In the summer of 1984, I attended a seminar in the physics department at Caltech. Richard Feynman was in the audience. The speaker was a researcher from a University of California campus. He and another researcher, who was not present, were using Feynman's approach to statistical mechanics to compute a result that was exact, to all orders in the Feynman diagrams. They were preparing a paper to submit to a physics journal.
A set of Feynman diagrams that describes a given physical process represents a way to sum an infinite series of interactions in that process. Mathematically, if an infinite series converges, you can sum it in different ways. The sum, if you carry it out to all terms, will be the same by each method. So why have different methods? Well, if you only sum a finite number of terms, then different methods will, in general, have different accuracies. Physically, the set of Feynman diagrams is a rearrangement of the infinite series such that each term can be represent symbolically by a diagram. Plus there are rules to actually write down the term, given the diagram. And each diagram is physically intuitive to a physicist. The more squiggles and more intersecting lines that there are in a diagram, then it represents higher order interactions between particles than a diagram that has fewer such symbols.
Well, it is rare in physics that you can derive a closed, analytic expression for all orders of interactions in a physical process. Rare enough that such events are worth reporting.
Now the audience was mostly theoretical physicists who specialized in high energy physics. Well, Feynman found out during the lecture, in real time, that the speaker was wrong. He had made an assumption that was invalid. Hence, his results amounted to only computing first and second order diagrams. The speaker and his co-author had obviously spent weeks on this but had missed the error. Plus no one else in the audience discovered it. These were top notch physicists, many less than half Feynman's age. The speaker was nonplussed and offered to stop his talk. But Feynman was very gracious and urged him to continue. I never found out, but I suspect they withdrew their paper.
I will always remember this. Seeing for myself Feynman's mind in action on a problem that he had not seen before. And how he was sharper than anyone else around. I was a grad student at the time. And my advisor had been a grad student in physics at Caltech in the 1960s. He told us that back then, students would dread having Feynman on their thesis committee. You might wonder why. A student would have spent 4 or more years studying the subject of his thesis. What error or awkwardness could Feynman find from a couple of hours of reading the thesis before the defense, or during the defense itself? But apparently, Feynman did so, on several occasions.
During the 1980s, this did not happen, because Feynman was not as active. He had gone into hospital several times, and just was not physically capable. So he rarely sat on thesis committees. So the grad students in the 80s only heard of this second hand.
Well, I saw it for myself.