Meaning in Mathematics

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.

1 - Is Mathematics Discovered or Invented?
2 - Exploring the Mathematical Library of Babel
3 - Mathematical Reality
4 - Mathematics, the Mind, and the Physical World
5 - Mathematical Understanding
6 - Creation and Discovery in Mathematics
7 - Discovery, Invention and Realism: Gödel and others on the Reality of Concepts
8 - Mathematics and Objectivity
9 - The Reality of Mathematical Objects
10 - Getting More out of Mathematics than What We Put In

Reverend Dr John Polkinghorne gained his PhD in physics at Cambridge University in 1955. After a brief period as Lecturer in Mathematical Physics at Edinburgh University, he returned to Cambridge until, in 1979, he resigned his Professorship to train for the Anglican Priesthood. He served as Dean and Chaplin of Trinity Hall and then President of Queen's College, Cambridge until his retirement in 1996. In 1997 Polkinghorne was awarded a KBE and in 2002 he won the Templeton Prize for Science and Religion. He is an elected Fellow of the Royal Society and his professional service has included membership of the Nuclear Physics Board and the BMA Medical Ethics Committee. He is a founding member of the International Society for Science and Religion and has been made an Honorary Doctor of Divinity by the University of Kent and Durham University, and an Honorary Doctor of Science by the University of Exeter, the University of Leicester and the Marquette University.