Rebecca Goldstein's Incompleteness: The Proof and Paradox of Kurt Gödel is a wonderful "life and work".
She successfully communicates both the context and essence of Gödel's contribution, and his opacity and paranoia. Goldstein provides a lucid outline of logical positivism; for the first time, I grasped the philosophical point of this movement, and it's relationship to Platonism. I began to get a handle on Wittgenstein, and, amazingly, I felt I understood the rudiments of the predicate calculus, the difference between truth and proof, and even the sketch of Godel's proof.
Goldstein also conjures up Gödel as an individual, and turns the fragments and glimpses of this very private man into a metaphor for his personality. One gets a sense of a how a few caring colleagues looked after him, in spite of his rebuffs and hypochondria. While a very different man, Gödel's eccentricity and circle of caring colleagues reminded me of another strnage mathematician evoked Paul Hoffman's fascinating book: The Man Who Loved Only Numbers : The Story of Paul Erdös and the Search for Mathematical Truth.
The book is fluently written, and I'm tempted to explore her novels. The explanations of abstruse mathematics are well handled, and she skillfully evokes the many peripheral personalities. The only jarring notes are a handful of gratuituous trips to the thesaurus.
This life of Gödel reminded me fondly of a book I read and loved more than a decade ago: John von Neumann and Norbert Wiener: A Dual Biography by Stephen J. Heims(Cambridge, Mass, MIT Press, 1980). Sadly, it seems to be out of print; I found it at my local university library, and I look forward to reading it again.