Infinity: The Quest to Think the Unthinkable

Rating:
Summary: Good look at math history through one idea
Review: I enjoy these types of books that track one idea through history. This book tracks the concept of infinity through history. It gives you a good look at the history as math as well as good insight into infinity. I thought Clegg did a good job making the concepts understandable for a "lay" person. If you are interested in math history, this book is a worthwhile read.

Rating:
Summary: Entertaining and somewhat informative
Review: I know that Clegg is trying to reach a broad audience and I think he writes well enough to succeed. But I think that by skipping certain details he underestimates the ability of his readers.

For example, I was disappointed that he did not adequately explain Weierstrass' great epsilon-delta explanation of limits, which turns infinity in the calculus into a facon de parler, nothing mysterious after all.

In his discussion of Bolzano, I learned interesting things about his political conflicts but it wasn't clear what he contributed to better understanding the real numbers.

He mentions that Gabriel's Horn has infinite surface area but volume pi, which is fascinating, but he gives no explanation of why these results hold.

But I did learn about the belated 1993 publication of an important work by Leibniz on indivisibles, as well as a few other valuable tidbits, so the book was useful to me as a professional.

Rating:
Summary: Pretty good, but I wish he'd give more details
Review: I liked the book. Clegg covers both the concept of infinity and its companion, the concept of infinitesimal, from Greek days to the present, in a way I found very readable. I have very little to complain about except that I found it sometimes frustrating that his treatment oversimplified and didn't give enough details.

(For example, he has a chapter on Abraham Robinson's nonstandard analysis. I think that, next to Cantor, Robinson's ideas are probably the most important on the subject of anyone who has worked in it, yet I felt I did not get an adequate picture of Robinson's ideas of infinity and infinitesimals from the chapter.)

Still, it is the best book on the subject at a "popular" level I have seen.

Rating:
Summary: To Infinity and beyond!!
Review: I love how Brian Clegg ingeniously expounds upon the concept of infinity challenging our minds to go beyond previously defined limits of the notion. Bizarre paradoxes, strange people and brilliant metaphors make the whole s move from the mundane to delightfully inspiring and I'm not really a fan of science.