John Stillwell

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have...

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to...

The first book surveying the history and ideas behind reverse mathematics, Reverse Mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and providing a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way,...

How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically...