“No, you’ve got that wrong. You must have made a mistake.”
Simon spotted the error too, and blushed.
“That,” said Conway, “is the beginning of the end.”
And it was.
* * *
1 Xenophobes.
33
We have a joke in Russia: Einstein has died and gone to heaven, where he meets God. And God says to him, “You, Einstein, you have worked hard, you deserve some reward. Ask me any question about anything you like, and I will give you the answer.” So Einstein thinks a bit, then says, “What is the equation of it all?” “Ah,” says God, picking up a piece of chalk, “it is like this,” and he writes a long formula on the board. Einstein looks at this very carefully, nodding and appreciating, then suddenly frowns and points at the formula. “But you’ve made a mistake.”
“I know,” says God.
Told to the author by a Russian mathematician, in Montreal
Twenty-five years after the publication of the Atlas, Simon appears in the back of a beaten-up coach, teeth bared in excitement, in the godforsaken seaside town of Scrabster, north Scotland. He has come for a holiday. His hair is bedlam—as if someone has slapped glue on his scalp and bounced him across a cornfield. Muttonchop whiskers scrabble smokily up his jaw. His eyebrows march across his forehead, one after the other, like African caterpillars.
Summer and winter, Simon wears the same clothes: a red or blue T-shirt that has started to decay along the seams, and a dark-blue puffa jacket under which he alternately sweats and shivers.
From Scrabster, we plan to take the ferry to Norway, a six-day cruise up the west coast to Lapland and the Barents Sea, then visit Russia (Murmansk, St. Petersburg) and come back to England through Belarus and East Germany. A seventeen-day journey in a heat wave for which Simon has brought two spare pairs of socks and one T-shirt.
I’m the only person in the world he knows who will be delighted to go with him.
I’m not living in Simon’s house these days. I’ve moved to London, and we haven’t met in months. I’ve discovered it’s easier in biographies of living people to pretend your subject doesn’t exist. Booted out of the door, he settles down in comfort on the page. But this much separation has started to make my ideas about Simon bland and easy, like fiction. His unsummarizable character has become simplified in my mind, even cartoonish, hemmed in by writing style and prejudices.
As Simon gets off the bus I’m quite surprised to see that he has legs. I’m taken aback that he knows how to use them to walk upright and negotiate obstacles. We settle down at a waterfront restaurant. It comes as a considerable shock to hear him order a meal of grilled sea bass and potatoes dauphinoise in faultless English.
The northernmost port in mainland Scotland, Scrabster is exactly as it sounds. A few houses and a dank bar quickly peter out into slabs of parking concrete, groups of cyclists with windcheaters and maps in plastic spongebags, who’ve arrived six hours too early, and a long concrete buttress against the savagery of the North Sea. Seals swim about in the harbor, nagging the fishing boats when they putter back home with the day’s catch.
Across the bay is the town of Thurso: burned-out payphones and yellowing takeaways.
There is one thing only to do in Scrabster: leave.
“Oi, fucking mind where you’re going! You want to keep him on a leash, mate.”
Bergen, the next morning. All the way up the funicular to the city park, Simon had clutched his map, but as soon as the doors of the crowded carriage opened, a breeze dashed into the folds and puffed the huge sheet of paper out to full size: Oslo slapped a woman across her cheek; Trondheim decapitated an ice cream; an expanse of North Sea leapt up and assaulted a man setting up his tripod to take pictures of the bay.
“On a leash, I’m fucking telling you!” the camera man raged.
“Oh, aggh, hnnnn, oh dear!” protested Simon, trying to shake the swollen map back into shape. “Hnnn, aaah, oh dear, ohhh!”
Simon is still doing excellent mathematics—occasionally. He may have vanished from the mathematical scene in some people’s eyes (at least, in terms of giving lectures and appearing at research seminars), but he’s still active in the remaining sixty trillion square meters of inhabitable earth outside the Cambridge Mathematics Faculty. New ideas constantly demand his attention. The one that leapt out of his sock drawer last winter is proving extremely fruitful.
It was as he was trying to decide what to put on his feet one morning that the question occurred to him: imagine that his socks, instead of all being slug-gray, came in three colors—say, red, blue and green. If exactly half the time he pulled two socks out of the drawer they were the same color (red and red, for example), what would this say about how many socks he has of each color?
It’s the sort of problem that darns a grin to Simon’s face for months.
He’s going to write it up for a book to be given to children competing in the Mathematics Olympiads. He wants it to be called “From Sex to Quadratic Forms.”
“Why sex?”
“Why not?” He chuckles.
“Why not? Simon! Because, for God’s sake, it’s…ah,” I stop, remembering myself. “OK. Why not call it ‘From Roast Chickens to Quadratic Forms’?”
“Because roast chickens are female.”
Simon is still studying the Monster, but it is slow going. He is working his way round its Group Table, gathering up clues in much the same way that he studies bus and train timetables, picking out unexpected connections, noting tidy circular journeys of numbers, bashing off emails of complaint to the editors of the website edition of the Atlas when he uncovers errors in the Monster’s tabulation…waiting for inspiration. For public transport, Simon uses the word “artistic” to describe a satisfying jaunt—one in which all his timetabling comes together with minute-perfect efficiency and he ends up back at Cambridge bus terminus at around 10 p.m., footsore, exhausted, duffel bulging with fresh tourist leaflets, and just in time to pick up a chicken biryani from the takeaway on Mitcham’s Corner.
For mathematics, he prefers the terms “elegance” and “beauty” to describe such exemplary performance.
Many people insist that Simon is barking up the wrong tree. The mathematician Richard Borcherds has come up with a brilliant explanation that links the Monster to certain symmetries in String Theory—what more do we need to know?
But to Simon’s mind Borcherds’s extraordinary ideas are partial and inelegant, the mathematical equivalent of a cobbled-together shortcut across rough terrain in the back of a borrowed Land Rover. And since, Simon says, in Group Theory “beauty” is what guides him toward truth, the true answer is still to be discovered. All Simon needs is a breakthrough, a clue that will bind all the loose ends together; it could happen any day now. He has had so many false starts…
“Socks are a generalization of sex,” Simon declares, swerving my thoughts back to why he’s become a mathematical pornographer. “Let us suppose, instead of three colors of footwear, red, blue and green, we make the problem simpler and consider sex: let there be α boys and β girls, such that if the chance of any two selected being of the same sex is precisely half, then the number of pairs of children is given by the equation ½(α + β)(α+ β − 1)…”
My brain spins.
The sense of panic I know so well takes over.
Starting in at the third or fourth rib below the heart, it spreads congealment and self-loathing.
Here I am, a man with a first-class degree in physics, and an MSc in applied mathematics, but my eyes tighten to my nose as soon as he begins this dreadful theoretical stuff; my ears ring, my body cramps with refusal to understand, and I’m as bad as those absurd people who giggle about how “appalling” they were at math in school, how they had to be kicked out of the class and failed their GCSE fourteen times.
Yuck.
“North! North! The path goes north here!”
Beside a lake in Bergen city park Simon suddenly turned off the perfe
ctly well-marked pavement, into a bush, came out the other side coated in leaves, and barged up a slope. “North! Keep to the map! North!”
He held the map up high, over his head, and jabbed at an edge.
“But Simon, we were on the path. This rut is an animal track, for very small animals.”
“North, north!”
I ran after him and dived in among the spruces. The sharp, bare branches were blackened with lichen and waterstains. Felled trees lanced the ground. Wood spikes stabbed at our backs and trouser legs.
Simon is an excellent guide on a walk. He spends so much time staring at his foul bed-sized maps, trying to figure out where on earth he might be, that he loses track of where he is. He takes a wrong turn, doesn’t notice that he’s just walked past a no-entry sign with a man holding a gun, and the result is adventures.
Plastic bags protruding from his duffel, he clumped through a bank of ferns, jolted right across fifty feet of sodden grass, and disappeared into a prickly mass of felled wood.
Simon doesn’t consult his map: he clings to it. It is his motor. If he let go, it would zip off, veering and slewing, refracting among the branches, racing out above the mountain canopy until it hit the horizon and disappeared in a blink. Then where would he be? Half dead, in his opinion: a heap of human lostness on the woodland floor, being nibbled at by ants.
“Yes, here it is! The path! The path! It goes west!” cried Simon, weaving through this chaotic thicket. Across the clouds in the west, a bolt of lightning cracked. I ducked a ghostly branch, then instantly had to change direction and leap over a fallen trunk. I felt like a weaver’s shuttle.
We emerged in desolate scrubland. For an hour after, the animal track meandered vertically, fit only for goats.
“Sometimes, when I am walking I get involved in a problem,” Simon flung back in breathless explanation, “and I have to know the answer, immediately!”
“Is that what this is about? A problem?” I called ahead. “You’ve had a breakthrough?”
“Yes!”
These sudden bursts of insight are a famous feature of mathematical discovery. They reach out of the sky and snatch mathematicians by the whiskers.
“You’ve discovered the answer?”
“Yes!”
In the tumult of discovery, they react in different ways.
J. J. Sylvester, the Victorian poet who invented matrices, describes discovering a new theory “with a decanter of port wine to sustain nature’s flagging energies, at the usual cost of racking thought—a brain on fire, and feet feeling, or feeling-less, as if plunged in an icy pail.” Sophus Lie, founder of Infinite Group Theory, walked naked through the countryside around Paris during the Franco-Prussian war in 1870, stuffing his mathematical writings into his knapsack. Henri Poincaré, the great French polymath, once worked on a problem for weeks, made not the slightest advance, and threw it aside in disgust. Several days later, as he was getting onto a bus, the solution suddenly popped into his head. The short period of calm had been essential after all those weeks of concentration. The solution had needed time alone in his brain, as if to brush its hair and oil its mustachio. Now it was ready to kick up its heels in public. Simon Norton responds to his mathematical discoveries by jolting off the public path and rushing through woodlands in Norway. I realized: this is what Simon’s public-transport jaunts are about—travel gives him ideas. It is his laboratory of thought. Simon really is physically hunting the Monster.
All I must do is make sure I’m the first person he contacts when the discovery occurs.
“Aagggh, uuugh…As I say,” Simon interrupted. “I wasn’t talking about a problem in mathematics. I meant I had to know the answer to where this path goes.”
It is not just that Simon’s perspicacity collapsed but that it vanished so drearily. From the greatest mathematical prodigy Cambridge had seen—the greatest “native” talent in the country for perhaps a century—he sank to chasing footpaths and hoarding bus catalogues. He became a cursed figure. Never, said mathematicians, had they seen such a spectacular and thorough demotion. From blessing to damnation with Classical Greek rapidity. Never a loss so tragic and complete. Unemployed, unemployable, Simon dried up like old pastry in 1985, and has been a bag of crumbs ever since. He is a morality fable about the dangers of rampant genius.
A great deal is written about genius, what it is, how it shows up, how the rest of us can snatch a slice of it, from “Eat baked tomatoes” to “Work like a crazed person for 10,000 hours.” There is nothing on why it disappears.
In 2007, before this trip to Norway, I went with Simon to a conference on the Monster at the Centre de Recherches Mathématiques in Montreal. Many of the major names were there: Conway, Harada (who co-discovered the Harada-Norton Group with Simon), John McKay…
When it was Simon’s turn to give his talk, he barged up to the front of the lecture theater as though he hadn’t the faintest idea what he was going to do next. For a while he poked about in the chalk box. Was there a nice boiled sweet in there? Then he walked across to the far right of the blackboard: “Uuuuh, if the letter C stands for the language Cherokee…” he said, and wrote the word out in large letters, with a capital C.
C-h-e-r-o-k-e-e
Good God.
“And R represents Romanian…”
R-o-m-a-n-i-a-n, he spelled out directly beneath the first word.
The audience gave a nervous titter.
“…and M is…uuugh…Maori.”
M-a-o-r-i.
“Then you will see that the initial letters of…uuuh…these three languages correspond to the acronym for this institute: Centre de Recherches Mathématiques.”
Most of the time, Simon does not face his audience. “I thought of that on the flight over,” he told the blackboard.
Another awkward flutter passed through the auditorium.
Earlier that morning, over coffee, a young man from Texas had pushed his way through the crowd to Simon.
“You must be the man of the day,” he’d said.
“Why?”
“Because you look even more like a lunatic than John Conway.”
Simon had laughed uproariously—then abruptly walked away.
As he stood in front of the blackboard, sticking the chalk through his whiskers, Simon seemed genuinely intrigued by the oddity of whatever point he was trying to make, then recollected himself.
“In many ways the evolution of a language parallels the de- velopment of the Monster. In the same way that Cherokee, Ro- manian and Maori are seemingly completely unconnected…” As he spoke, Simon rubbed out the words and replaced them with:
Congruence Groups
(“You’ll notice I’m preserving the initials.”)
Replication
Monster.
And at last, the audience began to sit up; they realized he was not mad. Pieces of notepaper were extracted from files and flattened, pens picked up in preparation. Congruence Groups, Replication and the Monster: three areas of mathematical study that had once been considered foreign to each other. The simile was as clear as the Canadian mountain air. Spotting coincidences (this was Simon’s point) has been our most effective weapon in the hunt for the Monster. We were back in the territory of the sane.
As we came out of the lecture hall following Simon’s talk, an eminent Professor of Group Theory from France sighed with pleasure. “Ah! Zat has made it worthwhile. Conway and then Norton. It eez worth flying 6,000 miles to listen to genius.”
Simon’s explanation for his loss of talent is that it is nonsense. He is as good at mathematics now as he ever was—better, perhaps.
In late afternoon above Bergen, we reached the top of the mountain.
“Now we want to go southwest,” declared Simon. “Let’s see, the sun is…uuggh, wait a minute, where’s the sun gone?”
“That bright yellow blob there, Simon, next to the cloud.”
“Ah, yes. Let’s see now, right, that means west is…there, and north there, and so Bergen i
s that way.”
“No, Simon, Bergen is that big collection of buildings down there, behind you.”
“Aaah, hhnn, you might be correct, but, aaahhh, I’m not 100 percent convinced. I am aaaah, 80 percent convinced…”
On the descent, Simon took another wrong turn because of his map, and sent us sliding down a muddy ravine on our bottoms.
“The place we’re heading for is where we were!” he cried.
“I think it is very important,” concluded Simon as we burst out of the undergrowth in front of an alarmed Norwegian lady pushing a pram, “that people be taught the skill of getting around.”
“Uugh, hnnnn…Are you allowed to eat tinned corn uncooked?”
Back at our Bergen apartment, Simon had agreed to make supper—Mackerel Norton, the only dish he knows how to cook—and had instantly run into complications.
The sweet corn had been packaged in Norway.
“And…aaagh…I can’t read Norwegian.”
“Simon, you’ve been eating uncooked sweet corn from tins for two decades. It’s the same food whatever language you eat it in.”
“Ugggh, hunnnh…I’m not certain how you can know that. What evidence do you have? Perhaps…aaggh… perhaps…oh dear!”
Simon lives in constant disquiet about outside chances. If a thing is possible, no matter how unlikely (one plus one might not equal two; Cambridge housing officials are going to evict him as soon as they’ve read this book; the number in the thirty-fourth column of the 192nd row of the Monster’s Group Table might be a seven; a can of sweet corn is different in Norwegian), he has to give it space to be heard and fretted over.
Simon approached the microwave sniffing, crouched, his brow knitted. When his nose arrived at a suitable distance from its door, he began to move from side to side, trying to see past the grid into the middle of the machine, smoothed his hand along the top, then gave one of the buttons a sharp jab.
Simon Page 20