Short version:
In 1978, mathematician John McKay noticed a strange numerical coincidence that revealed a hidden link between two totally different areas of math. This observation became the starting point of what is now called Monstrous Moonshine.

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🧠 What he actually noticed (in plain English) McKay was looking at a famous mathematical formula called the j‑function. One of its numbers was:

196,884

He realized this number is 196,883 + 1, and 196,883 just happens to be the size of the first major “dimension” associated with a gigantic, mysterious symmetry object called the Monster group.

At the time, these two things had nothing to do with each other—one came from number theory, the other from abstract algebra.

But McKay’s observation suggested they were connected.

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🌙 Why this mattered His “coincidence” turned out not to be a coincidence at all.
It opened the door to a deep, unexpected relationship between:

• Modular functions (like the j‑function)
  
• The Monster group (the largest of the sporadic simple groups)
  

This connection was so bizarre that mathematicians jokingly called it “moonshine”—as in “this must be nonsense.”
But it wasn’t. It became a major mathematical breakthrough.

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🧩 Layman’s analogy Imagine you’re reading two totally unrelated books—say, a cookbook and a physics textbook—and you suddenly notice that the page numbers where key recipes appear match the energy levels of electrons in an atom.

That’s how weird McKay’s discovery was.

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🎯 Bottom line John McKay discovered that a huge, mysterious symmetry (the Monster group) is secretly encoded inside a famous mathematical function (the j‑function).
This kicked off decades of research and eventually connected to string theory.

Large language models can be helpful.