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| ▲ | porphyra 5 hours ago | parent | next [-] |
| Yup I linked that in my other comment but copy-pasted here for everyone's convenience: The counterexample of the Dinitz-Garg-Goemans conjecture was basically just "keep going" and finally "enough of partial results. now finish with a complete unconditional counterexample" https://x.com/DmitryRybin1/status/2079904005652893709 https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0... |
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| ▲ | colechristensen 5 hours ago | parent | prev [-] |
| Yes, we're in the low hanging fruit stage where folks can just say "here's the problem" and "keep going" until a result is found and it will work sometimes. The low hanging fruit will run short. Ultimately mathematics is a field of subjective selections of problems and proofs as beautiful and interesting. Machines absolutely will struggle with what to study, what theorems are desirable, and when do be done with a proof. |
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| ▲ | bonoboTP 5 hours ago | parent | next [-] | | > Machines absolutely will struggle with what to study, what theorems are desirable, and when do be done with a proof And why do you think this would be the case? I'm not talking about today but in 1-2 years. For reference o1 was released less than 2 years ago, and we've had reasonable coding agents for 9 months or so. | | |
| ▲ | colechristensen 4 hours ago | parent [-] | | > why do you think this would be the case? Mathematics is ultimately an aesthetic pursuit. Outside of a well defined goal ML models don't have any sense of taste and regardless of the scaling that's been enabled in the last year or so of capability if they haven't memorized the process of doing something they have the same limitations of inability to make choices about unknowns not trained into them. Real synthetic intelligence seems to me to be still very far away and not a matter of making models bigger or more efficient. |
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| ▲ | pixl97 4 hours ago | parent | prev [-] | | While they may struggle on what to study, we'll be able to spin up millions of them. |
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