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I performed some research yielding useful information. I only used the mathematics that I learned in high school; I did not use any program or any scientific experiment. Is it possible to have my research accepted by a journal from Elsevier, even though it is my first research? Can a reputable journal accept research with simple equations? I’m 18 years old.

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You don't need credentials (or age) to publish mathematics in a reputable journal. You need a paper that is acceptable to the editor with advice from a set of reviewers that they depend on.

But in general, a math paper needs to be "interesting" to mathematicians. It can be interesting in one of two ways (at least). The first is that the result is new and non-obvious. In particular something that might be applied to other lines of thought to continue advancing the art. Classical unsolved problems, while not new per se become new if a proof can be devised.

The second way that a result can be interesting is when its proof is new in some way, even when it already has another proof. It doesn't need to use advanced techniques, but it needs to combine them in some novel way to arrive correctly at the result. A new way to attack an old problem can lead to other advances.

In many ways new proofs are more important than new results, since the insight that produces it can, perhaps, be applied to other problems in the field. My dissertation had such a proof (though quite advanced, in that case). I had two different proofs in hand, but one was quite different from the standard way of attacking the problem at hand.

You can certainly submit your paper to a reputable journal (Elsevier or other), but it is up to them what to do with it. You might hear back from the reviewers that it is trivial, in which case it is just a good learning experience of you and perhaps an incentive to continue. The first "paper" I ever wrote was like that, and not published. There was something that I didn't know about (math induction) that made the work rather trivial. But it was fun and induced me to follow the math genie wherever it went.


An example: The Four Color Theorem, has a proof that is unsatisfying to a mathematician since it depends on an analysis of a large number of cases in which a computer was used as part of the solution. While accepted, it is more brute force than elegant. A solution that depended only on simple ideas would be highly valued. Many people my age (old) worked on that for a bit and thought about it a lot but didn't have the insight required to crack it.

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