[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.
You do not understand how basic probability works. I recommend An Intuitive Explanation of Bayes’ Theorem.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.