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I just asked the question: prove that $\int_{0}^{1}x^{-x}dx=\sum_{n=1}^{\infty}n^{-n}$. I do not know of a good way to search an equation (nor did I know this equality is known as sophomore's dream) so I landed up asking a duplicate question.

What is the best way to search for an equation on the internet? Do you think searching for an equation using google and getting good search results will be possible in the near future?

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    $\begingroup$ Related (perhaps duplicate?): meta.math.stackexchange.com/questions/10169/… You can find some suggestions how to search for formulas there and in the questions which are linked there. $\endgroup$
    – Martin Sleziak
    Commented Mar 8, 2014 at 16:44
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    $\begingroup$ This seems related, too: meta.math.stackexchange.com/questions/5048/… $\endgroup$
    – Martin Sleziak
    Commented Mar 8, 2014 at 16:46
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    $\begingroup$ It usually takes me several steps; search with some key words, find a reference, look at the bibliography there, try some new searches. $\endgroup$
    – Will Jagy
    Commented Mar 8, 2014 at 20:02
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    $\begingroup$ The search engine used at MSE is not perfect (and searching for math expression is difficult). But according to this answer, it supports searching for special symbols (hence also in TeX). When experimenting with integral in your question, I have tried several queries. Searching for "x^{-x}" "n^{-n}" and "x^{x}" "\int" brought some results, which contained links to other questions. $\endgroup$
    – Martin Sleziak
    Commented Mar 9, 2014 at 6:43
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    $\begingroup$ What we need is some sort of intelligent search algorithm that's (among other things) blind to variable names. $\endgroup$
    – Jack M
    Commented Mar 9, 2014 at 10:22
  • $\begingroup$ @JackM labelled regular expressions? $\endgroup$
    – Guy
    Commented Mar 12, 2014 at 8:41
  • $\begingroup$ but we would need to be able to generate regexes for that. $\endgroup$
    – Guy
    Commented Mar 12, 2014 at 8:42
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    $\begingroup$ @JackM There are not that many variables that would be used for x in the above formula. The problem is that google strips the math symbols from the search. $\endgroup$
    – Phira
    Commented Mar 17, 2014 at 0:56
  • $\begingroup$ Here's a website whose purpose is to find mathematical equations symbolab.com $\endgroup$
    – user103828
    Commented Mar 22, 2014 at 14:01

3 Answers 3

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What if we created something like a "Wiktionary" for equations? A peer-to-peer site with a huge database of equations, linked to each other, with some description, their names, their related equations. Blind to change of variables and substitutions, blind to alternative forms and notation, indexed, commented, and with clear links to Wikipedia (and other sites) articles. For equations of applied areas, it should also contain information about the solutions.

Something editable by the whole community (I'd say wiki), that grows little by little, until it ideally contains all equations known.

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    $\begingroup$ I'd really like something that you could search like that with search terms in latex or something similar. $\endgroup$
    – ruler501
    Commented Mar 22, 2014 at 4:37
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    $\begingroup$ This would be incredibly useful for PDEs especially. $\endgroup$
    – user7530
    Commented Dec 20, 2014 at 20:06
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    $\begingroup$ so has this been done after almost 5 years? $\endgroup$
    – drerD
    Commented Dec 21, 2018 at 0:54
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    $\begingroup$ @drerD 7 years now, somebody should take the initiative. $\endgroup$
    – user845875
    Commented Jul 6, 2021 at 12:45
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See my side-project, it is developing its indices currently.

http://approach0.xyz

I will publish its first release when the entire math StackExchange is indexed.

Also, I am hoping someone interested can join and form a community to push this project forward, this is the reason I am posting here, even if this project is not fully ready for public using.

EDIT:

If you are interested in this project or have any amazing idea to help it improve, please follow this twitter account: https://twitter.com/approach0 , mention #approach0 to send feedbacks/questions. Approach0 will post updates on twitter too.

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    $\begingroup$ One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. $\endgroup$
    – Martin Sleziak
    Commented Aug 28, 2016 at 9:56
  • $\begingroup$ I hope you will not mind that if I leave a bit of my own feedback here in chat. $\endgroup$
    – Martin Sleziak
    Commented Aug 28, 2016 at 9:57
  • $\begingroup$ @MartinSleziak Thank you so much for your comments and suggestions here. I have took a brief look at your feedback, I really love your feedback and will seriously look into those points and improve approach0. Give me just some minutes, I will answer/reply to your in feedback in our chat. $\endgroup$
    – Wei Zhong
    Commented Aug 28, 2016 at 11:36
  • $\begingroup$ @MartinSleziak Thanks to your advice, I have appended more information on my posted answers. Will reply to you shortly in chat. $\endgroup$
    – Wei Zhong
    Commented Aug 28, 2016 at 11:51
  • $\begingroup$ Just want to confirm that i found the answer I was looking for, with an equation as key phrase, at first try. Good job! $\endgroup$
    – Jonatan Öström
    Commented Oct 20, 2016 at 17:13
  • $\begingroup$ This is a useful tool. I often use it. I have the following wish about a more refined pattern matching. At times, I want to search for a formula, say $x^3-3x+1$. Can I give weights to parts of the formula? Here it may easily happen that I am also interested in $y^3-3y+1$ or $n^3-3n+1$, but I know in advance that for my purposes any hit with, say $x^3+3x+1$ or $x^2+3x+1$, will be useless to me. Is there a way to freeze those constants so that only an exact match is acceptable? $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 1, 2019 at 5:02
  • $\begingroup$ This becomes more pressing, when I combine a rarely occurring formula with a common keyword. The search engine floods me with links to posts containing a fractional match with the formula, highlighting the keyword that was only a secondary search target, added only to filter out other noise. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 1, 2019 at 5:06
  • $\begingroup$ @JyrkiLahtonen I have left a short comment on this here in chat - but Wei Zhong will be able to provide a better answer. Regardless of this specific issue, when you are looking for some posts and you're having trouble finding it, feel free to post in the searching chatroom. There are a few users who visit it, perhaps if more people have a look somebody might have a suggestion how to find what you're looking for. $\endgroup$
    – Martin Sleziak
    Commented Feb 1, 2019 at 6:34
  • $\begingroup$ Thanks @MartinSleziak. Bookmarking that chatroom. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 1, 2019 at 6:38
  • $\begingroup$ @JyrkiLahtonen Hi Jyrki, thanks for posting this comment. When Approach0 gives inexact match of symbols, it may already failed to find exact symbols following those results. In short, it tries to prioritize exact constants match already. In this case, do you feel it is necessary to freeze the constants? If so, let me know and I would love to know your arguments. Thanks! $\endgroup$
    – Wei Zhong
    Commented Feb 5, 2019 at 14:14
  • $\begingroup$ @WeiZhong Thanks for the reply. I am uncertain. I guess the point I want to make is that in the above example I want to freeze both the $3$s, the minus sign, and the $+1$, but I will still be very happy, if Approch0 finds a match where the variable $x$ is replaced with another variable, say $y$ or $n$, as long as it is the same substitution in all the places. In other words. If givent $x^3-3x+1$ as the input, my strong preference would be for a search engine to think that $x^3-3x+1$, $y^3-3y+1$, ..., $n^3-3n+1$ are positive matches. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 5, 2019 at 14:20
  • $\begingroup$ (cont'd) But $x^3-4x+1$, $x^2-3x+1$, $x^3-3x-1$, $u^3-3v+1$ would not be matches. My understanding (and experience) is that when looking for near matches, Approach0 may not see the difference here. I don't know exactly how it sorts the partial matches. Some searches I have carried out suggest to me that "freezing" parts of the formula chosen by the user would help me find what I was looking for. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 5, 2019 at 14:23
  • $\begingroup$ The other suggestion I wanted to make was to be able to give "weights" to different search strings. Like: at least a partial match with the first string is a must, the second string is only a tie-breaker, and a perfect match with the second string should be trumped by a closer match with the first string. Or some such system. I am unfamiliar with the way search engines work, so this may not be possible :-( $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 5, 2019 at 14:27
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    $\begingroup$ @JyrkiLahtonen So in Approach0, "perfect“ substitution (those in all the places as you stated) should be prioritized to the top below the perfect match (which match even the symbols exactly). This is already part of my original design goal. If you see imperfect matches, again, that may imply approach0 has failed to find better matches. As for whether we should allow imperfect substitutions, I think we should still give some credits for them. $\endgroup$
    – Wei Zhong
    Commented Feb 6, 2019 at 10:09
  • $\begingroup$ (cont'd) But I do agree it may be beneficial to give options to control what level of substitution strictness a specific query wants to apply, although technically possible, my preference is still let search engine work on its side to prioritize better matches at the same time allow more possibilities in results to improve search recall. $\endgroup$
    – Wei Zhong
    Commented Feb 6, 2019 at 10:09
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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 ...).

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

P.S.: please, enclose formulas between \${}\$. e.g. \${x+y}\$.

EDIT:

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

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  • $\begingroup$ I didn't downvote your post (because I welcome the idea of tailored math search engines), but the comment given to Wei Zhong applies to you as well. By posting this in several places you make it more difficult for us in the sense that we won't necessarily see the comments given to other versions of your announcement. Please crosslink them, unless there is a place elsewhere where you want to see feedback. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 1, 2019 at 4:56
  • $\begingroup$ For feedback/question, see my recent comment to Wei Zhong. $\endgroup$
    – Jyrki Lahtonen
    Commented Feb 1, 2019 at 5:07
  • $\begingroup$ Hi Jyrki, thanks for your comment. :) I've included links to Feedback and Meta in all posts. $\endgroup$
    – Flavio Gonzaga
    Commented Feb 1, 2019 at 21:27

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