I’ve never understood what’s the point of giving a lecture nobody except you can grasp. IMHO, It could be justified only by the novelty of topic discussed, otherwise it’s just a waste of everybody’s time.
Understanding is not binary. They mean that the bright student walked away understanding X% (maybe 70%) of the major logical steps Von Neumann made.
Those students could then go home, open a book or the transcript of his lectures and spend 5-10 hours figuring out all the details, and exploring auxiliary stuff not covered in the lecture.
Lecture time is fixed, outside-lecture time is 10X lecture time.
Perhaps the requirement of giving a lecture helped him prepare knowledge in a communicable way. For me, when I'm asked to give a panel talk or prepare a presentation, I'm forced suddenly to better communicate that I otherwise might need to, and thus knowledge is stored in a better way.
There are a few famous instances where mathematicians ran seminars for close to a decade and developed extensive theories on that way. Von Neumann appears to have been one, Grothendieck is a famous other example. The lectures are basically then meant to be taken by people that dedicate almost all their time to understand them.
In other words they are lecturing as they are developing the new theory. Clearly such things probably happen much less often now a days, because the overall research landscape is such, that this is not really rewarded. On a smaller scale research seminars in mathematics still are like that though, the results discussed there are often only circulated among the participants, which then make them available to the public piece by piece. Peter Scholzes breakthroughs were widely discussed in Bonn long before they were accessible to the overall public and even then most of what was taught in the initial seminars in Bonn wasn't circulated.
Not commenting about this specific case, but I know some people just like to feed their ego, by lecturing so "high" no one can understand them, so they reinforce their believe, that they themself are clearly the most intelligent person around.
It's hard to prove that someone does this on purpose. Some lecturers indeed don't bother to go down to earth. But it's not necessary because of their ego. If a "high" presentation has a meaning and a reason, then it's justifiable.
Though some people indeed complicate their lectures for no reason.
I am not necessarily say people does this with clear purpose. Even though the specific professor I have in mind, probably did. But unconsciously, I'd say people do this a lot in general.
I sometimes do it, when I am angry at a person, not on par with me intellectual. Then out of bad old habit I speak a very high language to underline my competence and lower the other person for not understanding it. I witnessed that behavior quite some times with other persons, too and thats probably why I aquired it myself at some point. But I try to get rid of it, as it is not at all helping with communication.
And I think the high lecturing is in the same category. To boost oneself.
But agreed, most too high lectures are probably just happening out of lazyness or unawareness, to get down on the level of the students.
The interesting thing about this dynamic is that you'll often have people who can formulate cutting arguments on the spot, used against someone who is slower but who tends to think more deeply, given enough time. So, with some thought, those arguments are easy for the second person to eventually break down, and while the first can usually rebut quickly (often with more high-sounding nonsense), they're (if they have any self awareness at all) left with the nagging truth of the first conflict's takedown.
And now no one is happy.
Generally it's better to just be smart than to try to prove or weaponize it.
Hard to prove in words, because proving intentions, arrogance and other interpersonal subtleties is always hard.
But relatively easy to notice if you take time to watch lectures themselves. Ego driven complexity is different then inability to explain complexity or it is complicated complexity.
Also, seems kind of rude as a teacher to erase equations off the board "before students could copy them". Would it hurt so much to ask, has every written this equation?
