A Long Way from Euclid

by Constance Bowman Reid

Mathematics has come a long way indeed in the last 2,000 years, and this guide to modern mathematics traces the fascinating path from Euclid's Elements to contemporary concepts. No background beyond elementary algebra and plane geometry is necessary to understand and appreciate author Constance Reid's simple, direct explanations of the arithmetic of the infinite, the paradoxes of point sets, the "knotty" problems of topology, and "truth tables" of symbolic logic. Reid illustrates the ways in which the quandaries that arose from unsolvable problems promoted new ideas. Numerical concepts expanded to accommodate such concepts as zero, irrational numbers, negative numbers, imaginary numbers, and infinite numbers.
Geometry advanced into the widening territories of projective geometry, non-Euclidean geometries, the geometry of n-dimensions, and topology or "rubber sheet" geometry. More than 80 drawings, integrated with the text, assist in cultivating a grasp of the abstract foundations of modern mathematics, the search for truly consistent assumptions, the recognition that absolute consistency is unattainable, and the realization that some problems can never be solved.

Genres: Mathematics

292 pages, Paperback

First published January 1, 2004

Reviews

[Stacey · Rating 4 out of 5]

I'm going to count this as read, because I did read the whole thing, although there were large chunks that I didn't understand. I'll try again someday, and hopefully get more of it.

[Timothy Allen · Rating 5 out of 5]

I wish I had read this book the first time that I saw it, when I was 12 years old. It is a wonderful survey of a lot of the fields of modern mathematics. It’s fairly accessible.