Source of bool: I own this.
Every so often, I tackle a nerdy math book, just to stretch my brain and appreciate the language of the universe, so to speak.
This is a book I couldn’t find in our library system, so I waited until I saw a cheap library discard version online. Eventually, it ended up on my night stand as an offbeat read to browse a bit at at time.
Like the other nerdy math book I wrote about on this blog, Love and Math by Edward Frenkel, this one contains math that is definitely beyond my ability to understand - I didn’t take math past the high school level, so anything else I know is what I picked up in a non-systematic way. In this book, the author warns of the increasing difficulty of the math as each chapter proceeds. He does a fairly good job of explaining the concepts, though, so I was able to enjoy the ideas even when the calculations were over my head.
I should say that this book contrasts with some of the other math-related books I have enjoyed, in that the math itself is front and center, not the history. (See below for more math links.)
The basic idea of the book is to look at the nine non-zero digits, and explore the mathematical relationships which arise from them. To even begin to explain would be to get too far into the details of the book, but there are a lot of really fun tidbits in this book. I imagine someone with higher math ability than me would enjoy it even more.
I do want to mention a few lines. First is about Benford’s law, which gives the frequency of occurrence of each digit. They are not equal when it comes to their frequency in the real world. Mathematically, of course, they are all equal, but reality favors them in a particular order, namely, “1” is the most common, and the commonality decreases as you go up. This is hardly a mere academic exercise - as the book points out, the IRS uses number frequency as a way of flagging falsified documents - fake numbers tend to be more random than real-life ones, which have a lot more “1”s in them.
I also had to laugh at this observation:
When two people meet and one of them says, “I’m a mathematician,” the responses are somewhat predictable. After an awkward pause, the other person often exclaims, “I was never very good at math.” The mathematician wonders why when the same person meets a physician they don’t exclaim, “I was never very good at biology.”
How about this one? When asked to pick a random number between 1 and 10, the most popular is 7. Probably, that should not be surprising. The book even quotes Voldemort as saying “Isn’t seven the most powerfully magic number?” And so it has been considered in many human numerology systems. My favorite part of the chapter on 7 was all the ways that you can make circles tangent. (See: the Seven Circles Theorem) Did I mention that I really enjoyed Geometry back in the day?
Seven also lent itself to plenty of mathematical games. As Leibniz (quoted in the book) said, “Men are never more ingenious than in inventing games.”
And another observation:
Constructing a formal proof can be very different from the process in which the theorem was discovered. Mathematicians pride themselves on slick, aesthetic proofs, but sometimes the path to getting there is long and meandering, a process we’d like to forget. In published articles, the highly refined proof is typically all that is presented, depriving the reader of a sense of how the result was originally conjectured.
I guess maybe I could have put more math in this post, but I think it best just to read the book. And also, printing many of the equations on a screen would be daunting for someone of my tech level. But perhaps more than anything, I found the pithy quotes, anecdotes, and stories about the discoveries to be as much fun as anything strictly mathematical.
So, I will end with a quote from John Maynard Keyes, which he maybe said or didn’t, but is perhaps a defining idea in my own life:
“When the facts change, I change my mind. What do you do, sir?”
***
More math books:
The Nothing That Is by Robert Kaplan
The History of Pi by Petr Beckmann
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