too little, too late


At breakfast I proved the famous theorem of Pythagoras (again). I do this every now and then, as well as other quick calculations, e.g. deriving relativistic time dilation, average distance traveled of a random walk, ground state of the harmonic oscillator, etc. mostly to check that my brain is still working properly.

But this time it led to the question how many times this theorem has been proven already and I suspect the answer is several billion times. (I am assuming most kids have to do this at least once, but I am not sure if it counts if the teacher does it and they just watch.)
In other words the probability is very low that Pythagoras got it wrong. However, I cannot rule out that I already lost my marbles and, plagued by a combination of Alzheimer's and schizophrenia, only imagine that I calculated correctly and in reality it is all wrong.
But how would one estimate the probability for that? (*)

(*) Just another attempt to shake the Platonist worldview a little bit.