18 Unconventional Essays on the Nature of Mathematics

REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience and Descartes' Dream, which won the National Book Award in l983, and What is Mathematics, Really?

From the reviews: "This is not a book about foundations or formal logic. It is ... about the philosophy of mathematics, but perhaps more about the human practice of mathematics. ... This is a terrific collection of essays. ... all of the essays give us new insight into that curious thing we do when we do mathematics." (William J. Satzer, MathDL, January, 2006) "The current book is destined to become a classic as well for numerous reasons which will soon become transparent. ... Reuben Hersh is to be commended for orchestrating this masterful collection of essays from distinguished individuals ... . I predict that this book will become a classic for the coming generations of mathematics philosophers as well as for mathematics educators interested in changing dominant conceptions of what is mathematics, finally!" (Bharath Sriraman, Zentralblatt fur Didaktik der Mathematik, Vol. 38 (4), 2006) "Editor Reuben Hersh has orchestrated a highly provocative book, particularly for mathematicians, but also for anyone interested in the philosophy and practice of mathematics. ... This is a very appealing collection of essays. ... I highly recommend this book to those wondering how math is carried out, both mathematicians and laymen. I also recommend it to educators interested in changing the dominant view of math and how to do math." (Hector Zenil, Computing Reviews, January, 2008)

• A Socratic Dialogue on Mathematics.- “Introduction” to Filosofia e matematica.- On Proof and Progress in Mathematics.- The Informal Logic of Mathematical Proof.- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology.- Towards a Semiotics of Mathematics.- Computers and the Sociology of Mathematical Proof.- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management.- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics.- Does Mathematics Need a Philosophy?.- How and Why Mathematics Is Unique as a Social Practice.- The Pernicious Influence of Mathematics upon Philosophy.- The Pernicious Influence of Mathematics on Science.- What Is Philosophy of Mathematics Looking for?.- Concepts and the Mangle of Practice Constructing Quaternions.- Mathematics as Objective Knowledge and as Human Practice.- The Locus of Mathematical Reality: An Anthropological Footnote.- Inner Vision, Outer Truth.