The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development

by J.L. Bell

A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl.
Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

Genres: Mathematics

260 pages, Hardcover

First published January 1, 1999

About the author

John Bell (b. March 25, 1945) is professor of Logic and the Philosophy of Mathematics at the University of Western Ontario in Canada. In 2006-07, he was named the first Graham and Gail Wright Faculty of Arts Distinguished Scholar at the University of Western Ontario. In 2009, he was elected a Fellow of the Royal Society of Canada. He was admitted on a scholarship to Oxford University at the age of 15, and graduated with a D.Phil. in Mathematics at the age of 21. His dissertation supervisor was John Crossley.[1]

He was appointed assistant lecturer in the Mathematics Department at the London School of Economics in 1968, and was appointed reader in Mathematical Logic in 1980. He taught at LSE until 1989. During this time, he served as visiting fellow at the Polish Academy of Sciences (1975) and National University of Singapore (1980, 1982). In 1989, he took a position as professor in the Philosophy Department at UWO. He is also an adjunct professor in the Mathematics Department at UWO.[1]

John Bell's students include Graham Priest (Ph.D. Mathematics LSE, 1972), Michael Hallet (Ph.D. Philosophy LSE, 1979), Elaine Landry (Ph.D. Philosophy UWO, 1997) and David DeVidi (Ph.D. Philosophy UWO, 1994).

http://en.wikipedia.org/wiki/John_Lan...

Reviews

[Nick · Rating 4 out of 5]

Honestly, I only read half of it, but enjoyed it all. The rest looks good too, but not much of the stuff is new for me, and I'm ready to move on to another book for now.