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Mathematics talent runs in my family, but although I enjoy learning about things in mathematics and biostatistics, I am a biochemist by training.

So I read a blog post by a mathematician, and started thinking, and writing, and consulting with my younger brother (also a mathematician), and we have a theorem.

But, perhaps just like in biochemistry, there are many times where someone thinks that they have discovered something, only to find out that a thorough search of the literature shows that someone else was first.

In chemistry, if you have synthesized a molecule, and think that you might be the first to do so, there are databases of molecular formulae, structures, and spectra that you can search, before you embarrass yourself.

My questions are these:

  1. How does one go about searching the mathematics literature, to see if a theorem has already been proven, or addressed in a different way?
  2. Is there a searchable database of mathematics ideas that researchers can query?
  3. Are these databases and other information available to the hoi-polloi?

Many thanks in advance for your help?

Mauro ALLEGRANZA
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Michael Roberts
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    As a rule, try to get to your question quickly and then provide additional details if necessary. People here are trying to quickly determine if they can help, and putting the question close to the front helps them figure that out. – Thomas Andrews Mar 15 '23 at 18:14
  • You can learn a lot by searching the web and reading Wikipedia, and sometimes it takes some research just to figure out better search terms. Which area of math is your theorem in? If you tell us more about it here, we can help point you in the right direction. – Karl Mar 15 '23 at 18:31
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    It's not free but https://mathscinet.ams.org/mathscinet is one search engine I am aware of – Vasili Mar 15 '23 at 18:34
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    See here and here. Admittedly, you need an academic license or subscription in many cases. – Golden_Ratio Mar 15 '23 at 18:35
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    We're constantly finding out that results were duplicated by various mathematicians who didn't have communication with each other. Leibniz and Newton for calculus are the most famous but there are lots. – CyclotomicField Mar 15 '23 at 18:36
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    Without the risk of disclosure, can you say at least the relevant domains (keywords), otherwise we cannot help ! – Jean Marie Mar 15 '23 at 18:57
  • You could also ask the statement of your theorem (without proof) as a question on this site, and you'll quickly see how others approach it. – Karl Mar 15 '23 at 19:06
  • If your result is about a sequence of integers, you could try looking it up in the OEIS, the online encyclopedia of integer sequences. – kimchi lover Mar 16 '23 at 00:46
  • Also, it often takes a lot of "thinking, writing," etc. for a smart person without the relevant background just to reach insights that have been thoroughly internalized by mathematicians familiar with a topic, so unless you've had layer upon layer of divine inspiration, it's unlikely you've done something novel (yet!). We regularly get posts here (notably around the Collatz conjecture) from people guarding a secret idea that turns out to be a trivial observation (from the right perspective) once they finally reveal it. But maybe yours is different :) – Karl Mar 16 '23 at 01:23
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    Many thanks for everyone's input. Inasmuch as I don't plan on exploiting any alleged discovery that I may have made for exorbitant sums of money or fame, let me describe what I have:

    Define "rotation" of an integer as any division of the digits of that integer, and switching them. So, for example, 34512 is a 2-digit rotation of 12345.

    The theorem is this: For all integers N, having length m digits, if there exists an integer q that divides both N and $10^m – 1$, then q also divides any rotation of N.

    So, number theory? Bit shifting? Something else? Where should I go from here?

     – Michael Roberts Mar 17 '23 at 02:10
  • Neat result! That's definitely number theory. It seems to follow from some mod $q$ arithmetic: if $10^m\equiv1$ and $10^{m-1}x+y\equiv0$, then multiplying both sides by $10$ gives us $10y+x\equiv0$. If $x$ is a single-digit number, this is a single-digit rotation. – Karl Mar 17 '23 at 07:11

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