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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
by omaranto 11y ago
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.
- jsprogrammer 11y agoYes, 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?
- omaranto 11y agoBaez 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)."
- amelius 11y agoMy 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.
- omaranto 11y agoMaybe 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.