The search for certainty - Marcus Giaquinto

The nineteenth century saw a movement to make higher mathematics rigorous.This seemed to be on the brink of success when it was thrown into confusionby the discovery of the class paradoxes. That initiated a period of intenseresearch into the foundations of mathematics, and with it the birth ofmathematical logic and a new, sharper debate in the philosophy ofmathematics. The Search for Certainty examines this foundational endeavour from thediscovery of the paradoxes to the present.
Focusing on Russell's logicistprogramme and Hilbert's finitist programme, Giaquinto investigates howsuccessful they were and how successful they could be. These questions areset in the context of a clear, non-technical exposition and assessment ofthe most important discoveries in mathematical logic, above all Gdel'sunderivability theorems.More than six decades after those discoveries, Giaquinto asks what ourpresent perspective should be on the question of certainty in mathematics.Taking recent developments into account, he gives reasons for asurprisingly positive response.