In his book "The Universal Computer The Road From Leibniz To Turing,"
Martin Davis presents a history of the development of logic that focus on creating a system in which computation is purely symbolic .
Starting with Leibniz's 'wonderful idea' - a language based on an alphabet whose "elements represented not sounds, but concepts. A language based on such an alphabet should make it possible to determine by symbolic calculation which sentences written in the language were true and what logical relationships existed among them." In his exposition he takes a clear path from Leibniz to Boole to Frege to Cantor to Hilbert to Godel and then to Turing. As a former student of mathematics (in the 60's and 70's, and current teacher of computer science (since the 80's) my appreciation of his exposition was enhanced by my own recollections of the names and events he describes. Furthermore, he gives you the feeling that you're reading something written by an insider - telling us stories and tidbits that we on the outside can enjoy and appreciate. The book is nicely done with extensive notes. Give it a read when you get the chance.
A more detailed review is available at "Read This! The MAA Online book review column" , by Mark Johnson.Posted by ernie at September 2, 2004 03:23 PM