The Genius in my Basement. Alexander Masters

yellow people in blue boilersuits, should be treated the same as another packet, from a country 16,000 miles distant from the first, with brown people and cactuses? Cooking instructions have no appreciation of the slyness of variables.

      ‘Uugggh, do Mexican vegetables boil in the same way as Chinese?’ Simon asks, waving the packet at me through the kitchen door.

      In Simon’s kitchen there are no cobwebs. An aerosol of grease has killed them off. If you stand on a footstool, it is possible to find – original inhabitants, from before the Extinction Event (Simon’s purchase of the house in 1981) – dead spiders inhumed above the wall cupboards, in the Cretaceous layers of fat.

      There is evidence of urgent eating everywhere. The oil slicks on the melamine surfaces; eyebrow hairs embedded around the sink; foot and shoe grime that has gathered on the plastic embossed-tile flooring, making it look almost as though there is a rug on top; the curtains of grease moving down the sides of the sink like textured glass.

      Simon is not unhealthy. The principal source of serious infection in any house – the water supply – is cleaner here than in most places, because the attic in which the water head is stored is used as a room for tenants, and is therefore easily accessible and frequently checked. I can vouch for the fact that there are no mice floating in it, or spiders, woodlice, bloated and putrefying snails, or dead rats, as there certainly will be in the water tanks belonging to some of the people reading this sentence.

      He is not unhygienic, except in the eyes of today’s dainty obsessives and kitchen-product advertisers. He has a bath once a week and cleans his teeth daily. But he is not frightened of his digestion. Simon’s connection with decomposing food begins and ends, openly and honestly, as it does with all animals at ease: with a squelchy chew at one end and a sigh of release at the other.

      In a tidy kitchen, every knife, plate, whisk, frying pan, coffee mug, ladle, tea strainer, chopping board and all machines are stagnant with cleanliness, with the exception of the dishwasher murmuring disinfectant-speak under the sink. The object of the tidy and twee housekeeper is to remove all proof that he is a functioning organism.

      In Simon’s kitchen, Hunger has slobbered everywhere.

      Yellow smears splashed along the left-hand worktop are from cartons of chicken biriyani, the lid ripped off; the drips of purple, slightly granulated, are Fern’s® brinjal pickle; the intermingled slops of ochre green, Mr Patak’s® mixed pickle.

      ‘And what’s wrong with Mr Fern’s mixed pickle?’

      ‘I don’t know. I’ve never tried it. Do they do one?’

      Both types of stain are the result of scraping contents from jars with a plastic spoon that is too short, and rushing the findings back on a bombing run across the sideboards to the now dead chicken. By the sink, chicken in black bean sauce has added a brown tinge.

      This rancid atmosphere and the cold, soporific mood of the main rooms, together with the almost undetectable whiff of furniture polish from the paintings and mahogany items that Simon inherited following the death of his father – a homeopathic dose of plushness – combine to give the Excavation a pleasant smell. Warmed up, with perhaps a squeeze of lemon and lime shaving cream thrown in to suggest Life, it might even be cosy.

      All the same, it’s easy to get carried away by this bomb site. Simon isn’t universally messy, even outside his head. He’s as fussy as a surgeon when it comes to planning a journey. He manages two homes (he has a flat in London), has a turnover of satisfied tenants, and is never behind with bills, legal documents or financial dealings with his accountant. None of these is true of me. In addition, his transport newsletter comes out once every three or four months, is twelve to sixteen pages long, single-space, eight-point type, covers hundreds if not thousands of unfailingly accurate details about new routes, closures and timetables, and keeps careful account of all local outrages by the government Highways Agency. When Simon wants there to be order, he’s unmatchable. When not, a colostomy bag is not more disgusting. Simon insists that this basement is his catalogue: all it needs is pruning, sorting out, filing, and it will be an invaluable library of documentation.

      A list, from 1992, of a few of the bus and train journeys Simon made that year. He has a pile of such lists, over a foot high.

      ‘A documentation of what, exactly?’ I ask while he sits down to his supper.

      ‘Where I’ve been?’ he suggests.

      I call it his middenheap. These papers are just bones: all that is left after Simon’s banquet on their information relating to buses and trains: the public-transport detritus of a monstrous feast on facts that began when he was three.

      ‘How about if I take the focus of the story off the floor and into the air?’ I suggest breezily, returning to the battle. ‘“One of the greatest mathematical geniuses of the twentieth century lives beneath my floorboards,” I could begin, “in the dank, foetid gloom of his subterranean …”’

      ‘No.’

      ‘Not dank?’

      ‘No.’

      ‘Or foetid?’

      He shakes his head.

      ‘How about miasmic? I quite like miasmic. It sounds poetic.’

      Also no good: ‘Ungh-ungh.’

      I take a deep breath, slowly let out air, and reach across for Simon’s thesaurus. ‘Ponging?’

      *6 The Monster

      (Mathematical chapters in this book are quarantined by a *)

      That’s the name of Simon’s special area in mathematics, because of its gargantuan complexity and fiery insight into the fundamental structure of our universe.

      No one knows what the Monster looks like. It can be detected only through its mathematical traces. Like shadows and ghosts, it inhabits a penumbral landscape between abstraction and solidity.

      The Monster belongs to an area of mathematics known as Group Theory, or the study of symmetry.

      Groups are represented in textbooks by tiresome grids of numbers similar to sudoku tables, yet they are among the most startling investigative tools in human thought. Quantum Theory, Relativity Theory, predictions about the number and types of sub-atomic particles, the codes used to scramble military and financial information – all of it fundamentally reliant on the study of Groups. They have even been used to investigate incest among Aboriginal tribes.

      A sudoku table has nine rows and nine columns of numbers.

      The Monster has 8080174247945128758864599049617107 57005754368000000000.

      *7

      Introducing

      To understand Simon’s particular genius – how it developed and why for a few years he led the braying pack of mathematicians hunting down the Monster – the reader needs to know about squares.

      On the face of it, the study of symmetries is a subject for children. A square has symmetry: you can rotate it, and the result looks just as if you’d done nothing at all:

      The same goes for an equal-sided triangle:

      A circle, cube, sphere, and a host of other shapes with names like dodecadodecahedron (twenty-four faces) and icosidodecadodecahedron (forty-four faces) each has similar symmetrical properties.

      In order to develop mathematics out of such simple stuff, we have to keep a diary of these symmetries.

      For example, to keep track of these four moves,