Scales fall short of grand symphonies in maths

April 14, 2006

Pique children’s interest in maths with elegant epics, enigmatic mysteries and cold hard cash, says Marcus du Sautoy

World pi Day was marked at 1:59 on March 14 — 3.14159 being the beginning of the decimal expansion of pi. Although I am appreciative of any publicity mathematics can get, I found that most people were interested in how many decimal places I knew of this important number. They were disappointed that five was my limit. To me, that response revealed the deep misconception people have of what mathematics is really about.

Most people’s idea of what I do as a research mathematician is long division to lots of decimal places. But fundamentally, mathematics isn’t about numbers — it’s about finding structure and logic and connections that help us negotiate the complex world we live in.

The belief that mathematics is no more than long division is fuelled by the way most pupils are taught the subject at school. Imagine a student learning a musical instrument by playing only scales and arpeggios and never even hearing a symphony. No one would judge them for giving up. Yet all too often in pupils’ mathematical education, this is all they are exposed to.

Pupils I talk to are surprised to learn that there are complex mathematical equations controlling the evolution of their PlayStation games or that the sine waves that they learn about in trigonometry are the building blocks used by their MP3 players to recreate the sound of the Arctic Monkeys in their headphones.

Practical applications are a powerful way to awaken people to the importance of the subject. But beauty and elegance can also attract many to the subject. It is the great stories of mathematics, many of them unfinished, that I believe have the potential to capture pupils’ imaginations when they doubt the value of mathematics. Therefore, it is the responsibility of those who create these stories, the research mathematicians, to bring the subject alive. There is no escaping the hard graft of doing your arithmetic scales and arpeggios. But if these are set in the context of the big mathematical symphonies they help write, students may feel more inclined to apply themselves.

The story of the primes is one of the sagas that I have found can pull young people on to the mathematical bandwagon. They are the building blocks of all numbers. And as you play with them, they very soon draw you into one of our biggest mathematical mystery stories.

The great challenge is to understand how nature chose these enigmatic numbers. The search for a pattern behind the primes goes to the heart of what it means for me to be a mathematician. Yet intriguingly, our subject seems to be built out of numbers with no patterns to them at all.

The biggest prime we know has more than 9 million digits — a number that would take more than a month and a half to read aloud. But bigger primes will always be discovered — there is a prize of $100,000 (£57,000) waiting for the first person to break the 10 million digit mark. The records to date are not held by boffins with big computers but amateurs with desktops.

Money is a great incentive for getting kids’ eyes to light up. And one can use it to introduce the deeper meaning behind the headline. Once they have won $100,000, then they can move on to the million-dollar prize of finding the underlying structure that makes these numbers tick, which involves solving the Riemann hypothesis.

The National Centre for Excellence in Teaching Mathematics, to be launched in May, has the potential to communicate some of the big stories of mathematics to teachers who can, in turn, spread the word in our schools and colleges. But it is important for those at universities to play their part in keeping alive the narrative tradition. In our conferences and journals, we are all engaged in telling the tales of our mathematical adventures. If we want more young explorers to join us on the hard treks across the mathematical mountains, then research mathematicians have a part to play in telling those outside the ivory towers our best stories.

Scientific research consists of two important components: discovery and communication. Without one, the other will die. Oswald Veblen, in his opening address to the International Congress of Mathematicians in 1952, expressed well this need to perform our theorems: "Mathematics is terribly individual. Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind. Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge. Otherwise they can hardly be said to exist."

Marcus du Sautoy is professor of mathematics at Oxford University and author of The Music of the Primes , published by Harper Perennial, £8.99. This article is based on his inaugural Drapers lecture on teaching and learning at Queen Mary, University of London.

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