Mathematical Links

For the cutting edge in mathematical research, keep an eye on the arXiv (number theory and combinatorics are my usual haunts).

For any research-level question or procrastination, you can't do better than Math Overflow.

Any lower level mathematical questions belong at Math StackExchange.

For looking up definitions and background Wikipedia, Encyclopedia of Mathematics, and Mathworld are all good sources. Scholarpedia also has excellent survey articles on some topics.

If, like me, you shy away from learning how to use mathematical software and prefer the internet to do it for you, Wolfram Alpha can come in very handy. If you want to get your hands (moderately) dirty, my favourite tool is Sage, which runs on the Python programming language.

There are many excellent mathematical blogs worth following: I particularly recommend the blogs of Gowers and Tao, both for their regular interesting posts and their extensive list of other quality mathematical blogs.

Non-Mathematical Links

Cryptic crosswords are great fun. There a lots of free ones to do at the Guardian website and my helpful crossword solver website of choice can be found here.

I am a great fan of webcomics; some of my favourites are Girl Genius, Gunnerkrigg Court, Dr McNinja, SMBC, Sinfest, Buttersafe, Penny Arcade, Spiked Math, and xkcd.

Job searching

It can be difficult to find what positions are available in pure mathematics research. I've put together a page of useful links here.