TITLE: Where to publish a new proof of an old theorem?
QUESTION [26 upvotes]: A few months ago I came up with a proof for an old theorem. After being excited for a moment, I then tried to find my proof 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.

REPLY [5 votes]: A new proof of an old theorem, especially using modern machinery, could well be within the scope of the Graduate Journal of Mathematics, which seeks to publish work either by graduate students or that would be of interest to graduate students. From their website:

The Graduate Journal of Mathematics is an electronic journal that publishes original work as well as expository work of general mathematical interest which add to the literature, have pedagogical value and help make more widely accessible significant mathematical ideas, constructions or theorems...One main aim of our journal is to help researchers in mathematics in general, and graduate students in particular, gain access to important ideas and communicate interesting mathematics.

Full disclosure: I am on the editorial board. And I'd be happy to receive a submission with a new proof of an old theorem.