After the star-studded mystery thriller The Number 23 debuted in cinemas in 2007, many people became convinced that they were seeing the eponymous number everywhere. I was in school at that time, and some of my classmates would shudder whenever the number 23 appeared in any context. Other people became addicted to this form of numerology because as soon as you pay more attention to a certain thing—including a number—you get the feeling that you see it too often to be purely coincidence.
For a long time, people assumed that the late mathematician John McKay might have fallen victim to this same phenomenon, known as the “frequency illusion,” or the Baader-Meinhof phenomenon. In McKay’s case, the number that captured his imagination was 196,884.
It doesn’t seem too surprising that a two-digit number such as 23 might come up repeatedly. But would a six-digit figure do so? McKay came across this number by chance in 1978 when he was looking through a paper in a mathematical field that was not his specialty. He was working in geometry and was studying the symmetry of figures. That day, however, he was looking at results from number theory, which deals with the properties of integers such as prime numbers. He came across a sequence of numbers that started with the value 196,884.
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This figure sounded familiar to McKay. He had previously worked on a mathematical structure—still hypothetical at the time—known as the monster. This strange algebraic structure was intended to describe the symmetries of a geometric object that lives in 196,883 dimensions (only one fewer than the number 196,884). And because a one-dimensional point fulfills every symmetry anyway, the monster can also describe its…
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