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The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg

W. W. Norton
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The Great Equations caught my attention because I sometimes teach our department’s history of mathematics course and am always looking for additional resources. I often ask myself whether science isn’t the most applied form of mathematics; even so, I would classify this as more of a physics book than a math book. Crease is a philosopher who writes about physics, and this is apparent in the tone and flow of his writing style. This makes The Great Equations readable, and also leads to interesting notions like the “deeply democratic” nature of gravity (p. 82).

The two most mathematical chapters of The Great Equations are Chapter 1, about the Pythagorean Theorem, and Chapter 4, about Euler’s Equation eiπ + 1 = 0. The remaining chapters include two greats from Isaac Newton, Einstein’s equations for general and special relativity, Maxwell’s equation, Schrodinger’s equation, and the Heisenberg Uncertainty Principle. Each chapter begins with a quote, my favorite of which opens Chapter 5 by stating that not knowing the second law of thermodynamics is much like never having read a work by Shakespeare (p. 111). For some of the more physics-like ideas with which I was already familiar (i.e., the inverse square law), Crease’s explanations are very clear. For other ideas with which I have limited experience (i.e., quantum theory), I am really no better nor worse for the reading.

A theme which appears throughout The Great Equations has to do with the difference between the “treasure hunt” view of scientific discoveries, and the actual journey to discoveries or evolution of ideas. Many people are introduced in each chapter, along with their contributions to the respective highlighted equations, including an especially helpful chart on pages 112–113 about characters involved with the second law of thermodynamics. Between the chapters are brief sections called “interludes” which address a hodgepodge of information loosely related to the preceding chapter. A few of these discuss communicating science to non-scientists, the need for “science critics” parallel to art critics, and the lack of mention of science in history books.

I had a difficult time with some of Crease’s language regarding equations, proofs, and formulas. On p. 28 he describes the Pythagorean theorem as “the proof of the equation” as distinct from the Pythagorean theorem as “the empirically determined rule,” an idea which he repeats in the interlude following Chapter 1. In Chapter 5, Crease states that Euler’s formula “according to some definitions, is not an equation… for it contains no variables” (p. 103), which feels contradictory to both an entire chapter in his Great Equations book being about to this possibly non-equation, and the book’s introduction which highlights 1 + 1 = 2 as the simple yet powerful first equation most of us learn, even though it contains no variables. These ideas make me wonder whether Crease is in fact being inconsistent, or if my own ideas regarding these terms need some refining.

Although I don’t plan on using this book in my classes, it will be nice to have on the shelf for reference, and it has me thinking even after closing it, which is a good sign.

Christine Latulippe is an assistant professor of mathematics education at California State Polytechnic University, Pomona. Once the final exams have been graded, and the mathematics professional development workshops for K–12 teachers have been successfully completed, her summers are for traveling, reading, and evening concerts at outdoor venues.

Date Received: 
Wednesday, January 13, 2010
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Robert P. Crease
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Christine Latulippe
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Friday, August 27, 2010