What are really helpful math resources out there on the web?
Please don't only post a link but a short description of what it does and why it is helpful.
Please only one resource per answer and let the votes decide which are the best!
What are really helpful math resources out there on the web? Please don't only post a link but a short description of what it does and why it is helpful. Please only one resource per answer and let the votes decide which are the best! 


I have learned a lot of mathematics while reading Wikipedia. Allowing a wide audience to contribute to articles seems to work out well in the case of mathematics. 


I occasionally find mathoverflow.net rather helpful. In particular, there's a good list of answers to your specific question here. 


I use http://arxiv.org/ all the time. Researchers post their articles here, so it is a great way to see if anyone have already a proof or an idea on something. Some people regularly access it through



For enumerative combinatorics, it's hard to beat Sloane's Online Encyclopedia of Integer Sequences. It is what it says on the tin. A huge list of integer sequences, with references, links, formulas, and comments. 


Mathscinet, which contains summaries and reviews of published research papers. It's very useful when you want to get an idea of a paper without having to read it, and contains almost every paper ever published. 


Everything by John Baez. In particular This Week's Finds in Mathematical Physics, the nCategory Cafe, and the nLab. He has an amazing ability to make even the most esoteric topics seem obvious and inevitable. 


contains a lot of useful advice for people at various stages in their careers. In addition it contains a lot of discussions and explanations of the math that I find interesting. 


http://jmilne.org has lots of systematic, wellwritten courses. 


Detexify is a quick and easy way to find the name of a LaTeX symbol. 


Allows you to search for research articles. Gives you direct links to all online versions of the article it can find. Strenghts include that it can often give you direct links to files hidden on obscure (nonarXiv) preprint servers or personal webpages, and if you sit on a computer with access to ScienceDirect, Springerlink etc, you get direct links to these artices, via your university library. Weaknesses include lots of errors due to the reliance on their "intelligent" search engine rather than correct metadata from publishers, but this is likely to improve over time. To find what you really are looking for use the author tag, for example "infinite loop author:May" etc. 


If you haven't figured this out already, you can read large portions of textbooks before you buy them to decide if they're what you need. (If you actually want free books, there's a separate question that addresses that.) 


Don't forget http://gigapedia.com/ for tons of ebooks. 


The open source software package SAGE at sagemath.org can calculate, well, almost anything you want. The mission of the SAGE group is: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. The most useful resource online is www.sagenb.org, where one can log in and use SAGE online, without having to install any software. 


The nLab is an excellent resource, often containing more detail, explanation, and discussion than wikipedia, along with much more specialized and contemporary topics. (nLab was mentioned in the answer by Justin Hilburn, but it was listed there after other resources, and I think people scanning under the oneresourceperanswer dictum will miss it.) 





MathOnlineRecently launched by Andrea Ferretti Here one can collect lecture notes, survey articles, books and so on. All the material can be organized and searched by author, topic, language, level and so on. Registered users can add new books, add tags, write reviews, vote, keep a list of the favorite books and see other people's profiles. 


I am surprised nobody yet have put pointers to books and papers. For older stuff you can find a lot at Gottingen Digital Library, Numdam and JSTOR. 


Unfortunately Library Genesis is down and has been down for some time now, so I'm taking the liberty of editing this answer. A working site that is similarly useful is libgen.info and someone has collated a blog of links here. Original answer follows: At the Library Gensis or the translated version here, you can browse and download as many highquality and modern Mathematics books, surveys, etc as you wish. This iresource must be on every mathematician's ishelf. Here is some list: 599 books on Number Theory; 303 books on Complex Analysis; 325 books on Algebraic Geometry; 588 books on Partial Differential Equations; 97 books on Abstract Algebra; 107 books on Commutative Algebra; 181 books on Harmonic Analysis; 133 books on Fourier Analysis; 349 books on Functional Analysis; 356 books on Differential Geometry; 88 books on Riemannian Geometry; 783 books on Topology; 286 books on Combinatorics; 323 books on Graph Theory. This is enough for illustration. You will find more, enough to get you in a downloading craze! 


Sloane's OEIS has already been mentioned. A similarly useful site is ISC, Simon Plouffe's Inverse Symbolic Calculator. Here you enter the decimal expansion of a number to as many places as you know, and the search engine makes suggestions of symbolic expressions that the expansion might be derived from. The answer might involve pi, e, Sometimes, it becomes difficult to calculate symbolically. Therefore, you can proceed numerically instead, and hope to recover the exact symbolic solution at the end, using ISC: sometimes proving that an answer is correct can be easier than calculating, or discovering, it in the first place. It can also be useful for discovering simplifications of nested radicals, for example. 


The Tricki Quoting the site: "Welcome to a brand new Wikistyle site that is intended to develop into a large store of useful mathematical problemsolving techniques. Some of these techniques will be very general, while others will concern particular subareas of mathematics. All of them will be techniques that are used regularly by mathematical problemsolvers, at every level of experience." 


Very good articles with lots of references! (never mind the .de, it's in English!) 


Free downloadable (and streaming) video lectures from the Institute for Advanced Study at Princeton: http://video.ias.edu/ Not exactly a resource, but a great way to listen to talks given by experts on the latest results in Computer Science and Math. 


Mostly for the student, including high school. But has more advanced forums, too. Latex easily used. 


I'm just adding Wolfram Alpha to the fray so it can be voted on like other suggestions. For people who haven't heard of it, it's an online computational engine. 


ZentralblattMATH MathSciNet has been listed above, but I didn't see ZentralblattMath. It does much the same thing as MathSciNet, although it has in fact been doing it far longer. Most papers get reviewed on both databases, and this redundancy if often very useful (although people frquently argue about whether or not we really need both nowadays  there have been many long discussions about this in various places). Unfortunately, many students these days seem not to be aware of Zentralblatt. It is definitely a useful resource and if your institution pays for a subscription then it is certainly worth knowing about it and using it. 


http://wiki.henryfarrell.net/wiki/index.php/Mathematics/Statistics Large list of math blogs. Highly recommended in particular are Terence Tao's and Tim Gowers'. 


David BenZvi takes electronic notes on the talks he attends and posts them publicly. This can often be the best source of information for a subject which has not yet been written down. 


http://maths.dept.shef.ac.uk/magic/index.php Apparently UK has been building a depository/interactive system for graduate math courses. Click on "courses" to access archives. Many have lecture notes and other materials. I found this recently. Have not actually personally used it, but potentially very useful. 


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