These go by different names at different schools, but a grad student has to pass an oral exam, roughly at the end of their coursework and beginning of their dissertation phase. Sometimes called "orals," "comprehensive exams," etc.

By tradition, they can ask you anything. But in practice, they're not out to kill you. I went to a second tier university, and it was generally believed that the questions at a top school tended to be harder. I have no recollection of mine.

At this time, you also typically present a proposal for your thesis project. Passage of these hurdles makes you a "candidate," i.e., a candidate for a PhD upon defense of your thesis.

Princeton PhD students take a general exam as one of the major milestones of their PhD candidacy.

https://gradschool.princeton.edu/academics/degrees-requireme...

It's his "general exam" to start his PhD at Princeton

It's just faculty ensuring he has enough general knowledge of mathematics

At this point in time he would've been a teenager

I think when it is written "They passed me" it meant that he passed the exam.

it is an oral exam as part of a phd. this was years ago (1996?), so interesting as a retrospective.

He's one of the preeminent living mathematicians.