I'm currently in my third year of an undergraduate degree, mainly doing courses in abstract algebra. I'm enjoying my degree, but every so often when I'm swamped with difficult proofs, I feel like I need some extra inspiration to give myself more mathematical energy and remind me why I got interested in maths in the first place – otherwise I wear myself out. I do things like watching videos on numberphile, but I feel like this is aimed at a much lower level than I'm at.
My question: What is a good resource that features advanced mathematics and isn't shy about going quite deep, but is still fairly recreational in its nature? I don't really care what form this resource takes, it could be blogs, books, videos etc.
Any help would be greatly appreciated.
Best Answer
The Princeton Companion to Mathematics by Tim Gowers et al. is an astounding work. It has an entry for almost any mathematical topic you can think of, and you can get an feel for the flavor of all the areas of mathematics via the typically lucid, not-extremely-technical (for an undergraduate with some mathematical background, anyway) expository articles on the major topics. It's also full of biographies of mathematicians, historical exposition, and essays by leading mathematicians on doing and loving mathematics. Highly recommended.