This is one of the oldest (perhaps the oldest?) physical books I own and have yet to read. Goodreads suggests I’ve had it for nearly a decade. Oops. The truth is, I was never excited to read this. I love reading math books! But I am not particularly enamoured of books that explore one or two “special numbers,” and phi is perhaps my least favourite special number. The blurb from Dan Brown on the cover didn’t help. See, phi has been egregiously sexed up and romanticized by people, turned into a mystical number that recurs exactly throughout art and nature, and ascribed aesthetic properties it doesn’t deserve. I was nervous this book would repeat these claims. Well, I owe Mario Livio an apology. Not only does he critically challenge those claims and debunk a lot of the hogwash surrounding the golden ratio, but he also takes it upon himself to tell a broader and more complete story than focusing solely on this number. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number is a good story of the intersection of mathematics and society, and it provided one key insight that, as a math and English teacher, I find very valuable.
You would be forgiven for, having begun the book, thinking that Livio has entirely forgotten about phi for the first couple of chapters. Rather, he explores the history of numbers and counting in general, eventually ended up in ancient Babylon and Greece and making some connections with geometry. This creates a much richer backdrop for Livio’s later exposition of the golden ratio, and it also broadens the reader’s awareness for how various cultures developed and practised mathematics at different points in history. For example, Livio discusses the Rhind/Ahmes papyrus, which famously provides insight into Egyptian mathematics about 3500 years ago. He emphasizes the papyrus’ purpose as a teaching/reference tool—it specifically explains how to do practical calculations. Fast-forward a couple of millennia, and Fibonacci was doing the same thing—writing tutorials, essentially, for accountants.
See, I appreciate this, because most approaches to discussing the golden ratio focus on the idea that its use in architecture, art, etc., invokes certain ingrained aesthetic ideals in us. These approaches further seek to ground the golden ratio in the idea that its proponents and adherents throughout history have sought it out as a result of being fascinated with mathematical beauty. Livio, on the other hand, reminds us that a great deal of mathematics was (and remains) practical. It’s true that the Pythagoreans were a semi-mystical cult that believed their discoveries reflected the beauty of nature—but the problems they solved were motivated by questions of geometry and arithmetic that were relevant to life in Greece at the time. This has remained true throughout history: our development of mathematical approaches is driven by our needs as a society. The adoption of Hindu-Arabic numerals, for example, didn’t happen because they are “more beautiful” than Roman numerals—the accounts liked them better for arithmetic!
It might seem strange for a mathematician, especially one who loves pure math, to be arguing against the idea that beauty should be a foundational concept of mathematics. And I’m not, not really. But I agree with Livio that viewing mathematics in the past through a lens of beauty/aesthetics is ultimately an ahistorical reading that confuses more than it illuminates. Understanding the emphasis on practical applications for math helps us understand its place in our society.
And this is where The Golden Ratio really got me. Several chapters examine whether well-known artists used the golden ratio in their work. Livio discusses the works themselves, as well as numerous scholarly intrepretations both for and against the idea that the golden ratio played a part. I appreciate his extensive use of references and the way he engages with the topic as objectively as possible. Most importantly, Livio suggests that our desire to spot the golden ratio in this artwork undermines and devalues the artists’ general mathematical brilliance. If the aesthetic quality of a work of art were simply the matter of using the right shape of rectangle everywhere, what does that say about art and artists? Why wouldn’t we have made a computer program that can generate “the perfect work of art” by now? No, Livio concludes, the brilliance of these works of art is independent of their use, or lack of use, of the golden ratio. It comes from a far deeper grounding in mathematics than we care to credit—from the use of perspective to plane geometry, math is everywhere in art. He points out how some artists, like Durer, studied mathematics purposefully to improve and influence their artistic output.
I teach math. I also teach English. People treat me like a unicorn because of this, but I really don’t see them as all that different. Neither did Charles Dodgson, who wrote Alice in Wonderland. Livio cites numerous other poems and literary works that use math, as subject matter or metrical inspiration or both. He reminds us that this siloing of STEM is a recent and very artificial phenomenon, that throughout the majority of history, STEAM indeed was the rule of the day. The idea that if you have an artistic sensibility you must somehow be allergic to mathematics is ahistorical and untrue, for as Livio points out here, many of the most celebrated and famous artists studied, understood, and used math in their work.
In this way, The Golden Ratio provides a far more valuable story than simply “the world’s most astonishing number” (which phi is not). Livio’s tangents into philosophy, history, art, and music remind the layreader that mathematics is not this alien construct that only super-intelligent people can appreciate or do. It is fundamental to our lives, to our praxis, and to our pleasure—not for any innate beauty it possesses, but for the way its practice can help us create what we consider beautiful. The golden ratio does not play as big a role in this process as some want you to believe. Rather, as is usually the case, the truth is far more wonderful and broader in scope than the simple idea that one number can rule them all.