Essay on Science: Shadows of Evidence | Simons Foundation

(texte de février 2013)

▻https://www.simonsfoundation.org/mathematics-and-physical-science/shadows-of-evidence

**The Evidence of Coincidence**

In the early 1970s, the mathematician John McKay made a simple observation. He remarked that

196,884 = 1 + 196,883

What is peculiar about this formula is that the left-hand side of the equation, i.e., the number 196,884, is well known to most practitioners of a certain branch of mathematics (complex analysis, and the theory of modular forms), *(3)* while 196,883, which appears on the right, is well known to most practitioners of what was in the 1970s quite a different branch of mathematics (the theory of finite simple groups). *(4)* McKay took this “coincidence” — the closeness of those two numbers *(5)* — as evidence that there had to be a very close relationship between these two disparate branches of pure mathematics, and he was right! Sheer coincidences in math are often not merely sheer; they’re often clues — evidence of something missing, yet to be discovered.

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*(3)* 196,884 is the first interesting coefficient of a basic function in that branch of mathematics: the elliptic modular function.

*(4)* 196,883 is the smallest dimension of a Euclidean space that has the largest sporadic simple group (the monster group) as a subgroup of its symmetries.

*(5)* McKay gave a convincing interpretation of the 1 in the formula as well.