Sunday, October 18, 2015

From Primitive to Modern: The Evolution of Mathematics

Book Review: Clifford A. Pickover's The Math Book

From the very beginning in the Introduction, Pickover makes it clear that this book is not the complete, definitive list or the final word on what the milestones of math should be. As he mentions, these are his selections that cover a wide range of mathematical topics, from games to important theorems, and are written in such a way that an average person could understand, in a general sense, what the topic is about. And to his credit, Pickover does just that, and does it well.

The list is in chronological order and the topics have one-page summaries with an accompanying picture that can help the reader visualize the math concept or milestone featured. The breadth of time Pickover covers is from BC to the early 2000s. The list starts, surprisingly, not with a human mathematical milestone, but with an animal one. In fact, the first two milestones describe how animals such as ants and monkeys have mathematical capabilities. And the next milestone describes a mathematical pattern in Cicada (insect) behavior. The first human mathematical milestone, which is the fourth milestone in the book, is the presence of knots. Then the milestones become more historical with the mathematical advancements from ancient civilizations, like the ancient greeks. Famous games, equations, numbers, and texts are featured in this book, as well as technological advancements, like computers that can help prove conjectures.

The reason Pickover showcased the milestones chronologically, as he states in his introduction, is to have the reader see the evolution of mathematical thought, and how one milestone is connected and/or spurred another milestone. Pickover delivers on this goal, since I saw how mathematics is ultimately a compounding network of many topics, each connected - influencing, advancing and creating others. He not only points out these connections, he even lists the related topics at the bottom of the page. Furthermore, Pickover also points out how a milestone is important or useful outside the field of mathematics like in economics or the sciences. The best example of this are knots. Pickover mentions knots as the first primitive human milestone, and the topic continues to progress in complexity with advances in knot theory like Jones Polynomial, which has applications regarding the DNA molecule and proteins (pg. 24, 478, 490).

But why start the book, which is about mathematical milestones, with a mathematical capability of an animal, instead of a human? Why would it even be considered a milestone? Pickover discusses how mathematics is not solely human, and it implies how human mathematical capability has evolved from our animal ancestors.

All in all, this book is a great read for those who want a condensed history of mathematical milestones. Since this is my first major exposure to the history of mathematics, it's hard for me to compare this list to other milestones and say "Why isn't such-and-such in this book?!?" However, 3 out of my 5 milestones that I could barely come up with in this blogpost were featured in Pickover's book (Zero, Calculus, and Alan Turing). The first one that didn't show up was Albert Einstein's E=mc2, even though Pickover mentions Einstein in the book, and specifically that equation in the Introduction. The second was a milestone that happened after the publication of the book, which was the first woman to win the Fields Medal (1).

None of the people or organizations below have endorsed my work, nor am I affiliated with any organization or any person. I am a college student.

Pickover, Clifford A. The Math Book. Sterling Publishing Co., Inc. New York, NY. 2009.

(1) Ball, Phillip. "Maryam Mirzakhani Becomes First Woman To Win Prestigious Fields Medal." The Huffington Post.

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