These are some books that speak to me as a mathematician and have informed the way I think about my career.
- Timothy Gowers, June Barrow-Green, and Imre Leader (eds.): Princeton Companion to Mathematics. Contains introductions to (almost) all areas of modern pure mathematics. Great to broaden the mathematical horizon.
- Paul R. Halmos: I Want to be a Mathematician (freely available). Paints a good picture of what it’s like to be a professional mathematician in the US: Starting from high school, going through undergrad, grad school, postdoc, all ranks of professor and a department chair.
- Allison K. Henrich, Emille D. Lawrence, Matthew A. Pons, and David G. Taylor (eds.): Living Proof (freely available). Tells the stories of 41 mathematicians and how they got to where they are now, highlighting obstacles they had to overcome on their journeys.
- Steven G. Krantz: A Mathematician’s Survival Guide: Graduate School and Early Career Development. Describes Grad School in the United States, from the application process through the quals and the dissertation to (early) postdoc life.