6/2/2023 0 Comments Deep pocket monster![]() ![]() It seemed as if the j-function was somehow controlling the structure of the elusive monster group. The j-function’s second coefficient, 21,493,760, is the sum of the first three special dimensions of the monster: 1 + 196,883 + 21,296,876. However, the connection caught the attention of John Thompson, a Fields medalist now at the University of Florida in Gainesville, who made an additional discovery. Most mathematicians dismissed the finding as a fluke, since there was no reason to expect the monster and the j-function to be even remotely related. Strangely enough, this function’s first important coefficient is 196,884, which McKay instantly recognized as the sum of the monster’s first two special dimensions. ![]() McKay, of Concordia University in Montreal, happened to pick up a mathematics paper in a completely different field, involving something called the j-function, one of the most fundamental objects in number theory. Mathematicians weren’t sure that the monster group actually existed, but they knew that if it did exist, it acted in special ways in particular dimensions, the first two of which were 1 and 196,883. He had been studying the different ways of representing the structure of a mysterious entity called the monster group, a gargantuan algebraic object that, mathematicians believed, captured a new kind of symmetry. In 1978, the mathematician John McKay noticed what seemed like an odd coincidence.
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