This author has written a number of wonderfully informative books on math and cosmology, of which we have read at least half. Although he is a theoretical physicist, he writes in a conversational style that is non-scientist-friendly.

In the introduction of this book Barrow gives a short summary of different views about what mathematics *is*. One view holds that it is “a set of eternal truths that already ‘exist’ in some real sense and are found by mathematicians. The second sees it as “an infinitely large game with rules, which we invent and whose consequences we then pursue.” A third opinion defines mathematics as “the catalogue of all possible patterns.” Moreover, although the number of possible patterns is infinite, it turns out that a very small number of simple patterns characterize much of reality. It is this third view that shows why art and mathematics actually have so much in common, because pleasing patterns tend to be associated with great works of art. As Manil Suri points out (in his discussion of Pi), “This is characteristic of mathematics, whereby elementary formulas can give rise to surprisingly varied phenomena.”

Barrow demonstrates this premise in very pithy chapters that can be read in any order, ranging on topics from the design of art galleries themselves to the works they contain; from music, to book design, to sculpture, literature, dance, and music. Some of the essays have very little to do with art as one might conventionally define it, but they are interesting nonetheless.

While Barrow writes clearly with a minimum of equations and the inclusion of many illustrations, it is a *bit* too “math-y” for my taste. For Jim, on the other hand, who spends many afternoons watching free online lectures on math and physics from Stanford, MIT, and The Kahn Academy, the short essays don’t seem math-y at all! He opines that except for one chapter (using a Taylor expansion to calculate the value of an infinite series), you won’t need any more math background than perhaps a familiarity with algebra.

In spite of any math deficiencies I may have compared to Jim, I do love discovering new aspects of the intersection of math and art and their surprising co-evolution. For those, like me, who find this book – which is witty and fairly elementary – fascinating but still not basic enough, I have two other recommendations that focus more on the art than on the math.

One is *Art & Physics: Parallel Visions in Space, Time & Light* by Leonard Slain (William Morrow Books, 1991) and the other is *Exploring the Invisible: Art, Science, And the Spiritual* by Lynn Gamwell (Princeton University Press, 2002). Both emphasize the way in which paradigm changes in science spurred revolutions in art. Barrow’s emphasis is the opposite in a way; he shows you how art, or more specifically, patterns, reveal the math behind them.

The three of these books together would make a wonderful complement for anyone seeking to understand the close relationship between developments in math and in the arts.

**Evaluation:** Math and science fans will really enjoy this book, as will those who love finding out how the patterns that please us are not just random. Barrow also has very readable books on cosmology, such as *The Infinite Book*, and *The Book of Universes*. In addition, he has written *100 Essential Things You Didn’t Know You Didn’t Know: Math Explains Your World*, which is very similar in style and format to the book being reviewed here, and is also very entertaining.

**Rating:** 3.5/5

*Published by W. W. Norton & Company, 2015*

**Note:** I want to make special mention of his dedication “To Darcey and Guy who are still young enough to know everything.” Isn’t that the truth about kids!

I’m sure the list of essential things I don’t know is much longer than 100. This sounds interesting.

Hummm, not quite sure (though I was always good at math). But perhaps something for Mr. BFR.

Yes, this one is definitely for me. I have so many books about maths in my TBR, it isn’t funny! I have always loved maths – when someone can write well about numbers, it can make for really beautiful reading – although I don’t think I’d be like Jim and find this one not “math-y” enough!

Yeah, I’m with Kathy. But one that Jason might enjoy.