Mathematician Marcus du Sautoy has an imaginative formula to bring his subject alive in the classroom

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«If maths is boring, what is the answer?»

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Ученица 10 «А» класса Балковская

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28 апреля 2016 года

If maths is boring, what is the answer?

Mathematician Marcus du Sautoy has an imaginative formula to bring his subject alive in the classroom.

Dry subject: Many children are bored in the classroom.

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By Marcus du Sautoy

10:28PM BST 04 Oct 2008

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If a circle is one unit in diameter, what is its circumference? The answer, as every schoolchild ought to know, is π (pi), that enigmatic and beautifully irregular number. The value of π is 3.14 – or thereabouts.

The intriguing thing is that it has no finite decimal expression, cannot be written as a fraction, and has captivated mathematicians for more than three millennia.

There's something about π that grabs the imagination. It crops up across the sciences, from geometry and mechanics to statistics. If its superstar status was in doubt, there is a movie named after it.

The ancient Egyptians came up with one of the first approximations of it – 256 divided by 81 – derived from an early board game called mancala. For 4,000 years, the calculation of π has been a running theme through the history of maths.

Archimedes arrived at a well-known rough estimate – 22 divided by 7 – by drawing up his calculations from a 96-sided shape rather than a circle; his efforts were halted when he was killed by a Roman soldier.

Isaac Newton is said to have tried calculating it just to idle away the hours and made it as far as 15 decimal places. Today, a computer can easily calculate it to billions of digits, which must have helped Kate Bush write her song about π, in which she recites it to the 137th decimal place.

Who said maths was boring? And yet, many children are bored in the classroom. A report published by Ofsted last month claimed that pupils are simply turned off by the parrot learning of formulas to solve quadratic equations and the mindless application of the rules of trigonometry.

An obsession with teaching children solely to jump the hurdles of the testing regime is depriving a generation of a deeper understanding of the subject. Mathematics is taught as if it was handed down in some vast textbook with little context of where it came from.

Everyone responds to good stories and mathematics is full of them, so why deprive students of the wonderful dramatis personae that have created our subject? As a professional mathematician, I have found that unearthing the stories behind my subject has been a revelation.

At university I fell in love with a precise formula for π which involves alternatively adding and subtracting the odd fractions. I was taught in lectures that it was called the Leibniz formula, after the great 18th-century German mathematician Gottfried Leibniz, who discovered it using the powerful new tool of calculus for which he and Isaac Newton became so famous.

It therefore came as a huge shock to me to discover recently that a school of Indian mathematicians in Kerala in south India arrived at this formula several centuries earlier. It should, in fact, be called the Madhava formula, in honour of the Hindu scholar who first hit upon it.

π was not the only great mathematical discovery made in India. Negative numbers and zero – concepts that in Europe, as late as the 14th century, were viewed with huge suspicion – were being conjured with on the subcontinent as early as the seventh century.

The authorities in Florence temporarily "banned" the zero in 1299. Seeing how the mathematicians of the past wrestled with the same problems that contemporary students find difficult might help them realise that the discipline did not appear from nowhere. There is something empowering in knowing that mathematicians used to have trouble with the concept of zero and negative numbers.

Some eminent mathematicians made their breakthroughs while at school. The revolutionary French scholar Evariste Galois discovered a new language for symmetry as a schoolboy before he was killed in a duel at the age of 20 over love and politics. Some even went mad doing their maths. Georg Cantor spent many years in a mental asylum after contemplating the infinite.

Stories like these can bring the subject alive for those who find the excitement of pure mathematics hard to tap into. It's not as if mathematics and history are so far removed from each other; maths has an inbuilt historical narrative. Each generation builds on the foundations of results proved by those who had gone before.

Unlike in the other sciences, mathematical theories are not overturned; the discoveries of the ancient Egyptians are as true as they ever were. Students who learn to calculate the area of a circle using π, or the volume of a pyramid using calculus, are treading in the footsteps of 5,000 years of mathematicians.

The Egyptians needed such formulas to calculate how to tax pieces of land carved out by the winding Nile, or to know how many bricks to use in the pyramids of Giza. Today, when footballers position themselves in the box to tee up an incoming free kick, they are solving quadratic equations, a formula which, according to workings found on Babylonian clay tablets, was being applied as early as 1800BC.

Until recently, I didn't know a lot about the history of my subject. I believed that what matters most is the mathematics. If you understand the theorems and the proofs, is it important who created them or in what circumstances? The way we are taught in school and at university reinforces this ahistorical message.

Sure, it is possible to teach mathematics as pure reason that transcends cultural and national boundaries; that mathematics is a universal language is one of its attractions. But it is important to recognise that it is created by people. The stories of why they battled to solve quadratic equations and invent calculus provide a powerful motivation for one's own journey across the mathematical landscape.

I am certainly not advocating watering down the rigorous side of the subject. When you are learning a musical instrument you'll get nowhere without the graft of doing your scales and arpeggios. But supplement this with some of the tales of where mathematics has come from and we might be on to a more engaging approach to learning maths.

Marcus du Sautoy is Professor of Mathematics at Wadham College, Oxford.