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Great Calculations: A Surprising Look Behind 50 Scientific Inquiries

Colin Pask
Prometheus Books
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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This book looks closely at fifty “great calculations”, as judged by the author, who has produced other works in the area of mathematics popularization. The significant scientific calculations and formulae are presented simply and with historical context, including careful observation of the often tangled claims of priority. Readers are not required to have a significant mathematics background to understand the stunning implications and elegant innovation behind each of the fifty. The result is an accessible and engaging book covering a spectrum of mathematical breakthroughs that solved mysteries of our world, such as measuring the solar system, or revealed new mysteries, such the existence of dark matter and dark energy in our universe.

The historical context brings in key persons and often interesting side alleys. Thus is the balletic choreography of planetary epicycles reviewed in the chapter on the “Solar System: First Mathematical Models” is a part of the act, leading to the stunning, resolving scene featuring Kepler. Here also is the beautiful, if misguided, astronomical model based on the Platonic solids. As part of classical mathematics, Eratosthenes’ visionary seeing of the circumference of the globe in the bottom of a well is also here. So is Andrija Mohorovičić peering in to see Earth’s very bones with the aid of seismic waves.

The attempt to reach readers without high levels of mathematical sophistication brings the author to evaluate some equations for almost subjective aesthetics. Maxwell’s equations can be daunting even for accomplished undergraduates, but the author calms the reader with pragmatism and superlatives, “It is not necessary to understand the mathematics… these wonderful equations do tell us how the electromagnetic fields can vary in space and time.” Thus is the lead-in to “Maxwell’s Miraculous Calculation”.

Can such a list be compiled without criticism for some oversight? Probably not. I encourage you to read it yourself and come up with your own necessary additions. What would you part with to keep it to fifty? For me, in a list that includes (and rightly so) Archimedes’ insightful approximation of \(\pi\) must find room for Euler’s number \(e\). I would even say this could replace the entry for Euler solving the Basel Problem, since that, essentially, could be a footnote to the exploration of \(\pi\). Or, let it replace the valuation of annuities as calculated by Halley, better known for predicting his eponymous comet.

This is the class of thoughts the book will raise with any reader, and rightly it should. The author directly tackles the subject of necessary omissions, both generally and at the conclusion of the topical chapters. The end of Chapter 8 “About Us” suggests there could have been more on DNA, modeling nervous system signal transmission and Turing’s “mathematically elegant work on pattern formation”. Of course, there are many surprising and appealing entries, such as the World War II D-Day tide calculations based on work done by Lord Kelvin seven decades previous.

As can be expected, this work has an extensive, supporting bibliography. I very much appreciate an author that elevates titles out of the sterile appendix listing to make qualitative assessments of favored works. This author does that often and boldly, which resulted in new additions to my own “to-read” list. In a run up to time dilations, Right Hand, Left Hand by Chris McManus is called “entertaining”. The same adjective is applied to the paper “Lambda: The Constant That Refused to Die“ (John Earman) when linking Einstein’s \(\Lambda\) to a discussion of dark energy. We are also assured that Fred Hoyle’s autobiography Home is Where the Wind Blows is “captivating”. In this way nearly every page offers departure points for further exploration assessed as “fascinating” or another superlative descriptor. The journey this book takes the reader on is full of stunning vistas and promising side treks

Tom Schulte engages his mathematics students with the greatness of calculation at Oakland Community College in Michigan.

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