Mathematicians talking about their identity as a person and as a mathematician? I was wondering if any of you know of any books, articles, interviews, youtube videos, ... (etc) where a mathematician talks about his or her identity as a person and as a mathematician? Thank you for any sources!
 A: Walter Rudin wrote a wonderful autobiography that does a nice job of balancing between talking about his personal life and his mathematical pursuits.  Best of all, it reads like Rudin :)
A: Here are some for consideration.


*

*Russell

*Newman

*Hardy
I think it is unusual to write a biography about yourself. Let me qualify this. If you consider the ratio of mathematicians to ones that wrote about themselves, I think the ratio is very low. I have no statistics to prove that.
If you look at 'a' list of the '100' top mathematicians, which is highly debatable, how many do you suppose self published? Next question, how many have had biographies written about them? 
If you look at this list of mathematician biographaphical info, you get an idea of how many there are to choose from. The same question can be asked of the greatest physicists.
There are many biographies about mathematicians written by others like Nash, Erdos, ...
A: It might not fit the bill perfectly, but "Surely you're joking, Mr. Feynman," is about both Feynman's exploits as a physicist and as a general goof-ball.  I wouldn't say it's a deep book, compared to say Hardy's "Apology," but it's a good read and offers a bit of insight into his way of thinking about problems.  
A: A selection :


*

*Stanislaw Ulam 'Adventures of a Mathematician' should not be missed (MJD had it in his comments too)

*'Littlewood's miscellany' (anecdotes)  

*Laurent Schwartz 'Un mathématicien aux prises avec le siècle' translated as 'A Mathematician Grappling With His Century'

*Feynman's 'Surely you're joking, Mr. Feynman' and I found his book deep ! :-) A physicist of course but he could have been a mathematician if not for insisting for Mathematics to be 'useful'.

*Andreï Sakharov's 'Memoirs' (he had to rewrite his book three times because it was stolen probably by KGB!). He was a physicist too and an humanist and another point of view is always useful. 

A: The map of my life, Goro Shimura. And of course the stuff by Grothendieck
A: There is also Steven Strogatz "The Calculus of Friendship" although not very detailed and extensive but a very nice short easy to read mixture of his personal life and some math.
A: A mathematician's apology. G.H.Hardy
A: Consider looking for non-book sources. Mathematicians have also written essays, given interviews, and in general done things that give them a glimpse into the non-mathematical sides of their thinking. For example, Doron Zeilberger has interesting opinions on his website (be aware that his writing is often tongue-in-cheek). C. P. Snow's essay The Two Cultures is essential reading. And there are others.
Often you'll find great articles in the Notices of the AMS or such publications about specific mathematicians. Sometimes they are tributes to the recently deceased, and many mathematicians who knew them personally weigh in and share stories. Obituary tributes can also be found on personal blogs here and there.
Of course, a mathematician need not be deceased to have a good article written about them. I liked a recent one in the Notices about John H. Conway of free will theorem fame. The article included an interview and was a pleasure to read. If you're looking for interviews, the Notices are probably a good place to start.
A: "Théorème vivant" by Cédric Villani (2012) if you read french, or if traduced yet. 
May be what you are looking for, by a mathematician at mid-career.
