How Not To Be Wrong: The Hidden Maths of Everyday Life - Jordan Ellenberg
Just the appearance of an equation can induce fear and loathing in the most confident person, as memories of failing to fathom algebra come flooding back. But for many people, maths isn’t merely difficult; it also seems pretty pointless. Or at least most of the stuff we learn at school does.
Jordan Ellenberg feels our pain – which is surprising given he’s a former maths prodigy who could do algebra when barely out of kindergarten and is now a maths professor. He believes that the problem with school maths is that there’s way too much boring stick, and not enough tempting carrot. And in this breezily written but deceptively deep book, Ellenberg provides enough carrots to enthuse even the most mathematically mulish. His strategy is to use examples drawn from the subtitle of his book: the Hidden Maths Of Everyday Life.
His principal sources are arguably the two areas of maths richest in applications to real-life problems: probability and statistics. As the son of two professional statisticians, Ellenberg knows those two words conjure up images of boring problems about balls in urns and lists of coal production. Fortunately, he ditches such tedium and instead shows how they underpin everything from methods for spotting winning bets to extracting reliable insights from dodgy data. Along the way, he shows how some basic knowledge of the underlying maths can help spot howlers that even professional scientists make.
Some of his most telling examples focus on the concept of statistical significance. Not a day goes by without some researchers claiming to have found a ‘statistically significant’ effect from some new therapy, health risk or whatever. Which sounds pretty compelling… until you find out what statistical significance really means. As Ellenberg points out, it’s far less impressive than even many researchers believe – especially if they’ve rummaged through their findings desperate to find something ‘significant’ to report. Ellenberg cites research suggesting that for every reliable claim of a link between genes and schizophrenia, there are 500 bogus ones.
Inevitably the book contains a bit of maths, but nothing beyond simple school level. On the other hand, it comes jam-packed with great examples, entertaining anecdotes and uncommon wisdom.
Robert Matthews is Visiting Reader in Science at Aston University, Birmingham.