Formalized mathematics was a key issue at the end of the 19th century. Principia Mathematica was probably the high-water mark in this direction. The formalistic view of mathematics is striking in this volume for its absence. Human mathematics is a sort of dance around an unwritten formal text, which if written would be unreadable. This may not seem very promising, but human mathematics has in fact been prodigiously successful.
Proofs are the sine qua non of mathematics.
As the Gita teaches, one achieves knowledge and indifference at the same time. Although this is an official book, commissioned by the International Mathematical Union, its coverage of mathematics is far from uniform. Mathematical physics with contributions by Roger Penrose, Ed Witten and Cumrun Vafa is particularly well served. Discrete mathematics with contributions by Richard Stanley, Tim Gowers, Jean Bourgain and K. F. Roth has no cause for complaint. Number theory, everyone s favorite, is well represented by Alan Baker and Gisbert W stholz, Peter Sarnak and, yes, Andrew Wiles.