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.
I think the argument is that OpenAI should have done the work of cleaning up the proofs in the first place before dumping them onto the math community (or worked with mathematicians to guide the research process). It's as if an energy company dumped 20 tons of waste next to a village and the townspeople decided to clean it up. "How does this benefit the energy company" might not be the right question to be asking.
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.
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 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.
But pure math is a game that only cares about the rules and definitions as you choose to define them. It's not about understanding the world at all. The application of math in science (which is about understanding the world) is usually (but admittedly not always) after the fact.
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.
Sounds like a 2x2 matrix.
This is OpenAI’s etc version of getting unpaid internships from phd students
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.
I think the argument is that OpenAI should have done the work of cleaning up the proofs in the first place before dumping them onto the math community (or worked with mathematicians to guide the research process). It's as if an energy company dumped 20 tons of waste next to a village and the townspeople decided to clean it up. "How does this benefit the energy company" might not be the right question to be asking.
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.
This experiment might be relevant: https://github.com/offline-ant/wiggums-proof-loop
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?
We should burn the excavators and dig holes with our hands.
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.
A rather sad state of affairs...
But pure math is a game that only cares about the rules and definitions as you choose to define them. It's not about understanding the world at all. The application of math in science (which is about understanding the world) is usually (but admittedly not always) after the fact.
And now they can train on everything this community does. And with new models this community won't be needed anymore.
right, and this would be a positive for the world.
We’ve seen time and time again that "a positive for the world" is not something these companies align on
It might be a positive. It might not be. Better to have some humility about the situation.
There are always people left behind by technological changes. Better move forward than cling to the past.
Is your implication that progress is always generally positive for the average person?
My implication is that being left behind is worse than other choices.
For a world. A world some people will not be part of.
Yes, only Nvidia should exist. r/accelerate nutcase?
Have we ruled out Trisolarian involvement? IYKYK