“Just how far would you like to go?” the enigmatic Frank asks in the sleeve notes to the Dylan album John Wesley Harding. “Not too far,” comes the reply. “Just far enough so we’s can say that we’ve been there.”

Reading maths at the higher levels is akin to poetry – dense, abstract, often impenetrable, albeit with its own rewards. But there are plenty of books out there that offer a digestible taste of the good stuff without talking down to the reader. The Dover series of maths and science books are a case in point, offering insights into a complex and sometimes daunting world but written in an engaging way – not taking you too far, but just far enough.

Read the rest of this entry »

Alan does maths

April 7, 2009

Fascinating TV doc last week, whereby comedian Alan Davies was inducted into the mysteries of maths by Oxford professor Marcus du Sautoy. After recalling the dusty dry way in which he was taught maths at school, Alan started by imagining a four-dimensional cube (hypercube – You Tube video) before being introduced to Euclid’s proof of the infinity of primes.

It’s a beautifully elegant proof, along the following lines: imagine there is a finite number of primes. Then there must be the biggest prime, called k (say), which means we can produce a list of the primes up to and including k (2, 3, 5, 7, … k). Let’s multiply all these primes together and add 1 to the result (2x3x5x7x … k+1). Now this new number, which we’ll call p, is not divisible by any of the primes we’ve multiplied together to create it. Why not? Because whichever prime we divide p by, there will always be a remainder of 1. There has to be, since that is how we created the number p. That means p is either prime itself (and hence is a prime not on our original list), or is divisible by a prime which is not on our original list. Either way, the list we drew up was incomplete – as must be ANY such finite list of the primes. Hence there must be an infinite number of primes, because every time we try to list them all, we can always do the above trick to show we’ve missed one out. Read the rest of this entry »

Making journalists count

March 26, 2009

Journalists have a long and dishonourable tradition of playing fast and loose with figures, stats and numerical analysis. In part, this is because many journalism students have a phobia about maths which stays with them throughout their career – the only exception being when it’s time to work out their expenses, when all journalists suddenly transform into Einsteins. (Yes, I know Einstein was primarily a physicist, although the popular conception that he was poor at maths is misguided. The point is that there aren’t many mathematicians who are universally known – how many journalists have even heard of Gauss,  Riemann, Fermat or Cantor?).

But it doesn’t have to be this way. By introducing numeracy skills into the journalism classroom, reporters can acquire the skills they need to critically examine figures in the same way they routinely question other sources of information. We’re not talking about teaching advanced maths here, just the commonsense ability to put numbers into context and test their validity.

Most commonly, this involves being able to work out percentages and different types of average, which only needs the most basic maths skills.

For now, I’ll just recommend Darrell Huff’s classic How to Lie with Statistics [link opens new window], which is a great read despite the fact that many of the examples are from the 1950s, and John Allen Paulos’s A Mathematician Reads the Newspaper [new window].