Faculty Publications and Other Works -- Mathematics
LIOUVILLE'S PRINCIPLE
The book contains mostly original unpublished work.
Abstract
In 1857, analyzing the ancient formula 13 + 23 + ::: + n3 = (1 + 2 + ::: + n)2; Liouville had invented a wonderful new principle, what amounted to a powerful mathematical microscope which, when directed onto many innocent-looking formu- lae, reveals their deep and unsuspected meaning. Liouville had never stated his principle, and it has been completely forgotten by now. My aim is to resurrect it from oblivion and then apply this Principle with abandon to everything not nimble enough to hide, in the process awakening from a coma many an old formula. The Principle is explained in the ¯rst Section of the ¯rst Chapter. In the rough approximation, the Liouville Principle says that if you are going to negotiate with Gods (or going into the business of interpreting identities, which is the same), do it from a position of strength. Further approximations will appear in the subse- quent Chapters: the best sitting arrangements, the most advantageous shape of a conference table, the proper form of addressing the fellow conferees, etc.