- Pluses and Minuses: How Maths Solves Our Problems, by Stefan Buijsman. Text. $16.99.
Many people would dismiss any suggestion that they use mathematics in their daily lives. They would be happy to tell you of the pranks they pulled on their poor maths teachers and assure you that half a lifetime later, they have never had a need for quadratic equations. Yet we are told by economists and politicians, educationalists and journalists that mathematics is one of the most important subjects taught in schools. The focus of this book is to justify that opinion of mathematics by explaining some of the ways it is used.
The author was awarded his PhD at the age of 20 and is now doing post-doctoral research on the philosophy of mathematics. He deals briefly with the question of whether humans invented mathematics or whether it is all around us in the physical world, waiting to be discovered. He also looks at societies which either have no concept of number - one tribe on the Amazon do not even have words for simple concepts like two, three or four. From there he looks at the development of ideas about numbers and how to represent them, progressing from Mesopotamia to Egypt, Greece and China. He then touches on the greats like Archimedes, Newton, Leibniz and Euler.
Buijsman concentrates on three areas in particular: calculus, probability and statistics, and the relatively new discipline of graph theory. While skimming over the idea of a limit, he explains that calculus is concerned with measures of change, and gives a pleasant digression into a kind of 17th century World Cup between Germany represented by Leibniz and England whose hero was Isaac Newton, ending by modern agreement in a draw. His treatment of statistics concentrates on its use in predicting future events, something that moves smoothly into graph theory which takes up about one-third of the book.
When doctors began to use graph theory to predict the usefulness of certain cancer treatments, their success rate went from 60 per cent to 72 per cent. This is the same mathematics that Google and Netflix and Facebook use in deciding what sites come up when we do a search or load a url. At a time when this country is in the process of spending a large slice of its defence budget on combating cyber interference, it is a pity that his explanation of how graph theory works is necessarily skimpy and not very clear.
"Mathematics is about much more than formulas, which is why there are so few of them in this book," the author says in his introduction. That may please some readers, but it results in a book which while it tells at some length about the usefulness of mathematics, gives little place or room to treat of the elegance and beauty of the subject.