It makes for a fascinating story, though I repeatedly found myself consulting other books to pick up the logical steps Berlinski skips. I was expecting more. The author's previous book, A Tour of the Calculus , was a joyful romp through that subject, replete with personal anecdotes, experimental historical fiction, whimsical instruction, and some relatively painless math. It was high-wire act of sorts, an effort to keep the casual reader entertained by a difficult subject. Berlinski tries the same approach with algorithms but falls flat.
Advent reads like a rough draft of the follow-up to Calculus .
It's a shame that the story of mathematicians' search for completeness has been rendered so halfheartedly.