Review "How Not to Be Wrong" by Jordan Ellenberg

The power of mathematical thinking

"How not to be wrong" by Jordan Ellenberg, ISBN 978-1594205224

Any book by a professional mathematician who references Lindsay Lohan's character when talking about a divergent series ("The limit does not exist") is a must read. Any book that links Massachusetts' lottery, voting, throwing needle on the floor boards and French Revolution is an absolute must read. The author shows with a clear and powerful prose how the same principles connect phenomena spanning centuries and continents.

The book is targeted at the general audience, but the math is not dumbed-down. Instead the author skillfully explains each principle, making even complex subjects appear simple and straightforward.

The book's overall theme is the everyday application of mathematics. Different disciplines use math to understand, study and predict natural phenomena. To say that someone is not using math everyday of their life would be laughable after reading this book. The second theme closing the book is the discussion of the underpinnings of the modern mathematics itself. Is mathematics relying on an assumption that might some day turn out to be false? The author discusses sides to this fundamental question, then closing with a powerful and humanistic conclusion. We cannot prove that axioms at the core of the mathematics are consistent among themselves. We might one day discover a contradiction. What makes the study of the universe possible is that human mind can accept contradicting knowledge without grinding to a half. We are not machines!

Another interesting chapter at the end of the book should speak to many people who think that modern science is a playground of geniuses and child prodigies (think Sheldon from "Big Bang Theory"). The author argues that we should think of the total body of science as millions of steps taken by ordinary scientists seeking to understand and solve a particular problem. Once in a while someone takes a small step that reaches a particular important insight. It is not a work by a genius, but a genius work that matters.

I would give the following advice to anyone seeking to make an impact in science, engineering or technology. Instead of wondering if your IQ is high enough to make a breakthrough, work hard in your field. Try to solve common obstacles that you have, then communicate your solution to others. Keep improving your solution and after some time you will find your solution praised as a novel and clever invention. Iterative approach and hard work are your best bets, not the innate aptitude.