Theorems and Proofs: Existence, Non-Existence and Symmetry

Abstract

Most of the perturbative and numerical conclusions in this book are formal results. That is to say, algorithms have been applied with self-consistency checks, but without rigorous proof that the methods either converge or are asymptotic. The gratifying agreement between a multiplicity of different methods strongly suggests that this formal analysis gives true answers. However, the mathematical landscape is strewn with mines. The theorem/lemma methods of pure mathematics are very useful in clearing the minefields.

“I am happy to eat Chinese with theorists, but to spend your life doing what thay tell you is a waste of time.” — Samuel Ting (Nobel Laureate, Physics), in R. P. Crease and C. C. Mann,The Second Creation: Makers of the Revolution in 20th Century Physics, Macmillan, New York, pg. 286 (1986).