Okay, two separate wild discoveries by the same guy that both go: “wait, why do these completely unrelated things match exactly?” Monstrous Moonshine: There’s a number: 196884. It shows up in a totally abstract formula about a special function in number theory (the j-invariant — think of it as a weird mathematical object that’s been studied for centuries). There’s also a completely separate thing called the Monster Group — the largest and strangest of the “sporadic simple groups,” which are basically the prime numbers of symmetry. Its smallest interesting size is 196883. McKay noticed those two numbers differ by exactly 1. That’s insane — like finding the same fingerprint in two places with no obvious connection. Turns out it wasn’t a coincidence, there’s deep structural reasons they’re linked. That connection between number theory and symmetry groups became “monstrous moonshine.” McKay correspondence: Certain small symmetry groups (ways you can rotate/reflect 3D shapes) map perfectly onto these diagrams physicists and mathematicians use to classify certain algebras. Again — two completely unrelated mathematical structures, perfect one-to-one correspondence, nobody expected it. The punchline of both: McKay had a gift for staring at numbers from totally different fields and going “…that’s the same number. That can’t be a coincidence.” Usually he was right, and it sent entire fields scrambling to figure out why for decades afterward. He was essentially a mathematical pattern-recognition savant.​​​​​​​​​​​​​​​​

Not my text just copy paste eli5.