3 ms·

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this: > In particular, proofs for special graph classes, c

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this: > In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a complete nonexistence certificate are insufficient. which is infact a very important part of the prompt.

don_esteban 2mo ago
the fact that such things have to be explicitly in the prompt points to the fact that the underlying system is still far from where it needs to be (basically, lacks basic understanding what a proof is)
- famouswaffles 2mo ago
  They don't have to be. At this point, we have multiple results from 3rd parties where the prompts are very basic. To name a few: - https://xcancel.com/DmitryRybin1/status/2079904005652893709 https://xcancel.com/DmitryRybin1/status/2079904005652893709 - https://archive.ph/2w4fi https://archive.ph/2w4fi (https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba9c https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba...)
- skinner_ 2mo ago
  No, that's not what this is. This is a warning to the LLM that coming back with partial results is not good enough. Take a grad student with a perfectly good understanding of what a proof is. Their supervisor gives them a major problem to work on. Almost always, the problem is too hard, the student comes back with partial results, and student and the supervisor iterate from there. Now imagine that they have an unusually cruel and unreasonable advisor who tells them, do not dare to talk to me until you've fully solved the problem. This paragraph is exactly that. It's there exactly because the underlying system is smart enough to know that real mathematicians do not work like that.
  - don_esteban 2mo ago
    If that was the case, that elaborate listing of all things that might look like a proof to a naive student, but are actually not proofs (and not even just partial results, but fundamental misunderstandings of what constitutes a proof) could have been easily and equivalently replaced by 'I am interested only in a full proof, don't bother me with partial results'. Yet, they were not. To a real mathematician you would not have to list those explicitly, he/she would have understood that implicitly from 'give me a full proof'. That listing makes sense to say only to somebody who pretends to be a mathematician, but has not true understanding of how the math works. The models are getting better and better in this pretension, but prompts like that reveal that it is still just a pretension, not a true understanding.
- mathisfun123 2mo ago
  you cannot be serious

don_esteban 2mo ago

the fact that such things have to be explicitly in the prompt points to the fact that the underlying system is still far from where it needs to be (basically, lacks basic understanding what a proof is)

famouswaffles 2mo ago
They don't have to be. At this point, we have multiple results from 3rd parties where the prompts are very basic. To name a few: - https://xcancel.com/DmitryRybin1/status/2079904005652893709 https://xcancel.com/DmitryRybin1/status/2079904005652893709 - https://archive.ph/2w4fi https://archive.ph/2w4fi (https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba9c https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba...)
skinner_ 2mo ago
No, that's not what this is. This is a warning to the LLM that coming back with partial results is not good enough. Take a grad student with a perfectly good understanding of what a proof is. Their supervisor gives them a major problem to work on. Almost always, the problem is too hard, the student comes back with partial results, and student and the supervisor iterate from there. Now imagine that they have an unusually cruel and unreasonable advisor who tells them, do not dare to talk to me until you've fully solved the problem. This paragraph is exactly that. It's there exactly because the underlying system is smart enough to know that real mathematicians do not work like that.
- don_esteban 2mo ago
  If that was the case, that elaborate listing of all things that might look like a proof to a naive student, but are actually not proofs (and not even just partial results, but fundamental misunderstandings of what constitutes a proof) could have been easily and equivalently replaced by 'I am interested only in a full proof, don't bother me with partial results'. Yet, they were not. To a real mathematician you would not have to list those explicitly, he/she would have understood that implicitly from 'give me a full proof'. That listing makes sense to say only to somebody who pretends to be a mathematician, but has not true understanding of how the math works. The models are getting better and better in this pretension, but prompts like that reveal that it is still just a pretension, not a true understanding.
mathisfun123 2mo ago
you cannot be serious