Prime

I opened my eyes and immediately the numbers began. Not a slow trickling of figures, but a vast rush:

(2 x 3 x 5 x 7 x 11x 13 x 17 + 1) = 2 x 3 x 5 x 11 x 13 x 17 + 1 '¦
7

Ã¥1 to the power of s '¦
N

3,844 = 62² '¦

My mind whirred into action whether I liked it or not.
It hadn't always been like this. It was Mr. Wilkinson's fault. He was my secondary school maths teacher and had set my class a project.
« Now, what you need to do is build a house, » he said, the smell of his lunchtime cigar still hovering around him. « I want to know how much it is going to cost, how much to paint and decorate it, and then I want you to make a model of your house, to scale if possible. » The whole class slumped into a collective silence as we were ten years old and his project sounded impossible. Impossible and therefore I had to do it. It was stronger than me. That was the first time I fell asleep and woke up with numbers running around my head. And it didn't stop until a long time after that.

I first met prime numbers not long after I finished Mr. Wilkinson's project. He made us play a game where he counted from one upwards and the class had to shout out if the number was prime or not.
1 PRIME, 2, 3 PRIME, 4, 5 PRIME, 6, 7 PRIME, 8, 9...
« Prime! » shouted skinny Johnny who sat next to me at school.
« Nine isn't prime, you idiot, » I said, « Try using three! »
Johnny blushed as red as his hair.
Mr. Wilkinson frowned at me. « If you're so clever Zeta, how about 325? »
I fell silent and the class sniggered. When I went home that night I spent three hours working out if it was or not. The primes were a mystery that absorbed me, to the exclusion of all else.
And primes are the basis of Riemann's Hypothesis. I know I should remember when I first heard about it, but I don't. All of a sudden, it was there - this hypothesis which had never been proved, and which would, if solved, be able to predict where prime numbers fall, providing an exact Prime Number Theorem, which sounded so beautiful when I first heard it. And the challenge of proving something that no-one had been able to do before gave me the same thrill as Mr. Wilkinson's project, making my spine tingle when I thought about it.
But when I started dreaming about the theorem, the magic began to wear off. I couldn't sleep without having a recurring dream of solving it. There was no ceremony or prize giving - just an image of me screaming with delight, and a blurred answer I'd written on a blackboard that spanned the length of the room. If I was saying anything intelligible, it was probably « Eureka! » but it was a dream and I never spoke clearly in it. I would wake up exhausted and obsessed.

One definition of hypothesis is « a groundless assumption ».
How can you even begin to prove a theorem that deals with an infinite amount of numbers? How do you know that the disproof of your theory doesn't lie just around the next complex curve? You check 100 out of 100 and you have a result. But if the amount you have to check is never ending, how can you ever prove it?
« Primes are like women - you think you understand them and then one just throws you a curve. »
That was how my maths teacher at graduate school explained it. It was perhaps the clearest sentence he spoke the whole time I was there.
But in my soul I knew my role in life was to prove that theorem. And, if I did, the dreams would stop. I was sure of it. The rational side of my brain rallied against the romantic side, telling me to give up and listen to my mother:
« You should be having babies by now, not worrying about some goddamned theorem that only interests 2 percent of the goddamned population! »
My mother said goddamned a lot. It was the only curse she used, but she used it a lot.

By the time I got to university I knew I wanted to be a mathematician. I couldn't imagine myself doing anything else. Not only did I want to be a mathematician, but I wanted to prove the goddamned hypothesis.
I trained myself to see numbers in everything. The number 73 bus turned into 73² over 234 to the power of 6. I made myself work out these sums even if I knew it was pointless because, perhaps naïvely, I was certain the solution to the theorem lay in luck and determination as much as sheer brainpower: My theory was that the more equations I did, the more my possibility of success increased.
As I got older the games got progressively more complicated with imaginary numbers and logarithms and three-dimensional curves. Sometimes it felt like my brain was over-heating but I couldn't stop. All I could think about was maths and proving the theorem.

My mother despaired.
« Always with those numbers! What's wrong with you? The clock is ticking!! You ought to have at least three goddamned children by now! »
« Three - one of the first prime numbers, » I thought.

Each morning I woke up unrefreshed. The numbers never stopped, even when I finally collapsed into bed. My mother worried about me, even going so far to bring my Auntie Shirley into the equation.
« Zeta, sweetheart, you have to stop this. You're taking years off your mother, » she told me one evening.
« Taking years off her? What do you mean? »
« She so wants to be a grand-mother. You'll send her to an early grave if you're not careful. »
« But what about what I want? »
Shirley looked puzzled. « What you want? Since when has that been important? Your mother brought you into this world. You have a duty to her. »
She rambled on for quite some time but I switched off a few sentences after « duty ». My mother had already given me a similar speech when I started graduate school and I knew all the right places to nod.
What I didn't know was quite how worried my mother was. So worried that she had hatched a plan with Shirley.
Several nights later, I was getting ready for bed. My mother had already given me my cocoa, telling me it would help me to sleep. I started drinking it.
Sleep has two letter Es which is the fifth letter of the alphabet. Five prime'¦
« Goodnight Zeta, » my mother said, a strange little smile on her face. I didn't notice, as I was too busy watching the floods of numbers flash past my eyes. It usually slowed down once I took my contact lenses out but tonight it made no difference. My eyes felt so heavy. After squeezing three medicated drops in each eye, I got into bed, pulling the covers up to my chin.
I had been working on a proof of the theorem and I knew I was close. If I could just find the answer, then I could go and have all the babies my mother wanted. I tried to keep my eyes open.
And then it happened.
The flash of inspiration I had been waiting for. I tried to get out of bed but I couldn't move. I grasped for the pen I usually kept on the night table but only found the eyeliner my mother had given me.
« You have to make a goddamned effort at least to look beautiful, honey. »
It'll do!
In a drugged daze I scribbled the formula as fast as I could, which wasn't very fast as I was half-asleep. I couldn't tell if it was legible as I'd already taken out my lenses, but it didn't matter. When I saw the numbers in the morning, the theorem would be clear. I wrote down what I could on the pillowcase and collapsed into a numberless sleep. I knew I had cracked it. The proof was mine.

That night I didn't dream.

* * *

The next morning, I forced my eyes open. The numbers had stopped. My head felt swollen and leaden, but I forced myself to sit up.
I turned to look at my pillow but only a black smudge covered the side. I wanted to scream, but was having trouble stopping my head thumping. I picked up the pillow and stared at it, trying to make out what I had written the night before. My proof was more than just smudged - it was illegible.
I tried to stop myself panicking. I got up and put my contact lenses in, blinking as my eyes watered. I squinted at the pillowcase, as if this would make things better.
The proof was gone.
Stunned, I went downstairs. My mother was already there.
« Sleep well, honey? » she said, winking at me.
« Finally you slept, » she said, wiping her hands on the already damp dishcloth, « even if I did have to give you a helping hand. »
A feeling of dread descended on me. « A helping hand? What do you mean? »
« I put some sleeping pills in your cocoa. »
cocoa, five letters, five prime, followed by seven'¦ my brain started automatically, but I stopped it.
« How many? » I asked, panic weaving its way through my stomach. My mother regularly took three pills when she couldn't sleep.
« Four, » she said with a smile on her face. « It did the trick, didn't it? » I was speechless. « And now look at you, you mucky devil. Writing numbers on yourself! »
She spat on the cloth and rubbed it roughly over my cheek like a blackboard, wiping it clean.
« There. That's better. How will you ever find a man with those numbers written all over your face? »

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