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Infinitesimal: how a dangerous mathematical theory shaped the modern world – a review

Image of the book cover of "Infinitesimal" by Amir Alexander
Prior to the previous Alberta provincial election, the way math is taught in the province was one of the political issues. One party advocated that kids ‘learn basics first’ while at the same time promoting parental ‘choice’. The late Joe Bower, in his blog Return of the Math Wars, tried to make sense of this incredibly complex discussion. He noted that “Maybe math and children haven't changed, but our understanding for how children learn math is more sophisticated than generations ago.” He goes on to say “As for right answers, there is only one right answer if we limit ourselves to asking questions that have only one right answer, such as 4 + 3.” Meanwhile, a newspaper editorial informs us that Alberta Education has "dumbed down" math curriculum: “The discovery approach has no place in arithmetic at the junior elementary level. There is nothing to discover.”

The discussion continues. In the past couple of weeks, I’ve seen headlines like: Math experts say Alberta curriculum needs to be rethought; and another told us that Calgary parents discuss changing how math is taught. I might have been worried, but soon realized that there has been major controversy over the teaching of Math since before the beginning of the 16th century. In the book ‘Infinitesimal: how a dangerous mathematical theory shaped the modern world’ by Amir Alexander, I learned that nations actually went to war over the math curriculum.

Infinitesimal is divided into two parts. The first part examines the Protestant Reformation, the rise of the Jesuits as a teaching order, and the development of mathematics in Italy. This period culminated with the repression of the ideas of Galileo and his fellow Linceans with regard to the use of mathematical ideas that did not fit Euclidean geometry. The last part of the book follows the development of math to England and details the vicious debate between Thomas Hobbes and John Wallis. Hobbes looked at math as an intellectual pursuit and adhered to a strict interpretation of Euclidean geometry, while John Wallis thought of math as a useful tool. According to Alexander, first the Jesuits and then Thomas Hobbes saw Euclidean geometry as a metaphor for the societal order during tumultuous times. Galileo and Wallis and their followers developed mathematical methods that made assumptions about infinity and the infinitely small (thus: infinitesimal) that could not be demonstrated through geometry. They were on the leading edge of what was becoming the modern methods of algebra and calculus.

Alexander argues that:

At the opposite ends of the Continent, the struggle yielded opposite outcomes: in Italy the Jesuits prevailed over the Galileans, whereas in England, Wallis prevailed over Hobbes.”

If any land was likely to pioneer a challenging new mathematics, it was Italy, whose art and science had inspired Europe since the Renaissance. England, meanwhile, would likely have remained what it had always been, an intellectual backwater feeding off the scraps of its more cultured continental neighbors.”

But things turned out differently.” Alexander now sums up all the developments in math and science inspired by the mathematical leadership of Wallis, which gave England the upper hand in becoming such an industrial leader in the 19th century.

I really enjoyed reading this book. I pored over the history intertwined with the mathematics and the science that Alexander presents. It gave me a much greater appreciation for the math I know, and a desire to go back and review some of the math that I probably forgot immediately after I learned the algorithms in school. Yes, math can be taught as a series of algorithms, but it is understood better when learned through context. This book could appeal to adults and high school students who desire better appreciation of the history of how our math was developed.

By the way, while I was reading this book news came out that perhaps the Babylonians had invented astronomical geometry 1,400 years before Europeans. While this may be an interesting finding, their way of calculating planetary movement had no influence on the development of how we do math now, or on the more recent history of the world as presented by Amir Alexander.

And one more thing. All those little math puzzles that pop up on our social media streams that are to show how smart you are, how dumb you are, or how ridiculous the new math curriculum is; well, it turns out that for many of them, “You can interpret it in many ways; one way is no more correct than another. There are an infinite amount of possible answers.”

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Infinitesimal: how a dangerous mathematical theory shaped the modern world – a review

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