Feels like we need a new truth-state for mathematics: "Verified-but-Unproven" for results which we know to be true through formal verification, but without any coherent proof.
I would generally expect this state to resolve quickly to "Proven and Verified" (the tendency in mathematics historically has been for complicated first-proofs of results, followed by significant reductions in proof complexity as new tools and definitions become available), but may still be useful for assigning real credit to who/whatever produces reasonable proof for a brute-force-verified result.
> I would generally expect this state to resolve quickly to "Proven and Verified" (the tendency in mathematics historically has been for complicated first-proofs of results, followed by significant reductions in proof complexity as new tools and definitions become available),
A bit of an oversimplification, I think. Definitely there are some simplifications, but I wouldn't say really significant to the point where "resolve quickly" follows, along the lines of what you said.
Most complicated math is still nearly as complicated as when it was invented. Simplifications to presentation maybe, and some reduction in the proof difficulty yes, but not to the point of being significant in the way you describe. Any modern result that has been around for 20 years likely hasn't undergone a serious simplification, for example.
How does any of this benefit OpenAI? They already got the headlines, it's not like its going to be front page news when the mathematical community actually understands the results that have already been claimed.
The announcement doesn't say that the work will be using openai tools. If anything, the events over the past two months provide strong incentive to boost the capabilities of open-weight, local models.
I personally would never participate in this. I think clarifying proofs generated by a machine is a contemptible way to spend time. A lot of people will ask, isn't the purpose of math to generate results? I don't think so. I think the purpose of math is to gain a precise and clear understanding of the world through a shared human practice of math - human only.
I know most people here will disagree because most people here are at the top of the consumption food chain of just consuming the latest and greatest of whatever the world produces, so why not have more to consume? But slowly the joy is being sucked out of the world by AI for those not at the top and being replaced the narcissistic activity of enjoying superficial sensory stimulation in a vacuum.
The authors are all in computational mathematics and AI. This is the soft power version of the OpenAI repo to get people to work for free. Maybe call it OpenOpenAI.
If mathematicians didn't enjoy digging their own graves with formalization before, perhaps they will enjoy digging their own unmarked, mass graves now?
I would generally expect this state to resolve quickly to "Proven and Verified" (the tendency in mathematics historically has been for complicated first-proofs of results, followed by significant reductions in proof complexity as new tools and definitions become available), but may still be useful for assigning real credit to who/whatever produces reasonable proof for a brute-force-verified result.
A bit of an oversimplification, I think. Definitely there are some simplifications, but I wouldn't say really significant to the point where "resolve quickly" follows, along the lines of what you said.
Most complicated math is still nearly as complicated as when it was invented. Simplifications to presentation maybe, and some reduction in the proof difficulty yes, but not to the point of being significant in the way you describe. Any modern result that has been around for 20 years likely hasn't undergone a serious simplification, for example.
I know most people here will disagree because most people here are at the top of the consumption food chain of just consuming the latest and greatest of whatever the world produces, so why not have more to consume? But slowly the joy is being sucked out of the world by AI for those not at the top and being replaced the narcissistic activity of enjoying superficial sensory stimulation in a vacuum.
A rather sad state of affairs...