which might otherwise be difficult to clear for a non-established mathematician).
[*: At one time, journals were a means of making academic research easier to obtain; now, so far as I can see, all do they is make it harder to obtain (putting it up behind prohibitively expensive paywalls and so on). Of course, there’s the idea that journals provide peer review, but peer review simply means being reviewed by one’s peers… This could just as well be done post-publication (and, indeed, most importantly is done post-publication), even in an organized and disciplined way. As far as I’m concerned, the continued existence of the profit-seeking journal system in its current state is a leech on academia.]
One other point: I have no difficulty at all in believing that the OP has discovered some interesting mathematical relationship. The part that’s highly unlikely is that it’s a new mathematical relationship. Many’s the layman who has, all unknowing, stumbled across some theorem which has been known to mathematicians for centuries.
And to Indistinguishable’s point about journals, the most recent meeting of the journal-discussion seminar I’m in was covering a completely crackpot paper which had somehow managed to get published in Monthly Notices of the Royal Astronomical Society (a quite reputable journal). The paper was written by a biologist and purported to challenge the most fundamental tenets of modern cosmology, and wasn’t even consistent in the wide array of ludicrously incorrect physics it showed. Most of our discussion was centered around the question of how such a piece of work managed to get past the peer-review process, and what might be done to fix the system.
But where? You could post to your own website or blog, but who’s going to see that? For even Arxiv.org, which is about the most open place of any popularity that I can think of, you need to have someone endorse you before you can post.
That’s not that big of a bar, though, and I actually talked someone into endorsing me there a few years back, and put a couple papers up. Crickets chirped. Maybe they sucked, or maybe they just didn’t get read because there are so many other papers posted, and mathematically, I’m a nobody, so who would bother. Either way, no feedback.
Tracking down the Secret Academy of Math Wizards and pestering them might be a better approach.