ENTERTAINING WITH MATHEMATICS: DESTROYING A COMMON MISCONCEPTION

By Owen Daniel, Warwick student and speaker at TEDxWarwick 2011

Why does learning mathematics have such a bad reputation? What motivation can mathematics teachers give to promote their subject? Owen Daniel, Warwick mathematics student, part-time magician and speaker at TEDxWarwick 2011, suggests that by framing mathematics as puzzle and problem solving, we may be able to destroy common misconceptions about the subject.

It is a sad truth that in our current academic climate, mathematics is still received with dismay, or even distaste, by a large proportion of the British public, but there has never been a better time to turn this around! Television programmes expounding the virtues of science are broadcast on a weekly basis, and while most of this plays to the physical sciences, mathematics is getting a share of the attention.

Perhaps the problem starts at a young age: as children, many of us were fascinated by the colour-changing fluids of chemistry, and the hair raising effects of Van de Graaff generators, but what motivation can mathematics teachers give to promote their subject? What mathematics needs is a publicity plan and a marketing program of epic proportions. Now I will say straight away that mathematicians themselves are not necessarily the people to do this; whilst the stereotype of a mathematician is rarely accurate, it remains true that mathematicians are often very bad at explaining their subject. What mathematics really needs is people who can make the subject entertaining.

At first this sounds absurd. Most of us have sat through enough uninspiring school maths lessons to firmly believe that, at best, mathematics provides a good alternative to sleeping pills and could not possibly be classed as entertainment. So how do we rid ourselves of this equation-induced narcolepsy? The first step is simple; we find something which is enjoyed by everybody and we secretly hide mathematics in it!

Now I can envisage people reading this and thinking “yes, we should get Professor Brian Cox to write Eminem’s new album”, or that Gordon Ramsey could be persuaded to swap his favoured F-word for an educational alternative: “You’ve got to make that meringue more fractal!”. Certainly that would be an excellent help, but for the time being perhaps a little optimistic. Instead, I propose that we tap into the public’s love for puzzles. Since the advent of Sudoku and its multitude of spin offs, the public’s love of puzzling has grown exponentially. At heart, mathematicians are just overly indulgent puzzle lovers who don’t get enough by doing a morning crossword! When the television program Eggheads started, people were shocked that professional quiz competitors existed: well here’s the wake up call, professional puzzle solvers do too, and they’re called mathematicians!

Consider the following. If I were to tell you that I have a child (this is purely hypothetical, something I point out now, as after a recent talk a man questioned me on how it feels to have started a family at such a young age), then what is the likelihood that it is a boy? There are several answers to this: 50-50, 50 per cent, but all of them amount to "a half". Nothing puzzling so far. But what if I now tell you this: in fact I have two children, and one of them is a boy. What is the probability that the other one is a boy too? Have a think about it.

This question interests me for several reasons - it's simple to state, the answer seems obvious, (the answer is actually not obvious), but it is simple to explain. When I ask people this question, their reactions follow the same pattern - a guffaw, followed by “well its obviously a half”, a look of irritation when I tell them its not (sometimes followed by a heated argument), and then a grin of satisfaction when they see the solution. People enjoy hearing the solution; everyday people, not just mathematicians! But perhaps the most interesting thing about this problem is that mathematicians are just as bad at the reasoning as non-mathematicians are; the puzzle tricks everyone! In fact, it describes an important area of mathematics (conditional probability). Perhaps you would like the answer now...

At heart, mathematicians are just overly indulgent puzzle lovers who don’t get enough by doing a morning crossword!

Let G stand for girl, and B stand for boy. Listing children in order of birth, there are four possible outcomes for a family with two children: BB, BG, GB, GG (boy then boy, boy then girl, etc.) Now I have already told you that I have one son, so we cannot possibly be in the final case GG. If we look at the remaining three possibilities, in only one of them do we have two boys. i.e. one case in three, or ‘a third’. Simple.

The reason this tricks people is that they cannot see how the gender of one child could directly influence that of the other. What is important to note is that I never said that it was my first child that is definitely a boy; if that was the case, then the probability would be a half. In this way we ‘condition’ on information given to us and use this to limit our set of possible options. After posing this problem, I often follow it with this alternative: I have two children, one of them is a boy, and in particular he was born on a Monday. What is the probability that the other child is also a boy? By the way, the answer is not a third.

By posing puzzles like this, we can upset peoples perception of logic and intuition, and in providing a solution we serve both entertainment and education. People see mathematics very differently when you serve it in a manner that they can appreciate, whether that is by relating it to sciences, or by posing puzzle questions. And whilst these may be baby steps towards the goal of arousing national interest in the subject, they are steps well worth taking. When we reach that goal, as a nation we will have realised that mathematics is not about number crunching and manipulating equations, but that it is in fact a logical game which has been played since the birth of civilisation. Perhaps one day we will realise that it is in fact an art form too. Until then, keep puzzling.

If you'd like to find out more about the interaction between mathematics and magic, Owen Daniel took part in a live chat on the Knowledge Centre on 1 April.

Owen Daniel is a performer, entertainer and mathematician. At a young age he developed a passion for magic, leading him to be a finalist in the Magic Circle's Junior Close Up Competition at the age of 13. At 17 he set up Magico Theatre Company and directed two plays which went on to have sell out runs at the Edinburgh Festival in 2007 and 2008. For the last 4 years he has been studying mathematics at the University of Warwick during which his theatre career has been on hold, however he has been known to come out of hiding to do occasional shows and talks. He was most recently seen talking for Warwick's IATL group, on the subject of teaching mathematics in a creative environment.