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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!

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    $\begingroup$ I edited your question a bit, my main goal was to remove the reference to WolframAlpha; and make the text easier to read. But feel free to revert if you like! (You can see the edit history and revert by clicking on "edited ... ago") $\endgroup$
    – Ilya Nikokoshev
    Commented Nov 4, 2009 at 21:23
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    $\begingroup$ The answers below are great. Here's an idea I don't see that may be interesting to think about starting: An online example repository. This would be a place where one could upload and search various "first nontrivial example" notes. I think such a thing would really move mathematics along. $\endgroup$
    – Jon Bannon
    Commented Apr 20, 2012 at 13:38

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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, ...

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OntoMathPro, a crowdsourced ontology of professional math knowledge.

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For people who are interested in prime factorization : http://www.mersenneforum.org

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Very nice Notes and Videos from the Southwest Center for Arithmetic Geometry are available here!

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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

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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.

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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.

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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/

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http://www.math.fsu.edu/Virtual/

This site contains plenty of useful math resources.

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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

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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/

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http://functions.wolfram.com/

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    $\begingroup$ We have that already - see above $\endgroup$
    – vonjd
    Commented Oct 27, 2010 at 6:27
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NPTEL provides E-learning through online Web and Video courses in Mathematics organized by Indian Institute of Technology. http://nptel.iitm.ac.in/

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For knot theorists, there are two really cool databases:

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