A friend recommended Paul R. Halmos's I Want to be a Mathematician. Here was the e-mail I wrote him shortly after finishing the book:
I said that when I finished I Want to be a Mathematician I would write a long e-mail about it. I had the feeling, a quarter of the way through, that it would be something worth writing about. It is, and so here I am.
I like those books the most that I feel I could have written. Not that I know Halmos's mathematics or share his Archimedean ethic ("Do a small bit, steadily every day, with no exception, with no holiday")—I don't. But he, like Hofstadter, Joyce, or Vonnegut, tempts me to project myself into his writing. I imagine it's the same kind of envy that makes one imitate his older brothers.
What's not to admire? A great writer, teacher, and mathematician; an eager professional; well-traveled and well-liked; a happy smoker and drinker; a man truly in love with his work.
The book reads like a letter from abroad, or the epistolic equivalent of a good walk—comfortable, slow and playful and in love with the details, but directed by apparent purpose. It is one long great story with a soul of wit.
It helps that I basically agree with him. Learning is about solving hard problems (the modified Moore method), writing is re-writing (Strunk and White), and the beautiful parts of mathematics—the best theorems and ideas—are analogies among structures.
I like the way he thinks—and especially how he thinks by writing. I recall him saying that one's success in mathematics is better predicted by how you write and talk than how well you do in Calc II, and I think he means it. It is words that jostle in our brains when we read or ask questions. To know them fluently lets one "think without even thinking about it". You become a better translator: between languages, for sure, but also between their thoughts and yours, that structure and this one.
I had no idea how much these guys travel! Jet-setting to Florida, California, Texas, Hawaii, Budapest, Scotland, Russia, etc., rounding out your mind and belly at the same time: what a wonderful occupation! It wouldn't be math. for me, but I can't imagine a better mix of scholarship and fun.
It actually makes me wonder what the hell I'm doing, nearly twenty-one with no vocation. Ah, well: "You cannot win them all."
Maybe this is the best I can say: I have a feeling that the "Mathematician" in the title could be made more general, that maybe "Man" would do as well. But I know how much Halmos loved his concrete examples, "the special case." That's what he was, anyway.