Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander (2014)
I recently read Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander. This book concentrates on the “indivisibles” of Bonaventura Cavalieri and the “infinitesimals” of John Wallis (the man who introduced the ∞ symbol). As a history of pre-calculus, that’s rather incomplete. There are also some errors, noted by Judith Grabiner in her review for the MAA.
Alexander portrays the Jesuits as the “bad guys,” suppressing the idea of “indivisibles,” even though interesting and useful mathematical results can be obtained by using them. However, Alexander does not fully explain the Jesuits’ actions. There is not a word about their struggle with the Dominicans for intellectual leadership of the Catholic Church (although this played a major part in the Galileo saga). Nor does he explain the link between defending Aristotle and defending the doctrine of Transubstantiation. And, of course, the critics of Cavalieri and Wallis were actually quite correct. “Infinitely small numbers” greater than zero do not exist, and calculus did not have a rigorous foundation until the work of Cauchy and Weierstrass in the 1800s.
I was left rather disappointed with this book. GoodReads rates it 3.83, but I’m only giving it two stars.
Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander: 2 stars
Scientific Gems 