Genius At Play by Siobhan Roberts

Author:Siobhan Roberts
Language: eng
Format: epub
ISBN: 9781620405949
Publisher: Bloomsbury Publishing
Published: 2015-07-14T16:00:00+00:00

Dateline: Cambridge, 1973. The typical scene featuring Conway loitering in the common room had changed somewhat. Now he could be found crawling around the floor, as if under a hypnotist’s spell. He had printed out more than 100 feet of fanfolded computer paper and arranged it in a 12-by-9-foot tiling on the floor of the common room. The tiling formed a “character table” of numbers, describing and defining the Monster group (named by Conway!).

Earlier that year 2 mathematicians, Bernd Fischer at Universität Bielefeld and Bob Griess at the University of Michigan, had separately predicted the existence of this new group. They did so in a manner similar to how physicists predicted the existence of the Higgs boson, the quantum of the Higgs field that pervades the ether and endows elementary particles with mass. Circumstantial evidence indicated something was there. And so just as physicists went hunting for the Higgs boson, mathematicians went hunting for the Monster—for information, confirmation, clues or crumbs, scat or spoor.

The Monster has been likened to the titular creature in Lewis Carroll’s poem “The Hunting of the Snark.” Carroll, when pressed, would say only that his snark was inadmissible and unimaginable—though he indicated courage is needed on a snark hunt, and that the best tools to wield in its capture were thimbles, care, forks, hope, or else to “charm it with smiles and soap.” With the ragbag of groups that had been discovered during the Classification Project, mathematicians similarly used a ragbag of methods. Conway’s initial method for the Monster involved a Hamann Manus R mechanical computer. It had levers and gears and looked like a souped-up old cash register, and his girls liked to play with it and take it apart. Later he resorted to his handheld HP-65 programmable calculator, and by the end of the year he had calculated the Monster’s size, or its order, its number of symmetries. Fischer had laid the groundwork using what’s called the Thompson order formula, indicating a maximum size and that the size could be expected to fall within a certain arithmetic progression. Conway programmed the calculator with these constraints, left it running overnight, and when he awoke the next morning there was his answer. He sent a postcard to Fischer with the news:

Dear Bernd, The order of the Monster is . . .

And then a very big number, approximately 8 · 1053. Or, more precisely:

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