Steven Strogatz 2019. Infinite Powers. The story of calculus the language of the universe. London: Atlantic Books, 306 pp.

My 1972-1973 high school maths notebook is evidence that I once understood at least the basics of this stuff. Sadly no longer, but if I could have read this book then it may have made me wise enough to maintain some mathematical skill. Steven Strogatz has no trouble convincing the reader that of the importance and the rationale, however following the mathematical proofs I understood 46 years ago is another matter. But that is my failing not that of the author.

To me, now, most interesting for explaining how Archimedes (~287–~212 BCE) came so close to integration with his brilliant method for approximating pi, circumference and the area of a parabolic segment. Tellingly, Strogatz shows that Newton was taught this material in school (p. 187).

And for the reminder that Galileo qualifies as the first scientist for his experiments, seeking causes.

And forr showing how the geometry approach to mathematics (of the Greeks) and the algebraic method from the Islamic mathematicians was brought together by Fermat and Descartes, what a mongrel Descartes was, and how close Fermat came to discovering calculus (pp. 93-113).

And for setting out exactly which giants belonged to the shoulders Newton stood on (p. 194 ff.).

And for the reminder (pp. 297-298) of Paul Dirac’s breathtaking prediction of the existence of antimatter, the postitron (“anti-electron”).

And for the wonderful concluding pages where Steven Strogatz allows himself to philosophise a little on chess, computers, AI, and the comprehensibility of the universe.

And for a whole heap of further reading directions in the endnotes and bibliography.