While this book may have gotten praise from the likes of Martin Gardner and Sir Roger Penrose, I did not find it all that illuminating on the concept of zero, nothing, and the null set.
I am including two images from screenshots of the book to remind myself of the way he writes. The following is from pages 176-177.
“O Archimedes, this is wondrous strange!” Really?
Here is another book about mathematics. In this book, the author talks about his absolute love of the beauty of mathematics, and how it explains physical properties, such as features of subatomic particles and in quantum physics. For example, mathematicians postulated the existence of some particles before they were even found based on symmetry in the underlying mathematics.
I was particularly interested in this book, since the author attended college right around the same time I was going to college (he is one year younger), and he experienced the changing world at the same stage that my wife and I did. Even though he is one year younger, he graduated from his high school one year earlier than me at age 16.
In the book, he explains how he was singled out in the mathematics test to attend Moscow State University (or MGU) as a Jewish person. When he went in for his math test, the testers grilled him, and they found a reason to reject his application even though he is brilliant. Moscow State University does not accept people who are even just one quarter Jewish. He ended up going to the Moscow Institute of Oil and Gas (also called Kerosinka and officially called the Gubkin Russian State University of Oil and Gas) which has a pretty good applied mathematics program. They accept Jewish people. This allowed him to attend some lectures (first by jumping a fence, then getting an ID card) at Moscow State University, even though he wasn’t a student there. (See Chapters 3 and 4.)
In 1989, he received a Harvard Prize Fellowship to attend Harvard for a Semester to learn from some of the best mathematicians in the world. Most of the other recipients had graduate degrees and/or PhDs, while he just had an undergraduate degree from Kerosinka. He worked hard to prove that he belonged there with the fellowship.
He ended up staying in Boston for longer than a semester. He was able to get his PhD in just a year between 1990 and 1991. Below is his dissertation.
Frenkel, E. V. (1991). Affine Kac-Moody algebras at the critical level and quantum Drinfeld-Sokolov reduction.
After he gets his PhD, he works on the Langlands Program. This attempts to be a grand unified theory of mathematics. As noted at Wikipedia — “The Langlands program consists of some very complicated theoretical abstractions, which can be difficult even for specialist mathematicians to grasp.” Frenkel tries to explain some of the math in the program, and I caught some of it, but not very deeply. At the end of the book, he talks about the movie that he worked on, The Rites of Love and Math. The book was published in 2013, while the film came out in 2010, so the film preceded the book.
Took me several months to finish this one, and I finally did a couple weeks ago. I particularly liked Chapter 4 the Life of Pie and Chapter 7, Secrets of Succession.
I’ve always like how pi has digits that go on forever, since it is an irrational number. The Secrets of Succession chapter covers sequences of numbers. It mentions the Online Encyclopedia of Integer Sequences, which I had never heard of before. For example, the Fibonacci sequence has many notes, while other sequences are not as full.
I am reading another book that connects numbers with physics, and I learned that Fibonacci was not his real name. “The man’s full name was Leonardo of Pisa, or Leonardo Pisano in Italian. He was born in about 1175 in Pisa, a Tuscan town famous for its Leaning Tower. The name Fibonacci [pronounced fib-on-ach-ee] is short for ‘filius Bonacci’ or ‘son of Bonacci.’”
Overall, if someone is mathematically inclined, it is a fun read.
I recently read the book, Is God a Mathematician by Mario Livio. I picked it up at the JeffCo Libraries Whale of a Book Sale. I figured the book would not answer the question posed by the title, but I thought it would talk a little bit more about logical proofs for or against an all powerful being. In a way, I am glad that it did not do that. It was mostly on the question, is mathematics invented, or is it discovered?
My favorite chapter was probably chapter 5 on statistics and probability. I learned a little bit more about how games of chance helped influence mathematical thought. They discussed games of chance on pages 138-140, but it was involving dice. I thought that card games influenced mathematical thinkers more when it came to chance and probability of winning various hands of cards. That didn’t seem to come up in the book.
I guess I am on the side of the fence for mathematics being discovered. I think that prime numbers and the number pi exist with or without human involvement. It is just up to us to find them in the world of mathematics. But, math is more than just numbers, it also involves concepts such as functions, and algebraic concepts of unkowns in formulas. There is a lot of math in physical concepts such as waves of light or the Navier-Stokes equations in fluid dynamics. That math would still exist even if we did not find them. Other intelligent life forms would probably also know about pi, prime numbers, the speed of light in a vacuum, E = mc2, and the Navier-Stokes equations.
However, we can invent different ways to communicate the concepts of mathematics, just as calculus can be communicated using different terminology. So, the way to communicate mathematics can be invented.
Anyway, it was a good book. It was not earthshaking, and it did not answer the main question in the title, but it was an interesting read.
