Years ago, when I was surfing the web for math prelim study guides I found this link of Princeton’s Math Prelims. Apparently, at this elite school the aspiring grad students are expected to take an oral exam in which three Professors (who are usually some of the best in their fields) take turns quizzing students on results from their respective fields. Pretty scary, right?
Well, some of the grad students who survived this exam have written up the discussions during their particular exams and have shared these notes at this link:
Anyway it’s been fun for me to go back and read the exams of some of today’s top mathematicians and see what comments they had about the experience. Sometimes you’ll get to read some of the banter these top mathematicians have amongst themselves. In this link you can find people such as Terry Tao or Manjul Bhargava.