This is essentially irrelevant to the content of the post, but it's amusing to me that he casually mentions submitting to JAMS as if its acceptance were a mere formality.
It basically is a formality at this level. Many top math researchers now hardly even submit to journals at all and just put up a preprint.
At this scale, peer review happens by the audience. They don't need a journal to get people reviewing their work.
He has rejected papers too https://mathstodon.xyz/@tao/113721192051328193