# alex_zag_al comments on Rationality Quotes September 2012 - Less Wrong

7 03 September 2012 05:18AM

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Comment author: 05 September 2012 03:45:39AM 5 points [-]

At the Princeton graduate school, the physics department and the math department shared a common lounge, and every day at four o'clock we would have tea. It was a way of relaxing in the afternoon, in addition to imitating an English college. People would sit around playing Go, or discussing theorems. In those days topology was the big thing.

I still remember a guy sitting on the couch, 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." So we joked with the mathematicians: "We have a new theorem -- that mathematicians can only prove trivial theorems, because every theorem that's proved is trivial."

The mathematicians didn't like that theorem, and I teased them about it. I said there are never any surprises -- that the mathematicians only prove things that are obvious.

From "Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character

Comment author: 05 September 2012 06:58:43AM 6 points [-]

I've heard it said that "Trivial" is a mathematics professor's proof by intimidation.

Comment author: 05 September 2012 07:12:06AM *  5 points [-]

The view, I think, is that anything you can prove immediately off the top of your head is trivial. No matter how much you have to know. So, sometimes you get conditional trivialities, like "this is trivial if you know this and that, but I don't know how to get this and that from somesuch...".

Comment author: 02 October 2012 06:08:27AM 3 points [-]

Relatedly, a mathematician friend said that he uses "obvious" to mean "there exists a very short proof of it." He has been sometimes known to say things like "I think this is obvious but I'm not sure why yet."