Pluses and Minuses

May 4, 2020
Buijsman, a philosophy of mathematics wunderkind who earned his doctorate at age 20, delivers an illuminating history of mathematics that also touches on fascinating philosophical questions surrounding math. One of the central debates, he explains, is between those who contend numbers are a preexisting natural phenomenon waiting to be discovered and those who view them as a human-made set of principles with no intrinsic basis in reality. Buijusman doesn’t subscribe to either position, holding that the question of why math works is still unresolved. He does have a major thesis about math, which is that its primary value lies in its ability to simplify reality, as he demonstrates with lucid and accessible descriptions of mathematical breakthroughs and their applications throughout history. These include the simultaneous invention of calculus by rival 17th-century mathematicians Newton and Leibniz; graph theory, which provides a fascinating look at the driving force behind web searches; and probability and statistics, which enable the art of polling. Buijsman’s enjoyable survey makes a convincing argument that understanding these basics will provide the tools necessary to better evaluate the modern world’s information onslaught. Agent: Michael Carlisle, InkWell Management.

June 1, 2020
Sharp answers to "the question about what [mathematics] is good for." The answers come from a young Dutch mathematician and philosopher of mathematics. While Buijsman notes that you may never use the formulas you memorized in high school, he also emphasizes that math is everywhere in modern society. In his first book, he seeks to give readers a solid grasp of some of the math areas involved, whether it's the inner workings of a car's cruise control, the rules governing opinion polls, or how Google Maps designs efficient routes. The author acknowledges that there are still small hunter-gatherer groups that have no number systems or measuring tools but who can still build boats, bridges, and houses and barter goods. The importance of math surged with the growth of populations in cities and the expansion of agriculture and trade, which required the ability to reckon quantities of goods, levy taxes, and invent coinage. The author's focus on the practical utility of math dictates three chapters on calculus, probability theory, and graph theory, but he also ponders a philosophically intriguing question: Why do findings from the most abstract areas of mathematics have remarkable relevance to aspects of the real world around us? Buijsman spares readers from too many detailed notations and equations, concentrating on the basic concepts, major innovators, and the games or puzzles that inspired the scholars. In graph theory, that involved whether or not one could traverse all seven bridges of the city of K�nigsberg, crossing each bridge only once. In 1736, Swiss mathematician and physicist Leonhard Euler showed that this was impossible. Today, graph theory has broad applications, not only in mapping software, but also in artificial intelligence, neural networks, cancer therapy, and the countless algorithms that drive internet searches or allow Netflix to make movie recommendations. A welcome addition to the math-for-lay readers genre, with the hope for more to come.

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