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Many types of equations are being used in multiple contexts, so a search for specific formulas might be one way to identify scholarly papers that are conceptually related.

Is any website or tool actually providing recommendations of related content on that basis?

The closest I can think of is Springer's LaTeX Search, which allows to identify papers containing similar TeX strings, e.g. $\nabla [(k(T)\nabla T]$.

However, they seem to match the string as a whole, which gives undue weight to things like variable names or formatting, and while it is possible to identify related papers that way, they do not seem to use it to recommend related articles, nor have I seen this used anywhere else at publishers' sites, at arXiv or on Google Scholar, nor in readers like Papers or Mendeley.

Also, their system is proprietary, and I would be interested in a system that is open source and openly licensed. Any pointers appreciated.

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    $\begingroup$ I tried to visit the Springer Image Search site you linked to using the onboard WiFi during my KLM flight, and it blocks with reason "adult content"; presumably because of the name of the domain... $\endgroup$ – Carlo Beenakker Apr 5 '14 at 2:38
  • $\begingroup$ A Google search with the terms "latex search springer" should quickly lead you to the equation search engine I mentioned. If it is blocked by KLM, we'll have to wait until you're connected on the ground again. $\endgroup$ – Daniel Mietchen Apr 5 '14 at 2:43
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    $\begingroup$ I think it would be great to have more intelligent tools for searching and indexing the mathematical literature, but I do not think that they currently exist, and I am not sure that searching for equations is necessarily the way to go. In principle one could extract a huge amount of information by analysing the LaTeX source of arXiV articles, including cross references, terms that occur in definitions and in statements of theorems, and so on. But I am not aware that anyone has tried to do that. $\endgroup$ – Neil Strickland Apr 5 '14 at 8:56
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    $\begingroup$ @AlexDegtyarev If an equation type is new in some contexts but already well-described in others, reading up on those latter ones may mean advances with the former. For some examples, see Hammerstein, P.; Hagen, E. (2005). "The second wave of evolutionary economics in biology". Trends in Ecology & Evolution 20 (11): 604. doi:10.1016/j.tree.2005.07.012. $\endgroup$ – Daniel Mietchen Apr 6 '14 at 3:52
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    $\begingroup$ Some older questions at MSE related to searching for formulas: meta.math.stackexchange.com/questions/10169/… $\endgroup$ – Martin Sleziak Apr 6 '14 at 6:45
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There is MathWebSearch; from the site:

The MathWebSearch system (MWS) is a content-based search engine for mathematical formulae. It indexes ​MathML formulae, using a technique derived from automated theorem proving: Substitution Tree Indexing.

Indeed, zbMATH, already uses it to provide MathSearch. The interface uses LaTeX syntax. (MWS itself seems to support different interfaces.)

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    $\begingroup$ There is also a feature request to get this on MO $\endgroup$ – user9072 Apr 5 '14 at 13:27
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    $\begingroup$ Since it was asked explicitly I should stress this is free software (GPL). $\endgroup$ – user9072 Apr 5 '14 at 13:45
  • $\begingroup$ The project seems to have ended as of 2015, according to kwarc.info/projects/MathSearch . The project "TRAC" page seems to be down, though the code is still at github github.com/KWARC/mws . $\endgroup$ – j.c. Feb 6 '17 at 18:02
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Approach0 is able to find expressions with different variables:

https://approach0.xyz/search/?q=%24%5Cnabla%5Cleft(k(T)%5Cnabla%20T%5Cright)%24&p=1

However, its index does not include academic papers, it is only indexing Math StackExchange now.

That being said, I think this is still an option since Approach0 is open-source, and you can use it freely to index whatever content you want to perform search on. And in the near future, approach0.xyz is very likely to further include academic PDFs into its index. Just keep an eye on it!

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  • $\begingroup$ Thanks - that certainly looks interesting. I'm following it on GitHub now. $\endgroup$ – Daniel Mietchen Feb 10 '17 at 12:20
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I know this is already answered, but searchOnMath looks interesting too. Maybe it suits your needs.

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    $\begingroup$ I had accepted the MathWebSearch answer by quid because it fulfills the criteria set out in the question, but I remain interested in activities in this space, so thanks for the pointer. I gave it a few tries, and while it failed on several of them (e.g. the example given in the original post), it came up with useful results in other cases. $\endgroup$ – Daniel Mietchen May 29 '15 at 20:19

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