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A few months ago I came up with a demonstration for an old theorem. After being excited for a moment, I then tried to find my demonstration in the literature. Since I did not find it, then I started to wonder if it was worth publishing it.

I asked a few people about journals that could publish something like this, and they gave me two recommendations:

(1) The Mathematical Gazette, http://www.m-a.org.uk/the-mathematical-gazette

(2)The Plus Magazine, https://plus.maths.org/content/about-plus

First I submitted to the Mathematical Gazette, and my article was rejected because according to the reviewer I was trying to prove something very simple using something much more complex (although I just used undergraduate level math).

Then I submitted to Plus, and it was also rejected by the editors (it probably doesn't fit well with their magazine).

Do you have any suggestions? Thanks.

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9  
All else failing, you could always post it on arXiv (and indeed you might do this even if you do publish it somewhere else); obviously this isn't really a "publication," but it does make your work public. – Noah Schweber 8 hours ago
2  
One thing that is probably asking yourself: are there any advantages to the new proof over the previously existing proofs? (e.g. does it rely on basic complex analysis rather than the nuclear theory of Banach algebras). If the new proof is longer than the old one, then this is likely to be a problem. – Anthony Quas 8 hours ago
    
"Where to publish a new demonstration of an old theorem?" -- in a scientific magazine which ceased to exist before WWI, preferably before the original first published proof was conceived. – Włodzimierz Holsztyński 5 hours ago
1  
It all depends on what your "old theorem" is, and how your new proof of it looks like -- for example, if you have a 5-pages proof that all finite simple groups are either cyclic or 2-generated which does not use CFSG, I'd suggest you to submit to the Annals ... . – Stefan Kohl 4 hours ago
1  
If your proof is of pedagogical interest and/or can be integrated in a review of the subject, you could try L'Enseignement mathématique. – Gro-Tsen 2 hours ago
up vote 11 down vote accepted

If the old theorem is something commonly seen in an undergraduate math class (with the old demonstration), then this might be appropriate as a "Note" in the American Mathematical Monthly.

What could happen if you submit it? They may publish it. The referee may give you a reference for it. They may respond in the same way as the Gazette.

What if the old theorem is not commonly seen in an undergraduate math course? When you write a textbook on that area of math, you can include your new proof. But if you think it unlikely you will write a textbook on this, then probably there is little prospect for publishing this. Maybe if you make it known to the experts* then some day one of them may include it in their new textbook.

*Perhaps by posting somewhere on-line...

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thank you! I'll submit to the American Mathematical Monthly as you suggest, and let's see how it goes. (The theorem is very common, and I won't certainly write any book on the subject.) – M.Lopes 3 hours ago
up vote 12 down vote

This question, as stated cannot be answered. Everything depends on the theorem and on the proof, and this information you did not state.

For example, at least one Fields medal was awarded for a "new proof of an old theorem" (Selberg, 1950). A new proof can be published in principle in any mainstream journal, if the theorem is important and the proof gives an important new insight.

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1  
+1 for the prime number theorem example. As I was reading over the question and the other answers, I had this vague memory of an alternate proof of something that wound up being very famous, and then I realized what it was when I saw your answer. – Dave L Renfro 5 hours ago
1  
Thank you, Alexandre Eremenko. No, it doesn't give any new insight, that's why I wondered in the first place if it was worth publishing it. Then, I thought: why not? It's still interesting at least as a curiosity. – M.Lopes 3 hours ago
1  
It's not quite correct to describe Selberg's Fields Medal in this way. There was also at that time his substantial work on zeros of zeta and L-functions, and his development of sieve methods. – Lucia 2 hours ago
up vote 3 down vote

Alternately, when you write a paper on a related topic (ie, which already develops the necessary machinery), you could perhaps include it somewhere in that paper? I've seen this done numerous times.

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Thank you, Karl Schwede. I won't write anything related, because my research field is very far from this. I just came up with this demonstration while "playing" with some different problems on a Sunday. :) – M.Lopes 3 hours ago

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