“I’ll overlook this now,” he said, “but I must warn you that if you persist in these fabrications, if you repeat them to anyone outside this room, I will have to terminate your employment here, immediately.” He paused. “As for myself, I won’t speak of this to anyone. At all.”
“I see.”
“Do you understand?”
“I understand everything.”
“Then you’re a shrewd person, Hope. So please don’t let this foolishness continue.” He stopped at the door. “We won’t talk about this again,” he said, and left.
I worked hard that night. By the time I went to bed I had most of my article drafted out. I was pleased with my title too: Infanticide and Cannibalism Amongst the Wild Chimpanzees of the Grosso Arvore Project. The peaceful primate’s days were over.
FERMAT’S LAST THEOREM
Peano Curve. The Weierstrass Function. The Cauchy Condition. L’Hopital’s Rule. A Möbius Strip. Goldbach’s Conjecture. Pascal’s Triangle. Poincaré Map. The Fourier Series. Heisenberg’s Uncertainty Principle. A Cantor Dust. A Bolzano Paradox. A Julia Set. Riemann’s Hypothesis. And my favorite: Fermat’s Last Theorem.
What are these things?…Why am I so curious about them?…What is it about these names, these oddly poetic appellations, that is so beguiling and fascinating? I want to know about them, understand them, find out what they do, what they imply.
And this, I suppose, is every mathematician’s secret dream. To have a function, a number, an axiom, a hypothesis named after you…. It must be like being an explorer on a virgin continent, naming mountains, rivers, lakes and islands. Or a doctor: to have a disease, a condition, a syndrome called after you. There you are on civilization’s intellectual map. Forever.
Fermat’s Last Theorem.
Now, bear with me. I love the ring of this one, it sounds so good. Let’s see what we can make of it. (I found it hard too: formulae have a narcoleptic effect on my brain, but I think I’ve got it right.) Take this simple formula: x2 + y2 = z2. Make the letters numbers. Say: 32 + 42 = 52. All further numbers proportional to these will fit the formula. For example: 92 + 122 = 152. Or, taking the proportionality downward: 122 + 52 = 132. Intriguing, no? Another example of the curious magic, the severe grace, of numbers.
Along comes Pierre Fermat in the seventeenth century, a civil servant whose bobby was mathematics. He wondered if this same proportionality would apply if you raised the power above two. What if you cubed the numbers? Would x3 + y3 = z3? The answer was no. It never worked, no matter how high be raised the power. So be produced his notorious Last Theorem. THERE ARE NO POSITIVE WHOLE NUMBERS, WHATEVER, WHERE ‘N’ EXCEEDS TWO, SUCH THAT Xn + Yn = Zn.
For four hundred years no one has been able to prove or disprove Fermat’s Last Theorem, and they have checked every power of ‘n’ from 3 to 125,000. Intriguingly, Fermat himself said at the end of his life that he had a proof, though it was never found when his papers were searched after his death. What I like about Fermat’s Last Theorem is that it remains one of those conjectures about the world which are almost indubitably true, that no one would ever deny, but which, in the final analysis, we can’t actually, physically prove.
Hope trudged across the dewy field toward the hedgerow. It was eight in the morning and a gray mist off the sea lay over the downlands that stretched along the coast in this part of Dorset. She checked her map to make sure she was in the right place and veered over to a corner of the field. Reaching the hedge, she hooked the end of her tape measure over a protruding hawthorn twig and unreeled the tape for thirty meters. The hedge was thick, perhaps six feet across at its base, and was growing on a small bank. At first glance it looked like an ancient hedgerow to her, in which case, she reflected, it should conform to her dating theory. She walked slowly along its length. Predominantly hawthorn, but there was a fair amount of elder and blackthorn mixed in there too. On closer inspection she found some field maple, dogwood and, just within the thirty meter sample area, a small patch of holly. She noted this all down on the map and in her record book. Six species in thirty meters: according to the theory this hedge had been here for approximately six hundred years. She took a small sample of the soil for the geologist and then made another quick search for brambles, but there were none in this section. She sat down on a stile and wrote it all up.
The survey of the Knap estate was well advanced. Much of the archaeological work was already completed: the ancient barrows, the deer enclosure, the Celtic field systems, had all been thoroughly examined, mapped and described. The ecologist who had done the initial work on the hedgerows and woodland had resigned for some reason—hence the job vacancy—but Hope had found so many inaccuracies and inconsistencies in his estimates that she had told Munro she would have to start again from scratch. It meant that she had much more work to do than she had been contracted for, but it kept her busy, and for that she was grateful.
Her own approach to the problem of dating was based on a simple formula she had devised, namely, one shrub species in a hedge equaled a hundred years. She made many trial counts on hedgerows whose age was known (the earliest detailed map of the estate was dated 1565) and her method had proved to be surprisingly accurate, with an insignificant margin of error. So she had set about dating all the unmapped hedgerows with some confidence, and already she had discovered that there were many more medieval hedgerows than had hitherto been imagined. Feudal and Saxon field systems were revealed where previously eighteenth-century enclosure fields had been believed to exist. The landscape history of the estate was far more complex and thorough than had been envisaged. As a result of her efforts, one hundred and forty-seven new hedgerows had been classified as level one. In conservational parlance, they were of ancient and abiding historical interest and to be preserved at all costs.
To her vague surprise, Hope found she was thoroughly caught up in her work, in a way she would not have imagined possible. Sure, it was routine and methodical, but there was a profound satisfaction in that routine and method when it allowed her to draw clear and irrefutable conclusions.
Another bonus was that she was out of doors all the daylight hours, walking the downlands and the fields in all weathers. In the weeks she had been there, she had lost weight—almost fourteen pounds—and she felt markedly fitter. Now she had almost finished classifying the estate’s hedgerows and Munro was encouraging her to move swiftly on to the many woods and coppices.
She was keen to do so. She had forgotten this facet of her personality: the dogged application of, an exultation in, her expertise. This was what she had trained herself to do; this was why she was educated. Problems were presented to her and she found a way to solve them. It was a feature of her character that, when it was not required or employed, she somehow forgot. It did not feature in her private conception of herself. The fanciful, wishful version of Hope Clearwater tended to downplay the professional scientist in her.
Now she was working again she enjoyed and savored the unrelenting rigor of her approach to her task, the unswerving persistence of her routine and the evident success of her experimentation. In her work she was achieving something irrefutably concrete. However recondite, however parochial, she was adding a few grains of sand to that vast hill that was the sum of human knowledge. She was discovering aspects of the English landscape that were unknown or hidden; and what pleased her most was that she could prove she was right. As her steady documentation of the estate increased and as the maps were redrawn and dates corrected she developed a quiet but strong pride in her abilities. Her latent self-confidence—never far below the surface—re-emerged into the clear light of day again.
Munro was pleased, and said so. But he had other priorities, largely directed by the need to complete the project on schedule. Hope was stubbornly resisting his attempts to hurry her along, as she had developed another dating theory that was even more precise and she was impatient to try it. Munro was not so enthusiastic, as it might mean more delay. Her theory was that the number of bramble subspecies in a hedge
would follow the same pattern as shrub types, and she had proved the efficacy of the method to Munro very neatly one day, in an attempt to make him vote her more funds. (With a few assistants she could cover the entire estate in two months, she reckoned.) Munro was impressed but as yet undecided. He would see if there was any chance of hiring an assistant or two, he said, but he reminded her that the estate had fifty-three named woods and coppices and all but twelve of them were dateless.
She left the field and set off down a farm track toward Coombe Herring, a small village on the estate. There was a long ditch and bank there that ran up to the edge of the village that the project’s archaeologist had classified as part of the enclosure of an early seventeenth-century deer park. There was a problem in dating the hedge on the bank as it was almost entirely hawthorn. Out of curiosity Hope had done a bramble test on it and it had turned up a count of ten subspecies. She felt sure, as a result of this, that the ditch and bank belonged to a construction that was significantly older than the deer park—an old parish or manor boundary perhaps, or even a barrow mound. When she put this supposition to the archaeologist—a lean-jawed, pale-faced man called Winfrith—he had almost lost his temper with her. He reminded her that he had spent months plotting and reconstructing the configuration of the deer park, and he informed her that he had no intention of redrawing his maps because of a “bunch of brambles.” She planned to take several more examples from thirty-meter sections and confound him with the evidence.
She walked through the small village and up a sunken drove road that rounded a hill and eventually led on to East Knap, the village where she was living. It was a cool day, even for September, with a fresh east wind and the sky low and dense with packed clouds. She climbed up the bank off the road, went over a stile and cut through a small wood of coppiced hazel to the disputed bank and ditch.
She measured out her first thirty-meter section and with a pair of secateurs began to collect samples of the profusion of brambles that grew amongst the hawthorn. She worked steadily and carefully, placing the samples in plastic bags and labeling them. The wind stirred her hair, and her nostrils were full of the scent of earth and leaf mold disturbed by her feet and the dusty green smell of the hedge.
She picked a bramble berry and ate it, her mouth full of its winey, sour taste. She could hear birds singing and the restless thrash of the hedgerow elms above her being hustled and bothered by the wind. Through the gaps in the hawthorn she could make out the gentle rise of the coastal downs and sense, rather than see, the chill of the Channel beyond. Behind her back the landscape of Dorset unfolded. Its gentle hills, its fields and woods, the shallow valleys with their farmsteads and villages. Her mind was calm and full of her task and all her senses were stimulated as she crouched at the foot of a hawthorn hedge in a landscape she had come to know as intimately as any in her life. No wonder she loved her work, she thought, no wonder—she added guiltily—she hardly ever thought of John.
The project office was in the stable block of Knap House, a long attic room above a row of loose boxes. Every Friday there was a meeting to report on the individual progress of each project worker. Munro chaired it, invariably diplomatic and mild. Hope arrived a little late to find Munro and Winfrith waiting for her. She gave Munro, a soil geologist, the soil samples she had taken that day and sat down at the round table. Winfrith had motored in for the meeting from Exeter where he spent most of his time these days working with the project’s historian, a woman called Mrs. Bruton-Cross, whom Hope had met infrequently. These were her three colleagues, but she dealt mainly with Munro, who supervised and collated all their respective efforts. To all intents and purposes she worked on her own from Monday to Friday. Munro would telephone her in the evenings if he had anything of note to import.
The meeting lasted its usual half hour and Winfrith left at once for Exeter. Munro made her another cup of coffee.
“Here Saturday, Hope?” he asked her. “Marjorie and I were wondering if you’d like to—”
“Sorry. Going up to London, I’m afraid,” she said quickly, trying to keep the relief out of her voice. She had had one dinner with Graham and Marjorie Munro in their little cottage in West Lulworth and that had been sufficient. It had proved to be an eternity of strained conversation and wineless food. The one small sherry she had been offered—and had consumed—before dinner had turned out to be the solitary alcoholic component of the evening’s entertainment. As she ate her way through Marjorie’s special casserole (recipe happily provided if requested), Hope had been seized by such a craving for booze that she made an excuse (flu coming on) and had left before coffee, making straight for the nearest pub before it shut.
“Shame,” Munro said, genuinely. “Marjorie was looking forward to meeting John.”
“Oh, he’ll be down again,” Hope said vaguely. “I’ll give you plenty of warning.”
“Say hello to the Big Smoke for me,” Munro said.
“What?”
“Say hello to the—”
“Sure. Certainly.”
She drove back to East Knap and packed her bag and had a bath before leaving for the station at Exeter.
She sat in the train drinking beer and looking out at the dusky landscape. She missed Knap more each time she left it, she realized. Had she stayed she would have worked on all weekend. She didn’t need a break; these trips to London were proving to be something of a chore. And she found she was growing to dislike the city with its noise and dirt. She poured more beer into her plastic cup. But something was wrong, she said to herself: surely she should be happier at the thought of being with John again?
On Saturday morning John sat in his pajamas staring out of the kitchen window at the towers of the Natural History Museum that rose above the chimneys and gables of this part of Kensington. He was making little clicking noises with his tongue and tapping his chin rhythmically with a forefinger.
Hope watched him over the top of her newspaper. He had kept this up for almost ten minutes now—just staring out of the window and making clicking noises.
“D’you fancy a film this afternoon?” she asked, refusing to be irritated.
“Can’t, I’m afraid. I’m going into college. I’ve got some computer time booked.”
Hope forced herself to speak reasonably. “How long will you be?”
“Should be back…” He turned and looked at her, then cocked his head, figuring. “Early evening. All being well.”
“OK.” She stood up. She put on her raincoat and picked up her bag. “I’m going out.”
“Fine. See you later.” He looked back at the towers of the Natural History Museum.
Sunday was better. They went for lunch with some friends the college, Bogdan and Jenny Lewkovitch. He was a plump, fair-haired Pole; Jenny was English, petite and self-effacing. They lived in Putney and had two young children. Over lunch, John was lively and amusingly malicious about their colleagues.
Bogdan was a physicist. John had said on the way to lunch that, despite this fact, he respected his mind. “Which,” he added, “is pretty unusual for me, because normally I don’t have much time for physicists.”
“Why?” Hope said, wondering vaguely where he ranked ecologists who dated hedgerows in Dorset.
“Why? Because they refuse to admit—most of them—that what they do is basically all about mathematics. They think they’re doing something grand with their expensive machines, something in the world. But it’s all mathematics, really.”
They were driving down Fulham Palace Road toward Putney Bridge. Hope looked out of the window at the trees in Bishop’s Park. The sun was shining and the horse chestnuts were just beginning to turn yellow. She thought of the work that lay ahead of her in the woods and coppices of Knap and longed to be back there. For the first time she felt a little sorry for John and his clean, airless world of perfect abstractions.
“Don’t you think that’s a little childish?” she said.
“What?”
“My discipline’s bett
er than yours. Na-na-nana-na.”
John smiled. “Ask Bogdan. If he’s honest he’ll tell you I’m right.”
That evening they made love.
“You’re a difficult bugger,” she said, kissing his long nose.
“I know,” he said. “Just as well you’re not, or we’d be in deep shit.”
“Yeah.”
He slipped his hand across her belly, fitted his palm briefly to her hipbone, then ran it up over her ribs to cup a breast.
“Bones, bones, sharp angles,” he said. He flipped back the sheet. “Hey. Your tits are getting smaller.”
“I’m not fat any more.”
“All that tramping around the turnip fields of Darzet,” he said, in a stage West Country burr.
“You should be pleased.”
He lay back smiling to himself.
“How’s the work going?” he asked.
“My God, I don’t believe it. You really want to know?”
“Sure.”
“Let me tell you about this fascinating technique I’ve developed for dating hedgerows.”
“Oh yes?”
“It’s all to do with counting the number of subspecies of brambles. You see—”
“Good night.”
As she unlocked the door to her cottage in East Knap on Monday morning, Hope felt an agreeable shift in her gut, an excited tightening of her sphincter. She realized she was glad to be back. She felt somewhat guilty about this because, all things considered, the weekend had been quite a success, after the difficult Saturday. But it was hard to contradict or suppress the palpable sensations she was feeling.
She busied herself about, first unpacking and then making herself an early lunch of a corned beef sandwich. As she ate, she remembered that John didn’t like corned beef. He couldn’t stand the smell of it, he said. He didn’t like her to eat it either—he claimed he could smell it on her breath hours later…