Mathematical Links:
For the latest in number theory, keep an eye on the arXiv.
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 and Mathworld are both good sources.
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.
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:
If you're after a masochistic way to procrastinate, try getting frustrated at the puzzles on John MacQuarrie's page.
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 is difficult to find what positions are available in pure mathematics research. I've put together a page of useful links here.
For the latest in number theory, keep an eye on the arXiv.
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 and Mathworld are both good sources.
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.
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:
If you're after a masochistic way to procrastinate, try getting frustrated at the puzzles on John MacQuarrie's page.
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 is difficult to find what positions are available in pure mathematics research. I've put together a page of useful links here.