Symmetry is all around us. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry's elusive qualities.

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Symmetry
A Journey into the Patterns of Nature

Chapter One

August: Endings and Beginnings

The universe is built on a plan the profound symmetry of which is somehow present in the inner structure of our intellect.
Paul Valéry

Midday, 26 August, the Sinai Desert

It's my 40th birthday. It's 40 degrees. I'm covered in factor 40 sun cream, hiding in the shade of a reed shack on one side of the Red Sea. Saudi Arabia shimmers across the blue water. Out to sea, waves break where the coral cliff descends to the sea floor. The mountains of Sinai tower behind me.

I'm not usually terribly bothered by birthdays, but for a mathematician 40 is significant—not because of arcane and fantastical numerology, but because there is a generally held belief that by 40 you have done your best work. Mathematics, it is said, is a young man's game. Now that I have spent 40 years roaming the mathematical gardens, is Sinai an ominous place to find myself, in a barren desert where an exiled nation wandered for 40 years? The Fields Medal, which is mathematics' highest accolade, is awarded only to mathematicians under the age of 40. They are distributed every four years. This time next year, the latest batch will be announced in Madrid, but I am now too old to aspire to be on the list.

As a child, I hadn't wanted to be a mathematician at all. I'd decided at an early age that I was going to study languages at university. This, I realized, was the secret to fulfilling my ultimate dream: to become a spy. My mum had been in the Foreign Office before she got married.

The Diplomatic Corps in the 1960s didn't believe that motherhood was compatible with being a diplomat, so she left the Service. But according to her, they'd let her keep the little black gun that every member of the Foreign Office was required to carry. 'You never know when you might be recalled for some secret assignment overseas,' she said, enigmatically. The gun, she claimed, was hidden somewhere in our house.

I searched high and low for the weapon, but they'd obviously been very thorough when they taught my mum the art of concealment. The only way to get my own gun was to join the Foreign Office myself and become a spy. And if I was going to look useful, I'd better be able to speak Russian.

At school I signed up for every language possible: French, German and Latin. The BBC started running a Russian course on television. My French teacher, Mr Brown, tried to help me with it. But I could never get my mouth around saying 'hello'—zdravstvuyte—and even after eight weeks of following the course I still couldn't pronounce it. I began to despair. I was also becoming increasingly frustrated by the fact that there was no logic behind why certain foreign verbs behaved the way they did, and why certain nouns were masculine or feminine. Latin did hold out some hope, its strict grammar appealing to my emerging desire for things which were part of some consistent, logical scheme and not just apparently random associations. Or perhaps it was because the teacher always used my name for second-declension nouns: Marcus, Marce, Marcum, . . .

One day, when I was 12, my mathematics teacher pointed at me during a class and said, 'du Sautoy, see me at the end of the lesson.' I thought I must be in trouble. I followed him outside, and when we reached the back of the maths block he took a cigar from his pocket. He explained that this is where he came to smoke at break-time. The other teachers didn't like the smoke in the common room. He lit the cigar slowly and said to me, 'I think you should find out what mathematics is really about.'

I don't quite know even now why he singled me out from all the others in the class for this revelation. I was far from being a maths prodigy, and lots of my friends seemed just as good at the subject. But something obviously made Mr Bailson think that I might have an appetite for finding out what lay beyond the arithmetic of the classroom.

He told me that I should read Martin Gardener's column in Scientific American. He gave me the names of a couple of books which he thought I might enjoy, including one called The Language of Mathematics, by Frank Land. The simple fact of a teacher taking a personal interest in me was enough to spur me on to investigate what it was that he found so intriguing about the subject.

That weekend my dad and I took a trip up to Oxford, the nearest academic city to our home. A little shopfront on The Broad bore the name Blackwell's. It didn't look terribly promising, but someone had told my dad that this was the Mecca of academic bookshops. Entering the shop you realized why. Like Doctor Who's Tardis, the shop was huge once you had entered the tiny front door. Mathematics books, we were told, were down in the Norrington Room, as the basement was known.

As we went downstairs a vast cavernous room opened up before us, stuffed full of what looked to me like every possible science book that could ever have been published. It was an Aladdin's cave of science books. We found the shelves dedicated to mathematics. While my dad searched for the books my teacher had recommended, I started pulling books off the shelves and peering inside. For some reason there seemed to be a high concentration of yellow books. But it was what I found within the yellow covers that grabbed my attention. The contents looked extraordinary. I recognized strings of Greek letters from my brief foray into learning Greek. There were storms of tiny little numbers and letters adorning x's and y's. On every page there were words in bold like Lemma and Proof.

Symmetry
A Journey into the Patterns of Nature. Copyright © by Marcus du Sautoy. Reprinted by permission of HarperCollins Publishers, Inc. All rights reserved. Available now wherever books are sold.

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