A few years ago, the BBC reported that Opeyemi Enoch had proved the Riemann hypothesis, and we (@aperiodical) immediately said "no, he hasn't" - aperiodical.com/2015/11/rieman…
Now, Sir Michael Atiyah claims he's proved it and we said "well, let's see".
Why the difference?

@aperiodical Enoch looked like any crank: went straight to the wrong venue - BBC News, not other mathematicians - didn't publish his proof in the open, and presented it at a very scammy looking conference run by Nina Ringo, who we've encountered before.

@aperiodical And we'd never heard of him. The false-positive rate for "anyone on the planet" with a claimed big proof is much, much higher than for, say, professors of maths in big universities.

@aperiodical Atiyah, on the other hand, has a Fields medal, an Abel prize, and a very long list of publications. We still think he probably hasn't proved it, based on his other recent pronouncements, but he says he's going to present his proof, so we give him the benefit of the doubt.