This is not so much "how to *do* mathematics" (to quote the OP), but more how it feels to do mathematics. A *New Yorker* review said this book "is less about math than about mathematicians—how they live, how they work, and how they talk to one another." I found it inspiring. > Villani, Cédric. *Birth of a Theorem: A Mathematical Adventure*. Farrar, Straus and Giroux, 2015. ([Guardian review](https://www.theguardian.com/books/2015/feb/25/birth-of-a-theorem-mathematical-adventure-cedric-villani-review). [AMS review](http://www.ams.org/notices/201402/rnoti-p172.pdf).) <hr /> [![Villani][1]][1] <hr /> [1]: https://i.sstatic.net/wQOlG.jpg