To Infinity and Beyond by Eli Maor
Review: Maor has written a book for both mathematicians and poets. Since he is a mathematician himself there is, to be sure, plenty of math in Maor's book. But the book should also appeal to the aesthetic side of many readers (me included) by exploring human perspectives of infinity, such as how we try to relate to the concept at a personal level, and how different people have tried to capture the notion in art and prose. The book is arranged in four parts, dealing with the mathematical concept of infinity (how it shows up in algebra, etc.), geometrical infinity, aesthetic infinity (both art and poetry) and cosmological infinity. The section on mathematical infinity has the typical assortment of historical examples, beginning with examples like the runner's paradox made famous by Zeno. There are also examples of infinite series that converge, including examples of how ancient mathematicians invented infinite series for transcendental numbers like pi. There's a plethora of little tidbits found throughout this section in little mini chapters that are short essays, only a few pages long, that give surprisingly succinct, tantalizing, and often delicious examples of mathematical infinity. Reading this book I was struck by what good reading it makes for any student preparing to take a class in calculus. Some of the author's most interesting material is the author's discussions about infinite series. I particularly enjoyed his examples how the associative property doesn't hold for infinite series (a nonintuitive fact that often comes as a surprise to many new students). Ordinarily, if you have a string of numbers that are connected by addition (x1+x2+x3+..+xn) for example, you can rearrange their order and get the same result. One of the strange things about infinity, though, is that rearranging the terms in an infinite series can result in the limit of the series changing from one number to another. Of course no discussion about infinity would be complete without mentioning Cantor, which Maor does with particular clarity for firsttime readers. Indeed, this is one of the things I like about Maor best  he's written a book that is fun to read, even if you already know most of the stuff. It's engaging and entertaining, and full of "ahh" and "ohhh" even when you find yourself reading about something you studied many years ago. At the same time this is a good introductory text for anyone (I'm thinking youngsters in high school) who wants to start exploring some of these mathematical concepts, and need a friendly introductory text. If you can manage firstyear algebra you have the tools you need to follow what Maor is talking about, though be advised that he doesn't shirk when producing equations, though most of the math is relegated to the appendices. The section on geometric infinity is punctuated by nice illustrations and those geometrical shapes that you may have heard about  the ones with things like finite volume but infinite surface area. This was one of those rare occasions where I found myself wishing Maor had gone a little further. Instead of simply showing how such objects exist in mathematics, he really should have explained the apparent "paradox" (it's not hard). Instead, he makes the example more of a "paradox" than it really is by mixing metaphors in talking about "painting" the surface. Of course mathematicians have one idea about painting a surface (mathematical paint has no thickness), but the beginning reader is likely to be mostly confused  too bad, since Maor clearly has the skill to explain the trick. Maor's exploration of the infinite is (almost) infinite.
He has a wonderful section on tiling, and some brilliant
plates representing some of the best mathematical art that
attempts to depict the nfinite. The section on cosmology
and the infinite is a nice summary of the history of astronomy
and how astronomers and cosmologists have vacillated over
the years between a cosmos that is infinite, then finite
and bounded. I thoroughly enjoyed reading this book. It
is well written and both easy and fun to read. My only
complaints are rather minor. Several times Maor treats
infinity as a "big number" (it's not a number
at all, and he makes that clear, but his terminology on
this score isn't as consistent as it should be).
And, he refers to mathematics as a science. Well, I suppose
he's entitled to his opinion on that one, The fact these inconsequential gripes are all I can find to complain about tells you what a really fine book this is. If you love mathematics, this book really needs to be in your library. — Reviewed by: 
Reviewers, authors and publishers have been asking for this feature and we're listening! You're proud of the work you've done for Northeast Book Reviews and now you can get something to show that you're a part of the team. Check out our online storefront ISSN: 15585956NEBR is an online magazine published by Eleven Limited, LLC.


© Northeast Book Reviews  Book Reviews for the Discriminating Reader! NEBR is owned and published by Eleven Limited, LLC. 