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The joke is found on this comment chain on Reddit. One user told the joke:

The version I heard is that Pauli was lecturing, and he said "this is obvious". A student raises his hand and says "sorry professor, I don't think that is obvious". Pauli stares at the board, back at the students. He thinks for a bit. He starts pacing in front of the class, thinking. He looks back at the board. Eventually he leaves the room, comes back 20 minutes later and says "I've thought about it and yes, it is obvious".

The main characters are said to be Pauli, Wiener and Lax, Hardy, von Neumann and Einstein. So who were the real characters?

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    $\begingroup$ What brings you here? Suddenly this question attracts new traffic $\endgroup$
    – Ooker
    Jan 11 at 18:23
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    $\begingroup$ It was linked from a comment on academia.stackexchange.com/q/181016/65745, which is on HNQ $\endgroup$
    – Bear
    Jan 11 at 18:27

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The closest to an attribution that I could find is by Matt Calhoun on Math SE, who claims "it was personally told to me" by "my mechanics professor (G. Horton) [who] took lectures from Pauli..." G. Horton is presumably George Horton who held a physics post-doc in Zurich in 1949-51. Pauli stayed in Zurich from 1946 until his death in 1958, so they did intersect. Horton moved to Rutgers in 1960 where he taught until 2009. He was popular enough for students to dedicate a memorial website to him. The anecdote is most often told about Pauli, but the story does show many signs of being made up, no first hand source, lack of detail, revolving names, etc.

It is also reminiscent of another, older story, with a somewhat better credentials but the opposite ending. Reid reports it in her book on Hilbert (p.93) (she also gives no direct attribution but implies that it was reported by Göttingen students whom she interviewed for the book):

""This theorem has not yet been proved, but that is because only mathematicians of the third rank have occupied themselves with it," Minkowski announced to the class in a rare burst of arrogance. "I believe I can prove it." He began to work out his demonstration on the spot. By the end of the hour he had not finished. The project was carried over to the next meeting of the class. Several weeks passed this way. Finally, one rainy morning, Minkowski entered the class followed by a crash of thunder. At the rostrum he turned towards the class with a serious expression on his gentle round face. "Heaven is angered by my arrogance," he announced. "My proof of the Four Color Theorem is also defective. He then took up the lecture on topology at the point where he had dropped it several weeks before."

Even assuming that this does have some basis in reality the "several weeks" and the melodramatic effects are most certainly embellishments.

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I have reason to believe that's an apocryphal story, as it's been told to me by different professors at different universities with different (often local "legends" ) as the protagonists.

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This story is often told about G. H. Hardy. You will find it in Lion hunting & other mathematical pursuits, by Ralph P. Boas Jr. It says: “The story is told of G. H. Hardy (and of other people) that during a lecture he said ‘It is obvious… Is it obvious?’ left the room, and returned fifteen minutes later, saying ‘Yes, it's obvious.’ I was present once when Rogosinski asked Hardy whether the story were true. Hardy would admit only that he might have said ‘It is obvious… Is it obvious?’ (brief pause) ‘Yes, it's obvious.’”

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I first heard this story from Dr. Troy Hicks in the 1980's. I posted the story in a few different places online over the years, probably dating back to the late 90s or early 2000's. Professor Hicks was a rather conservative Christian who was very careful about his words, and was not inclined to exaggerate. When Dr. Hicks told this story, he said that he had heard it at a conference from Mary Ellen Rudin, who was a well-known Topologist, and the wife of Walter Rudin. Dr. Hicks said that, "she told it on her husband Walter." Walter came back right as the class was ready to end and declared that it really was obvious! Mary Ellen was a Professor at Wisconsin as well; apparently she first heard it from some of Walter's students, soon after it happened. Mrs. Rudin confirmed that it really did happen.

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A first-person account that covers the major points of the question appears in the book, "Surely You're Joking, Mr. Feynman" by Richard Feynman (The specific story is titled "A Different Box of Tools"). The real characters were a group of math and physics grad students at Princeton. The specific student who made the claim of triviality is unnamed.

I still remember a guy sitting on the couch [in the shared math/physics department lounge], thinking very hard, and another guy standing in front of him, saying, "And therefore such­-and­-such is true."

"Why is that?" the guy on the couch asks.

"It's trivial! It's trivial!" the standing guy says, and he rapidly reels off a series of logical steps: "First you assume thus-­and-­so, then we have Kerchoff's this­-and-­that; then there's Waffenstoffer's Theorem, and we substitute this and construct that. Now you put the vector which goes around here and then thus-­and-­so..." The guy on the couch is struggling to understand all this stuff, which goes on at high speed for about fifteen minutes!

Finally the standing guy comes out the other end, and the guy on the couch says, "Yeah, yeah. It's trivial." We physicists were laughing, trying to figure them out. We decided that "trivial" means "proved."

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