The proof is in the pudding: the changing nature of mathematical proof Krantz, Steven G.

In modern times, strict rules for generating and recording proof have been established. At the same time, many new vectors and forces have had an influence over the way mathematics is practiced. Certainly the computer plays a fundamental role in many mathematical investigations. But there are also fascinating social forces that have affected the way that we now conceive of proof. Daniel Gorenstein’s program to classify the finite simple groups, Thomas Hales’s resolution of the Kepler sphere-packing problem, Louis de Branges’s proof of the Bieberbach conjecture, and Thurston’s treatment of the geometrization program are but some examples of mathematical proofs that were generated in ways inconceivable 100 years ago. Krantz treats all of them---and more---in some detail; he names the players and tells all the secrets.
Many of the proofs treated in this book are described in some detail, with figures and explanatory equations. The reader is given a dose of modern mathematics, and how mathematicians think.Both the joy and the sorrow of mathematical exploration are communicated dynamically and energetically in this exciting new book.