Customer Reviews

Infinity: The Quest to Think the Unthinkable

5 star:		(2)
4 star:		(3)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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.

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.

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.

This is an excellent read for someonre who wants to take a little journey into the World of Mathematics and particularly the concept and theory of Infinity.
I developed an interest in Mathematical Recreations in high school,though I didn't know that what I found interesting about numbers,puzzles and math was called Recreational Mathematics. After high school,I went on to University and obtained a degree in Mathematics and a degree in Electrical Engineering;in 1959.I have retained my interest in Mathematics and Recreational Mathematics for these many decades,but must admit that my knowledge and skills have pretty much disappeared;though my love and fascination for it all has remained.I have written many reviews on books about Mathematics,Puzzles,Mathematicians,etc., and enjoy finding new ones on the subject.
When I came across this book,I thought it would be interesting and I wasn't disappointed. At my ripe old age of 74,I must admit these abstract concepts are not as easy to digest as they once were.What is really eye-opening is the things being talked about in this book were seldom ,if ever discussed in "applied math" at the undergraduate level during the late 50's.Imaginary numbers,Differential and Intregal Calculus,Vector and Tensor Analysis,Differential Equations,Venn Diagams,Matricies,and such,were everyday subjects at that time;but Set Theory,Boolean Algebra,Quarks,Fluxions,and many other terms and concepts found in this book ,may have been in the world of higher or modern abstract Mathematics;but certainly not common at the undergraduate level.
As to the concept of Infinity,it seemed pretty straight forward to us aspiring engineers at the time.We wrote it off as unattainable as the pot of gold at the end of the rainbow,the search for a limiteless supply of beer,or the perfect female beauty. I guess this is what seperated us engineers from the abstract mathematicians; thus resulting in fewer breakdowns in our chosen professions.
All that aside,this book is a great read for someone interested in Mathematics for Mathematics sake;and gives a real insight into what some of the famous names in mathematics tried to resolve over the centuries;and still have to solve in the fuure.
If anything,this book makes one ponder the depths and reaches of the universe. While we usually think of Infinity in terms of great distances or numbers or whatever;Infinity also goes the other way ,and just as endlessly into the vastness of the infinitestimally small. And what about man,who thinks himself in the center of the universe,smack dab in the middle of the far reaches of space and the inner world of the molecules and atoms of the matter around us?
When mamkind thinks that he has really solved the secrets of the universe,or in fact anything else around us;it is worth thinking about what Einstein had to say about Infinity;

"Only two things are infinite,the universe and human stupidity,and I'm not sure about the former."

However,that's not to say we should quit searching for answers,because that's all that differentiates man from everything else in the universe.

Get ready to have your mind blown away with thoughts and concepts of the endless that cannot be contained because infinity is bigger than even that!!

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.

Unfortunately this book ignores the contributions of the ancient Indians. Infinity did not start with the Greeks. In fact, the Greeks had big troubles with infinity. The ancient Indians had much more fruitful investigations into infinity, especially the Jains before Aritstotle. After the ancient Greeks, the Indians continued to study infinity, including Aryabhata and the Kerala School.