How to google search mathematical notions and expressions?

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 $E_0^*(G)$?

Solution 1:

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 ...).

The following video illustrates how it works: SearchOnMath - a brief guide.

EDIT:

We’d love to hear your feedback. We also posted on Meta.

Solution 2:

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:

"\aleph_1" "2^{\aleph_0}"
"\aleph_1=2^{\aleph_0}"
"2^{\aleph_0}=\aleph_1",
"\aleph_1" "\mathfrak c"

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:

integral frac "cos x+sin x"
integral frac "\sin x+\cos x"
integral frac "\sin x/(\cos x+\sin x)"
integral over "\sin x+\cos x"
integral over "\sin x+\cos x"
integral frac "\cos t+\sin t"

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:

$\lambda$ could be recognized as A; "Ax" eigenvalue,"Mx=Ax" eigenvalue
$\sigma$ could be recognized sa o; "o-algebra" Borel set
$\pi$ could be recognized as n; "nr2" circle
$\infty$ could be recognized as oo; "loo" functional analysis

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

Solution 3:

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.

Solution 4:

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.