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It is usually not difficult to google search mathematical notions; for example, one can search (with quotation marks) the term "brunnian braid" and find the definition and other related materials. Occasionally some math terms are difficult to google search directly as the same expression is widely used under different meaning by people from other fields. One such example is "Johnson filtration"; other more familiar examples include "support", "almost everywhere", "ideal", etc. Is there any solution to this situation?

To me, some expressions are almost hopeless to search with google. For example, I have no idea how to search $e^{i\pi}+1=0$ unless I know the name of the identity. Another example is to search $E_0^*(G)$, which is the graded Lie algebra associated to a discrete group $G$. Unless one knows the name of the terminology, how can one google search $E_0^*(G)$?

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    $\begingroup$ Indeed it's quite hard :/ Btw, $\mathbb{e}^{\mathbb{i}\pi}+1=0$ is Euler identity :D $\endgroup$
    – servabat
    Commented Dec 7, 2014 at 11:18
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    $\begingroup$ @servabat, this one is famous. But not every identity has a universally accepted name; even if it has, one may not be aware of it. $\endgroup$
    – Zuriel
    Commented Dec 7, 2014 at 11:19
  • $\begingroup$ Sometimes, i'm trying things like e^(i*pi) + 1 = 0. Doesn't work everytime, but.. $\endgroup$
    – servabat
    Commented Dec 7, 2014 at 11:22
  • $\begingroup$ Related older question: math.stackexchange.com/questions/74609/… (There were also some related discussion on meta.) $\endgroup$
    – Martin Sleziak
    Commented Dec 7, 2014 at 13:05
  • $\begingroup$ @MartinSleziak, thank you for the references!! $\endgroup$
    – Zuriel
    Commented May 31, 2017 at 22:34

5 Answers 5

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A few years ago we developed the search engine SearchOnMath, in order to search for mathematical formulas. Recently our tool has indexed both: Mathematics and MathOverflow.

Currently, SearchOnMath is the mathematical search engine with the largest number of indexed sites (including Wikipedia, Wolfram MathWorld, among others ...).

EDIT:

We released on September 2021 a Beta version for arXiv, available at searchonmath.com/arxiv.

Since March 2022 some results may be available only for subscribers. If you like SearchOnMath, please consider subscribing. This will help us on paying for our servers.

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  • $\begingroup$ Thanks! I have searched $a^2+b^2=c^2$ but no results were found. Did I miss anything? $\endgroup$
    – Zuriel
    Commented Jan 31, 2019 at 20:32
  • $\begingroup$ Hi, please, enclose formulas between \${ }\$. So, you should write as follows: \${a^2 + b^2 = c^2}\$. $\endgroup$
    – Flavio Gonzaga
    Commented Jan 31, 2019 at 20:35
  • $\begingroup$ Searching for $a^2 + b^2 = c^2$ $\endgroup$
    – Flavio Gonzaga
    Commented Jan 31, 2019 at 20:39
  • $\begingroup$ It works now! It is a great website and I appreciate your answer very much! This is exactly what I was asking for. I am pleasantly surprised to find that it also works for ${E_0^*(G)}$. I wish I had seen your answer earlier. $\endgroup$
    – Zuriel
    Commented Jan 31, 2019 at 20:40
  • $\begingroup$ I don't know why it took me so long to find out about this. Works really well @FlavioGonzaga ! Handy tool to find standard results and theorems, and figuring ut solutions to smaller subproblems :) $\endgroup$
    – user738244
    Commented Jan 21, 2021 at 11:25
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In comments and other answers it was mentioned that there are some other search engines which could be better when searching for mathematical expressions. But I think that as nowadays several pages uses LaTeX syntax (Wikipedia, this site, to mention just two important examples). Additionally, some people have also TeX-sources of their documents online. So it is not entirely hopeless to google simply for the LaTeX version of the formula. However, there is problem that many things can be typeset in LaTeX in many different ways. Another problem is choice of variables. It is often useful to restrict search to some site(s), for example, "x^2+y^2=z^2"+site:math.stackexchange.com+OR+site:wikipedia.org.

Searching for TeX using Google

Let us try some concrete examples.

Continuum hypothesis

For example, let us assume that I know that there was something like $\aleph_1=2^{\aleph_0}$ was mentioned in the class, but I do not know the name of this formula. (But, luckily enough, I know to typeset it in TeX.)

If I try some reasonable search queries, for example:

in all of them we can find at least some things related to continuum hypothesis.

Euler's formula

You mentioned Euler's formula. Simply searching for "e^{i\pi}" returns Wikipedia article about Euler's identity among the top results. Searching for "e^{\pi i}" also returns some relevant hits.

An integral

Let us say that I am looking, for some reason, for the integral $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\,\mathrm dx$.

Here are some examples of searches, which seem reasonable when searching for this particular integral:

Triangular numbers

In this post, I have mentioned some examples of the search for the formula $\frac{n(n+1)}2$ for the $n$-th triangular numbers, although it was in a somehow different context.

Searching in Google Books

Google Books contain a lot of data. Google usually do a good job in OCR-ing these books. However, they don't OCR Greek letters, math formulas, etc. Occasionally it is possible to guess how some math symbol would be OCR-ed.

For example:

Of course, this trick only has a very limited usability.

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My general strategy is to iterate through related added keywords or to get rid of themes by using the feature to subtract words in the search. In particular, adding "Wikipedia", "StackExchange", "nLab" and things like that narrow search down strongly.

For example, if you search for the Tits group (Wikipedia), then google image search for 'tits group math' or 'tits group diagram' is much closer to what you want than if you just search 'tits group' (google images).

You can try to google LaTeX code, but it hardly helps. There is software like latexsearch for that, although from what I tried I wasn't amazed either. As a remark, there is detexify if you don't know how to generate some symbols. Often the related section of Stack Exchange questions matches the title well, so for $\mathrm{e}^{i\pi}$ you can surely find the concept via this box. What I also very often do is go to Wikipedia, a related concept, and click "what links here" (pages related to Jacques Tits) on the side.

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    $\begingroup$ I clicked by mistake your link to "tits group", and, oops! $\endgroup$
    – Zuriel
    Commented Dec 7, 2014 at 11:51
  • $\begingroup$ @Zuriel: Whether you refer to abstract algebra or human bodies, there's no need to be afraid. But can I interest you for a Wiener sausage? $\endgroup$
    – Nikolaj-K
    Commented Dec 7, 2014 at 12:07
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    $\begingroup$ @NikolajK: a similar problem happens if you do a google image search on "coset." The concept can be tricky when you first learn it, so when I was teaching group theory I wanted to see if there were any helpful images of cosets on the web that I could use in class. Needless to say, nothing I found was going to explain cosets to anybody. $\endgroup$
    – KCd
    Commented Jan 11, 2015 at 10:34
  • $\begingroup$ The link to LaTeXSearch seem to be dead. Still, various screenshots showing what it used to look like can be found online: google.com/search?tbm=isch&q=latexsearch+springer google.com/search?tbm=isch&q=latexsearch $\endgroup$
    – Martin Sleziak
    Commented Apr 25, 2021 at 14:08
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Approach Zero: A math-aware search engine.

This search engine supports LaTeX and currently searches through Mathematics StackExchange and ArtOfProblemSolving (AOPS). I use this everyday for searching my Homework questions.

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    $\begingroup$ Shouldn't you be attempting your homework questions yourself $\endgroup$
    – user50229
    Commented Apr 8, 2022 at 20:19
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I have found this search engine useful, called (Uni)quation. You can search for mathematical expressions using TeX.

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    $\begingroup$ Uniquation now seems to have disappeared $\endgroup$
    – user50229
    Commented Mar 4, 2020 at 11:21

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