The Proof is in the Pudding

Krantz takes the reader on a journey around the globe and through centuries of history , exploring the many transformations that mathematical proof has undergone from its inception at the time of Euclid and Pythagoras to its versatile, present-day use . The author elaborates on the beauty, challenge [...]
Visa längre beskrivning

Krantz takes the reader on a journey around the globe and through centuries of history , exploring the many transformations that mathematical proof has undergone from its inception at the time of Euclid and Pythagoras to its versatile, present-day use . The author elaborates on the beauty, challenges and metamorphisms of thought that have accompanied the search for truth through proof. The first two chapters examine the early beginnings of concept of proof and the creation of its elegant structure and language, touching on some of the logic and philosophy behind these developments. The history then unfolds as the author explains the changing face of proofs. The more well-known proofs , the mathematicians behind them, and the world that surrounded them are all highlighted . Each story has its own unique past; there was often a philosophical, sociological, technological or competitive edge that restricted or promoted progress. But the author's commentary and insights create a seamless thread throughout the many vignettes. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. This is shown in noting some of the more prominent discussions currently underway, such as Gorenstein's effort to classify finance groups, Thomas Hale's resolution of the Kepler sphere-packing problem, and other modern tales. Most of the proofs are discussed in detail with figures and some equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book. TOC:Preface.- What is a Proof and Why?- The Ancients.- The Middle Ages and Calculation.- The Dawn of Modern Age.- Hilbert and the Twentieth Century.- The Four-Color Theorem.- Computer-Generated Proofs.- The Computer as a Mathematical Aid.- The Sociology of Mathematical Proof.- A Legacy of Elusive Proofs.- John Horgan and "The Death of Proof".- Methods of Mathematical Proof.- Closing Thoughts.- References