Re:Any smooth cubic surface contains 27 lines
by omaranto on Tuesday February 16, 2016 @06:55PM
(#11114072)
Are you asking for a proof of the "fact" that all proofs of the theorem about cubic surfaces having 27 lines are non-trivial? If so, then no, there is not even a definition of non-trivial proof, let alone a proof that any specific proof is non-trivial or a proof that there exists a fact all of whose proofs are non-trivial.
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Re:Any smooth cubic surface contains 27 lines
by amelius on Wednesday February 17, 2016 @09:53AM
(#11118191)
My definition of a trivial proof would be a proof that is mechanically verifiable. I.e., it is verifiable by even something as "dumb" as a computer.
Of course, such proofs tend to be longer than most proofs that are considered non-trivial.
Re:Any smooth cubic surface contains 27 lines
by omaranto on Wednesday February 17, 2016 @03:10PM
(#11120877)
Maybe years ago that would have been a plausible definition, but by now many proofs have been verified by computer, including several which probably no-one would feel comfortable calling trivial.
Re:Any smooth cubic surface contains 27 lines
by jsprogrammer on Tuesday February 16, 2016 @07:11PM
(#11114144)
Yes, that is what I was asking for.
What does the sentence mean then?
One particular proof (of which we do not know if it is exclusive) is non-trivial (whatever that means)? Or, perhaps, all known (to the author) proofs are non-trivial?
Re:Any smooth cubic surface contains 27 lines
by omaranto on Tuesday February 16, 2016 @07:29PM
(#11114217)
Baez didn't mean that as a mathematical statement rather as a statement in the field of history and human psychology: "So far nobody has been able to devise a proof that is widely regarded by people who study it as being trivial (where triviality of a proof is a subjective judgment for which there is (1) no formal criterion, but also (2) a surprising amount of agreement)."