aussiematt,

It would have to be Gödel’s Incompleteness Theorem. Such a beautiful proof that shakes mathematics to its core.

The science communicator Veritasium made a nice video about it: https://youtu.be/HeQX2HjkcNo

I first learned about it in Douglas Hofstaedter’s masterpiece Gödel Escher Bach: An Eternal Golden Braid

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