Collecting math websites [duplicate]

Solution 1:

I have found these extremely useful, from time to time:

Online Encyclopedia of Integer Sequences

NIST Digital Library of Mathematical Functions

They both provide facts of a specialized nature, rather than understandings or arguments. That is, they are thin on explanations and proofs. The OEIS does have very thorough references, so this is not a serious problem. The DLMF also has many references, which I then skim with MathSciNet.

I have mixed feelings about Wikipedia's mathematics articles. Individual articles are often imprecise, more interested in giving the gist of a topic than in giving precise details; this is especially bad when it comes to precise statements of theorems or (worse) of proofs. There is usually only a loose connection between the cited references and the contents of the article: which (say) of the six cited sources contains details of this or that statement in the article? And there is poor coordination between collections of articles, which often use differing terminology and notation. On the other hand, it is a good source for understanding (say) current usage of mathematical terminology. I typically find 75 percent of MSE questions use some technical term in a way I do not understand, and Wikipedia often gives an indication of what the questions' posers had in mind.

Solution 2:

Great question. It would probably also be interesting to think about what could be useful but is not yet out there. Here are a few picks that I can think of:

• A useful website for ring theorists is the Database of Ring Theory. It is actually managed by rschwieb, a frequent user of MSE. You can look for examples or counterexamples of your favourite properties of rings and modules in the database.
• In a similar vein, here is a Database for Number Fields.
• Super useful for number theorists is also LMFDB. It's another database with which you can look for number-theoretic objects with certain desired properties.
• For category lovers, the equivalent of the Stacks Project is Kerodon on Higher Category Theory. I think this one is still growing.
• And of course, obvious ones like Wolfram Alpha and Wikipedia!

Maybe I should also mention certain social media meme groups in which you can apply your knowledge to understand the most recent homological algebra memes. But maybe this is not quite the right place for that... ;-)