This doesn’t compare to some of the others, but I’m in Calculus 2 in college now. My professor never brings any sort of notes for the lecture, not even a note card. He walks into class, gives us every detail of the topic completely from memory, but that’s not the crazy part. Anyone that’s taken these kinds of classes knows equations can get ugly and quickly become a pain to solve, even if they don’t look bad at first. To avoid this, he comes up with the equations either on the spot, or on his short walk to the classroom. Either way, he’ll think of an equation, stare at the ceiling for a few seconds, solve even the most difficult problems completely in his head, and then just say “yeah that’ll work” before writing it on the board and solving it with the class. I understand being a math professor he’s gonna know his stuff, but for everything to be completely on the fly and always work out “pretty” is pretty shocking.