Most helpful math resources on the web 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!
 A: Sci-Hub is pretty helpful in accessing articles, even for those researchers who already have access to several journals. The interface is great, the site is pretty fast, and the database is huge. See this article and other linked articles there for a nice overview of who all are downloading pirated papers. 
Edit: as pointed out in the comments, it should be noted that there is an ongoing lawsuit against the website. 
A: http://www.projecteuler.net
From website:
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.
From me:
I have personally found it beneficial to go through these to help work at how I think about math problems.
A: 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.
A: While not as comprehensive as wikipedia, if you find an article on the scholarpedia on a topic, it should be the first place to look:
http://www.scholarpedia.org/article/Main_Page
A: I recommend archive.org. Books from Fourier, Lagrange, Euler... old stuff.
A: Everything by John Baez. In particular This Week's Finds in Mathematical Physics, the n-Category Cafe, and the n-Lab. He has an amazing ability to make even the most esoteric topics seem obvious and inevitable.
A: Detexify is a quick and easy way to find the name of a LaTeX symbol.
A: http://www.physicsforums.com/ 
Hosts high-level maths discussions, forums have inline LaTeX rendering.
A: Alexandre Stefanov keeps an extensive list of free math books / lecture notes. The list is divided according to subject and updated frequently. I have found some very nice books there.
A: It seems this link hasn't appeared above http://www.ams.org/mathweb/index.html
The resources there are too rich to describe.
A: All math.[institution].edu/~[professor]/ sites are great with, in of themselves, many links to the favorites of the page's professor. 
It is like walking up to the professor at coffee and asking him about the tools he uses (resources) and how it applies to his research . A big cafeteria with the world's professors ressembled and willing to answer any questions... or at least those who keep their site up to date. 
An example: http://www.math.ucla.edu/~tao/ 
Professor Tao's page is mostly blue (links).
A: Overleaf.com is an excellent online LaTeX platform that allows you to collaborate with others, track changes, etc.
It also has many helpful pages on how to use Latex.
A: Terence Tao blog 
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.
A: http://scholar.google.com/
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 (non-arXiv) 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.
A: http://jmilne.org has lots of systematic, well-written courses.
A: The manifold atlas is pretty cool. I haven't spent enough time on it though... It seems like a different type of mathematical venture. Hopefully, it will inspire other similar projects.
http://www.map.mpim-bonn.mpg.de/index.php/Main_Page
A: Resource for books is book.fi - select English from upper right.
Resource for (mostly free) papers is projecteuclid.org
A: http://citeseer.ist.psu.edu/ caches a lot of papers that has been posted online. It often comes up within the first few search results in Google.
(But you cannot view the cached documents online, since they are directly downloaded.)
A: http://www.proofwiki.org
It is a Wikipedia, for proofs.
A: *

*Mathematical Constants by Steven R. Finch.

*All-Russian Mathematical Portal.

*Gallica

*The Center for Retrospective Digitization, Göttingen (GDZ)

*The Somos Sequence Site

*Problems in the points contest of KöMaL
A: I don't know if this reference is of sufficient generality:
Finite Calculus: A Tutorial for Solving Nasty Sums
by David Gleich
https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20finite%20calculus.pdf
(The original link at http://www.stanford.edu/ no longer exists.)
It is only a paper, but it describes the methods of the so-called "umbral calculus": a really useful technique to know.
A: www.optimization-online.org
The optimization community seems to prefer this specific online repository instead of the more broad one arxiv.
A: Since someone mentioned The Digital Library of Mathematical Functions, we better also include The Wolfram function site: http://functions.wolfram.com/
It's really useful for special function identities - especially since they are also available in Mathematica input form that you can copy straight into your code.
A: Many free Mathematics e-books are available to view and/or download here.
A: Topology Atlas at York University is a great site with an awesome Q&A board (it of course, was not just restricted to Topology) and has been around for years.
A: Quite impressive is this site:
"PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible" - or how they put it: "Math for the people, by the people":
Planetmath
A: LMFDB has been officially launched yesterday (10th May of 2016).
It is an integrated knowledge database of L-functions and modular forms with a nice web interface that helps visualize the connections between these mathematical objects.
A: I use
https://groupprops.subwiki.org/wiki/Main_Page
e.g. for looking up less well-known definitions in group theory.
A: http://books.google.com/
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.)
A: 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 high-quality and modern Mathematics books, surveys, etc as you wish. This i-resource must be on every mathematician's i-shelf. 
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!  
A: Don't forget http://gigapedia.com/ for tons of e-books.
A: 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.
A: 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 one-resource-per-answer dictum will miss it.)
A: There are some great things here at the small but fine Clay Institute Online Library
A: People: consider http://www.digizeitschriften.de/ tons of classical papers in english...
I think it is worth to check the 39 journals collection on world class referee-ed mathwork.
One paper on Mathematische Annalen (which is the very amusing): "On the holymorphic flow with an isolated singularity", is the famous GSV, gives you an index formula... 
A: A good online LaTeX equation editor: Here
A: For people who are interested in prime factorization :
http://www.mersenneforum.org
A: Two sites created by my former wonderful A level Mathematics teacher:
www.whitegroupmaths.com
www.a-levelmaths.com
He has generously written tons of topic summaries, worked revision problem sets and other learning material made mostly free to us students. Felt he deserves a mention for all his efforts :) Thanx n hope u will benefit from them!
Estella 
A: Jahrbuch Database
http://www.emis.de/MATH/JFM/
A sort of Mathscinet and Zentralblatt for the period 1868-1942. Most of the reviews are in German. It is interesting to read the reviews written by mathematicians like Frobenius, Hilbert, Minkowski, Hasse, E. Noether, Artin, Mittag-Leffler, Landau, Van der Waerden, ...
A: OntoMathPro, a crowdsourced ontology of professional math knowledge.
A: A community database of rings examples, searchable by properties:
http://ringtheory.herokuapp.com/
It is very similar to pi-base, which is a more famous database but for topological spaces examples.
A: Videos from MSRI.
A: 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.
A: MIT OpenCourseWare
A: http://mathworld.wolfram.com/
A: Zentralblatt-MATH
MathSciNet has been listed above, but I didn't see Zentralblatt-Math.  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.
A: 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, sin, cosh, sqrt, ln, and so on.
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.
A: MathOnline
Recently 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.
A: CiteULike (by Springer), to organize in a library the titles and abstracts of one's preferred papers and books.
http://www.citeulike.org/
(From the FAQ:) CiteULike is a free service to help you to store, organise and share the scholarly papers you are reading. When you see a paper on the web that interests you, you can click one button and have it added to your personal library. CiteULike automatically extracts the citation details, so there's no need to type them in yourself. It all works from within your web browser so there's no need to install any software. Because your library is stored on the server, you can access it from any computer with an Internet connection. 
A: Very nice Notes and Videos from the Southwest Center for Arithmetic Geometry are available here!
A: For students (or even teachers!),the   Abdus Salam International Centre for Theoretical Physics has lots of lectures in Advanced Math.Every year the lectures are different.Enjoy!
http://www.ictp.tv/diploma/index08-09.php?activityid=MTH
A: Mathematics Dictionary & Glossary for students  at http://www.tuition.com.hk/mathematics/ 
This is a very comprehensive source of mathematical definitions. 
With over 2000 terms defined, this dictionary is ideal for supporting students who are studying mathematics or related subjects. All terms in our dictionary are cross-referenced and linked for ease of use, making finding information quick and easy.
A: The Tricki
Quoting the site:
"Welcome to a brand new Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving 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 problem-solvers, at every level of experience."
http://www.tricki.org/
A: http://www.wolframalpha.com/
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.
A: http://eom.springer.de
Very good articles with lots of references! (never mind the .de, it's in English!)
A: I occasionally find mathoverflow.net rather helpful.  
In particular, there's a good list of answers to your specific question here.
A: The Art of Problem Solving
Mostly for the student, including high school.  But has more advanced forums, too.  Latex easily used.
A: 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.
A: 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'.
A: David Ben-Zvi 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.
A: 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 a SPIRES search engine at https://inspirehep.net/
A: Proceedings of all past ICM-s can be found here: http://www.mathunion.org/ICM
The following nlab pages list some of the main resources


*

*http://www.ncatlab.org/nlab/show/Online+Resources -- a long list of math blogs and forums

*http://www.ncatlab.org/nlab/show/math+institutions -- main institutions 

*http://www.ncatlab.org/nlab/show/math+archives -- preprint/journal/book/review archives
http://numdam.org is a collection of old issues of many mainly French math journals. 
http://www.mathnet.ru site has links to free old issues of most of the Russian math journals (and even some video lectures) in Russian and links to some non-free English versions. There is also an English mode of the site: http://www.mathnet.ru/index.phtml?&option_lang=eng. A smaller free depository of old issues of Polish math journals is http://matwbn.icm.edu.pl (click on the flag for English).
Max Planck maintains links to a very long list of journals, most of which are proprietary and usable only from their site, but the list is still useful because a sizeable fractions of links are also to free journals or some volumes of journals which are free, and those are mainly usable from all locations. The current URL is http://rzblx1.uni-regensburg.de/ezeit/fl.phtml?bibid=MPIMA&colors=3&lang=en&notation=SA-SP
Many resources can be found at the sites of main world math institutes like ihes, mpim-bonn, Oberwolfach, msri, kitp, ictp, rims, ias, Steklov, Clay, crm Barcelona, Mittag-Leffler, Banff, Fields, Newton, ihp Paris
AMS keeps a long list of math societies throughout the world with links to their sites, which are often useful. One should also recommend more general AMS directory of links Math on the Web http://www.ams.org/mathweb/index.html.
A: http://www.wikipedia.org
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.
A: http://maths-magic.ac.uk/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. 
A: edit by jc: As of May 11, 2010, the work has been completed!
This is a reference that is not yet complete, but it should be very useful when it finally does arrive:
Digital Library of Mathematical Functions (DLMF)
(book and associated website;
will replace Abramowitz & Stegun's Handbook of Mathematical Functions)
NIST / Cambridge University Press
expected 2009/2010
http://dlmf.nist.gov/
This will contain diagrams, tables, properties of, principal values of, and relationships between many important mathematical functions. For example, the trigonometric and other elementary functions are described, with very many formulae relating them.
The Handbook is very good; the Digital Library will be even better.
A: 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.
A: I just found a very interesting site which has lots of free math videos even up to some more advanced topics:
http://www.hippocampus.org/
A: http://www.math.fsu.edu/Virtual/
This site contains plenty of useful math resources. 
A: An excellent catalogue of mathematical information available on the web is Keith Mathhews' 
http://www.numbertheory.org/ntw/gateways.html
and if you are interested in Number Theory, see 
http://www.numbertheory.org/ntw/
A: http://functions.wolfram.com/
A: NPTEL provides E-learning through online Web and Video courses in Mathematics organized by Indian Institute of Technology.
http://nptel.iitm.ac.in/
A: For knot theorists, there are two really cool databases:


*

*knotinfo and its cousin linkinfo, both maintained by Cha and Livingston.

*knotatlas, maintained by Bar-Natan.
A: https://www.sympy.org/en/index.html
SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.
If you ensure that the following code runs every time you start an iPython session:
from sympy.abc import *
from sympy import *
import sympy

init_printing(unicode=True)

Then you will have a CAS experience comparable to what you get with Sage. Now while on paper Sage might have more features, I keep finding myself moving back to Sympy in my own work. Also, the UI and function names are fairly similar to what you get in Sage, so you can easily move between them. I recommend giving this a try.
Also, avoid using the utility isympy as a substitute to running the above five lines of Python code.
A: If you want to find a relationship between data in the form of closed form formulas this tool is - to the best of my knowledge - the best one:
http://ccsl.mae.cornell.edu/eureqa
