April 6, 2012
The good professor shows how probabilities become counter-intuitive as soon as a modicum of complexity is introduced. We all know that the chance of guessing heads on a coin-flip is one-in-two, and it’s fairly straightforward to show the chance of scooping the National Lottery jackpot is just under one in 14m.
September 17, 2009
Spent far too much money in bookshops during a recent visit to Hay on Wye – but heroically avoided splashing out on a beautiful set of Pope’s translation of the Iliad (although at £450, temptation wasn’t that hard to resist).
But among the bargains I did snap up were Mario Livio’s The Equation that Couldn’t Be Solved, an account of the profound societal changes wrought by a special class of equation, called the quintic (containing fifth powers, as opposed to the quadratic, which contains squares). Read the rest of this entry »
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 »