Publishing elementary proofs of theorems

I'm an undergraduate student and I believe I found another proof of Heron's formula. I have a bunch of questions:

I would like to publish this "proof" (I haven't found mistakes yet) in some magazine. But as you would expect I don't want to discuss the proof with someone else from my university (perhaps they can steal it?) or who knows. Anyway I'm confused what to do, would it be wrong if I write the paper in .tex and submit it to some magazine? what is the typical procedure in this case? with whom shall you discuss your "proof" ? is it common to submit "proofs" of theorems and then be noticed by the editor that your proof is actually wrong?

Can you please give some advice?

Don't let yourself get discouraged. It is wonderful that you have such aspirations!

But, in my opinion, it would be best to aim for developing your skills, poise, maturity (in the sense of mathematical sophistication), and confidence, by undertaking a series of "smaller" and somewhat challenging steps:

• researching; engaging in an exchange of ideas;
• writing;
• revising;
• consulting peers;
• consulting faculty member(s);
• continue researching;
• rewriting;
• revising;
• presenting your research in a poster session at a conferences for undergrad/grad research;
• revising your paper;
• presenting your paper - at an informal gathering -- then perhaps, to your department;
• revising your paper;
• submitting a paper to journals that publish primarily undergraduate and graduate research/articles, etc.;
• revising as suggested by editor (if it hasn't been rejected...etc.);
• resubmitting paper;
  $\qquad \vdots$
  
• Did I say revising?

Better to experience, learn, and build from a series of small successes (even perhaps a few not-so-successful experiences) en route to publication, than to try, from the starting line, to take a huge leap for which you may not be prepared and will likely fail.

Note: There are also magazines and journals whose target audience is undergraduate and graduate students, and hence much more likely to showcase the work of students. (I'm assuming you're a student, given your reference to your "teachers.")

See for example the MAA's (Mathematical Association of America) site addressing venues for publication of undergraduate research in mathematics: MAA webpage here

Excerpt from the site:

Venues for Publications

In addition to the traditional mathematical journals where the authors are usually research faculty, there are some journals that specialize in mathematical research done by undergraduates. These include the Pi Mu Epsilon Journal, The Pentagon: The Official Journal of Kappa Mu Epsilon, Rose-Hulman Undergraduate Mathematics Journal, Furman University Electronic Journal of Undergraduate Mathematics, and the Morehead Electronic Journal of Applicable Mathematics.

These journals are all excellent venues for undergraduates to present their research, however it is generally accepted that they are not at the same level as traditional faculty-oriented journals.

[Of all such journals, however, I'd suggest looking at some issues of] the new undergraduate research journal, Involve – A Journal of Mathematics, which is in a class by itself. The journal boasts an impressive editorial board of distinguished faculty and articles are to be reviewed by MathSciNet and Zentralblaat Math, a known distinction for quality journals This distinction also allows student work to be more easily searchable and citable! [Brackets mine.]

(from MAA Resources)

More information on Involve: A Journal of Mathematics can be found here.

I'd encourage you to look into some of these sites and publications!

Good luck!

I'd second Beni's comment - originality is probably a greater worry than correctness in this case. And the best way to confirm originality is by showing it to someone more experienced. And if you don't trust the math faculty at your university to refrain from stealing your ideas, then you shouldn't trust them to teach you math, either. You've got to trust someone - what's to stop the magazine editor from putting her name on your paper and publishing it as hers?

Do you know about the arXiv? Anyone can put anything up there, and it gives you some protection against plagiarism, as it shows when you made the work public.

EDIT: Gerry's answer, which was posted right before mine, is more succinct and comprises the same ideas. I'll leave this here anyway, but read his first.

To be honest, I doubt you'd be able to find a journal that would be willing to publish a new proof that isn't in some way spectacular. If you can prove it using homological algebra or stochastic differential equations, you may have something. If it's an elementary argument, chances are it's very close to an existing proof (close enough to not warrant getting published). Even if it isn't, Heron's formula is both a rather basic result and easy to prove, with proofs easily shorter than a page. Mathematicians simply aren't interested in reading such an argument, and journals definitely aren't going to publish something no one will read. Plenty of very good math goes unpublished, and something has to at least break some new ground to be worth considering.

If you really think you have something special, I suggest to you 2 possible courses of action. The first is to show it to someone in your department, and ask them if it is anything special. If you are really scared of them stealing it (I doubt they would), you can post it here. In that case, it would be very difficult for anyone to steal it, because there is a log available. I would advise against going to journals directly, firstly and foremostly to save both your time and theirs. I also suggest you read some modern math papers and see what one really comprises of (though if you have read some, you may disregard this).

In addition to post it here and send it to arXiv, you can also create a website, for example on wordpress, to present it. Being a blog site it will show when you created it.