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Assume that I have a math problem, I want to find results, theorems (as much as I could find, in maximum number) relevant to the problem, how can I do that efficiently?

For example, one way could be to look for the latest survey paper related problem, but I have seen that survey paper does not exist in every case.

Second example, is searching using key words, but it does not help in mathematics much, as search engines are not compatible with mathematical notation... is there any technique to optimize search related to the specific topic or problem?

Is would be nice to have a optimized flow-chart for searching, collecting and compiling related to the problem or topic.

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    When searching it helps to know the vocab that defines the branch and subset of what you are searching for. – Solar Mike Aug 3 '20 at 19:01
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    Here's an old post on MathOverflow asking a related question. – Anyon Aug 4 '20 at 14:10
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You're asking for the impossible. Almost every mathematician with more than a few papers has had the experience of submitting a paper or circulating it as a preprint and having some relevant work they didn't know about (and are not expected to have known about) pointed out to them.

If you are asking about one or two specific narrow questions or equations/formulas, then usually the best thing to do is to figure out who the friendliest expert who might know is, and ask them. Even if they don't know, they might refer you to another friendly expert. (Some subsubsubfields have friendlier experts than others, and this difference definitely influences the popularity of the subsubsubfield.)

If you're looking to break into a new subsubsubfield with lots of history without an advisor, then some subsubsubfields have friendly conferences, but, in general, ...uhh... good luck.

  • "..a few papers has had the experience of submitting a paper or circulating it as a preprint and having some relevant work they didn't know about (and are not expected to have known about) pointed out to them" .. do u mean they rediscovered already published result? Seriously?? I didn't know that... if there is any literature on it, plz write it down in comment, also your suggestion fits for researcher affiliated to research institution (like in Russia) or university, not for independent researcher.. – Michael Aug 4 '20 at 8:24
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    @Mike SQ: do u mean they rediscovered already published result? Seriously?? --- See the paragraphs under "IV. MOST C-INFINITY FUNCTIONS ARE NOWHERE ANALYTIC" in this 9 May 2002 sci.math essay. (See also Bruce Blackadar's most recent comment under this question.) For those actually interested in this topic, a Part 2 follow-up was posted on 19 May 2002. – Dave L Renfro Aug 4 '20 at 11:06
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    In my first published paper (arXiv version arxiv.org/abs/math/0409490), reference [34], which has our results in an important special case, was pointed out by a referee. In another published paper (arXiv version arxiv.org/abs/0809.2981), the reference [ALP92]. which has a somewhat weaker version of our results in different form, was also pointed out by a referee. – Alexander Woo Aug 4 '20 at 13:49
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    I think my suggestion works for people who personally know the community in their subsubsubsubfield, regardless of whether they are currently affiliated with a university, and doesn't work for people who don't personally know the community, again regardless of whether they are currently affiliated with a university. – Alexander Woo Aug 4 '20 at 14:08
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    Just be glad you're not working in a subsubsubfield where many people will discuss their latest results in conferences and then (out of laziness) take 5 years to actually write a paper. (In that case, frequently the papers end up implicitly using, without explicit statements and proofs, folklore lemmas everyone in the community knows but no one has actually written down anywhere.) In that situation, any outsider finds themselves automatically 5 years behind. – Alexander Woo Aug 4 '20 at 14:15
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No single strategy is likely to be optimal for all (math) searches. I would start with math key words (not symbols), both on the full web and in google scholar. You will get hits to math papers and books and stack exchange postings. Those links will suggest next steps.

You can also post a request for references at math.stackexchange.com if you are specific enough about the problem.

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    For math searching, I would probably not not use Google Scholar, but instead I would use MathSciNet. – GEdgar Aug 3 '20 at 20:45
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A literature search might not be effective, but might work.

Start by finding one or a few articles that are as relevant as you can manage. Read their introductions and check for cited articles that are more relevant, or at least equally relevant.

Then check which artiles cite the article you are considering (from Semantic scholar og Google scholar, for example; both tend to link to PDF files when accessible). Do some of them seem promising?

Then you just iterate through the eternally expanding collection of interesting articles. As you become familiar with a subfield, you learn to ignore articles which are not of interest, which speeds things up, but this is still a long process, and it is only as good as the bibliographies in the relevant fields are. You want to start somewhere reasonably close to have any change of finding what you are looking after, too.

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