Links
I have linked a collection of interesting and useful websites below, broken into rough categories.
If you have any suggestions for me to add to the list, please get in touch!
The ArXiv - a pre-print server for papers in Mathematics, Physics, Computer Science and many other subjects
MathSciNet - a searchable online bibliographic database created by the AMS
Mathematics Genealogy Project - find your academic relatives and see who you can trace your PhD supervisor back to
Number Theory Web - for things of interest to all number theorists
Number Theory Web Seminar - a weekly online seminar from number theorists across the world
MacTutor History of Mathmatics Archive - a page full of biographical information on thousands of mathematicians
Keith Conrad's Webpage - amongst other things, dozens of excellent expository papers
Terry Tao's Webpage/Blog - a blog full of useful information from expository articles to career advice