When I was a Bateman Research Instructor at Caltech many years ago, I was fortunate enough to have some memorable encounters with Feynman.
As a Bateman, I had only one course to teach, which was devoted to
mathematical logic. It was attended by some undergrads, some grad
students, and even 2 faculty, one from economics and the other from
One day my office phone rang and the voice on the other side said something like "Hi, I'm Richard Feynman and I teach physics here." I assured him I knew who he was. He said that he had been giving a series of outside lectures, I believe it was at Hughes Aircraft, on subjects on which he was an expert. Now he wanted to give a lecture on a subject with which he was not familiar, "Godel's Theorem", and would I help him. I said sure, when would it be convenient for me to come to his office. He responded that he insisted on coming to my office at my convenience.
He came to my office sometime later and people in the Math Department were in an expectant mood. He and I quickly established that we were born in adjacent parts of Brooklyn, though some years apart, and it was a pleasure to hear someone who knew how to pronounce English properly. It goes without saying that he was a very good student. I seem to recall thinking that if I didn't know this was Richard Feynman, because of his great unchecked enthusiasm I might wonder about this guy. He arranged for a second visit to confirm that he had understood the material, and, of course, he had. I think he later also confirmed that the lecture had gone well.
After that I mainly ran into him in the student cafeteria, then nicknamed "the greasy", (I never saw him at the Faculty Club ) though I never interacted with him on a one to one basis again. I do remember a lecture of his on so-called Feynman diagrams, but I didn't have the background to really appreciate it.
P.S. Curiously, I later had 2 phone conversations with Godel, but never met him in person.
A year after leaving Caltech, I was looking for a tenure track
position. Early in that year I received an invitation from the
Institute for Advanced Study, where Godel was still active.
Since I really wanted a tenure track position and the position at the
Institute was only for a year, a tried to put off the decision until
something more permanent would present itself. I called the Institute a
number of times, speaking to secretaries (it occurs to me that nowdays
one would email instead and the call would probably never have
happened) to apologize for my delay, knowing that there were other guys
out there dying to spend a year at the Institute in my place.
After I had made several such calls, the phone rang one afternoon. My wife answered and a moment later came in to tell me that Godel was on the phone. You can imagine my shock. As far as I was concerned, he could have dropped the last two letters of his name and that would be an accurate description of his place in the intellectual world. (I noticed just now for the first time that the final two letters also mean God in hebrew.) He was incredibly gracious and assured me that the place was reserved for me and would not be given to someone else, and that I could take all the time I needed.
Soon after I was contacted by Notre Dame. I went out for an interview and loved the place. When they subsequently offered me a tenure track assistant professorship, I accepted and postponed my visit to the Institute until the following year, which Notre Dame was kind enough to allow. (I ended up staying at Notre Dame for the next 11 years during which time I became a full professor. I enjoyed my time there very much and still keep up some ties, but then decided to leave the academic world.)
The down side was that when I did go to the Institute and year later, Godel had already retired and I never met him in person. When I was leaving the Institute, I called him to thank him for the wonderful year I had had there. As a side note, when I was in Princeton, I lived in the house of a famous catholic philosopher, Jacques Maritain, who had donated his house on Linden Lane to Notre Dame. Godel's house was also on Linden Lane, a few blocks further from the Institute. I would often pass it as I did my jogging. I recall that there were pink flamingos in the yard. I knew he was not well and always thought about that when I went by. It was very sad when he died soon after.