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> 1/3rd of papers have false theorems in them Despite the wording in the article, this is false. A theorem is not false if there is an error in a proof for it.
by archgoon 8y ago
> 1/3rd of papers have false theorems in them
Despite the wording in the article, this is false. A theorem is not false if there is an error in a proof for it. They only showed that 1/3 proofs of theorems had an error. It doesn't say if these were minor errors (omitting an edge case where it's still true, but not handled in the proof, but easily covered), or major (the theorem is actually false).
Quoting the article:
> Some of them were false because the proofs were wrong, and some were false because they relied on wrong proofs.
This is not what 'false theorem' means. This might be pendantic, but isn't that kind of the point here?
- loup-vaillant 8y agoRegardless, unproven theorems should not make it to publish papers. At the very least, they should be marked as "conjectures".
- gizmo686 8y agoThere is a difference between unproven, and the published proof contains a mistake.
- loup-vaillant 8y agoSeriously, who cares? When you publish the proof for a theorem, you're generally the first to do so. Aren't you? If there is an error in the only published proof ever, your theorem is unproven. QED. Edit: to downvoters: please explain my error. I thought I was only telling the obvious here.
- cma 8y agoMaybe they feel you didn't rigorously prove your case.
- loup-vaillant 8y agoThey more likely didn't read past the first sentence. I suspect a very thin skin. Seriously though, I don't know what makes this forum tick. Someone's gotta explain what is socially acceptable around here. I know we're not supposed to complain about votes here, but I genuinely don't understand what happened. (Or rather, what is happening, the votes seem to flow up and down for no discernible reason.)
- pvg 8y agoWhining about downvotes and then trying to goad other users is bad and you shouldn't do it.
- loup-vaillant 8y agoPerhaps, but it looked like it worked. Somehow. For now. At the time I write this, the comment you are replying to is still positive (edit: oops, no longer), while it clearly breaks the stated rules of this forum (sated both officially and by you just now). And I'm pretty sure that if I didn't do it, my "who cares" comment above would have been further downvoted. I observed this several times on several forums, sometimes votes have a momentum, and breaking the rules like I did can sometimes stop that momentum. (This works the other way too: popular comments often stop having further upvotes after the first reply that disagrees.) Incidentally, I really think a good proportion of downvoters hit the button before reaching the end of the comment. Not because they're personally offended, but because their troll filter judge quickly, from the very first words (thinking back with a cooler head, I can't blame them). Starting a comment by something that looks offensive if taken out of context is a pretty sure way to get it downvoted to oblivion. Still, the threshold looks pretty damn low.
- pvg 8y agoPerhaps, but it looked like it worked. That's not the reason you shouldn't whine about downvotes or goad other users. Not a 'perhaps' thing.
- Bahamut 8y agoNot all published proofs are necessarily proving a new theorem. Sometimes they are new approaches to proving known theorems. One example of that is the Prime Number Theorem, for which there have been multiple proofs over the years exploring different angles.
- amelius 8y agoTranslating this to computer science/programming: what would you call an unproven program?
- barrkel 8y agoOne that fails to compile with a type error. Probably, pseudocode - enough to convey the concept, but eliding some details that a compiler may require.
- loup-vaillant 8y agoOne that isn't machine checked to conform to the specification (with Coq or similar). My standard is even higher for programs than it is for mathematical statements, because they tend to be orders of magnitude more complex. On the other hand, it's okay for a program to not be proven, because it can be useful even if it has bugs.
- AnimalMuppet 8y ago> On the other hand, it's okay for a program to not be proven, because it can be useful even if it has bugs. True, and a very important point. But... if the program has bugs, do they affect the results? Do they affect the results enough to matter? How do you know? In particular, what is your objective proof that the program does what you need it to do? For many programs, such concerns are extreme overkill. For some, though, you have to prove that it does what you need it to.
- loup-vaillant 8y agoThat's where you quit proofs, and start experimenting. I found tests to be extremely effective at rooting out most bugs. Especially if you use property based tests. Programs that do need a proof still have model checkers like TLA+, and proof assistants like Coq.
- AnimalMuppet 8y agoSure, tests are part of what I meant by "objective evidence".