Mostly pretty straight forward. The idea that proofs be desloppified, attribute existing literature properly, and published somewhere expediently where it can be commented on, with artifacts for verification, is all very uncontroversial stuff.
I think the spicy take is definitely this stance that longstanding mathematical problems shouldn't be used as benchmarks for (specifically proprietary) models. Stated right at the very top.
The justification is pretty clear.
> The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline.
It is all fun and games (for non mathematicians) when mathematicians can't compete with AI labs but I think the more dangerous direction is when this starts being true for the rest of everything. For example cybersecurity or whatnot. Hence why I think Anthropics whole stance of being completely against open anything is actually *extremely* dangerous due to the centralization of power which they completely ignore as a risk factor.
The most discussable thing in this is certainly the idea that labs should fund mathematicians to do expositions.
> One of our principles is that AI labs have a responsibility to provide support, including funding, for the development of human understanding of the AI mathematical output that they release.
Obviously this directionally sounds like the role of mathematicians would be shifting towards interpreting AI results instead of making proofs. I'm not sure who would should really be billed for that. Plus how would you decide who gets the grant?
An interesting thing is that by stating that that the lab that dropped the result provide the funding, this is *directly* proposing an example of taxing AI labs for displacing knowledge workers.
Am I the odd one, or is this, like... absolutely insane logic?
"The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline."
Are mathematicians' private brains unfair if they're way better at solving open math problems than anyone else? Are they required to share everything they're working on, as they're working on it?
Should Andrew Wiles have been condemned? Wouldn't these arguments all have applied to him? Besides him working at more human speeds.
It's not insane when you realize that in mathematics, the goal isn't theorems (we have always been able to generate correct theorems, this is a basic programming exercise).
The goal is to expand and extend our understanding.
When an LLM produces a proof, nobody (including the LLM) gained new understanding ... Unless, of course, a human being sits down and understands it, and communicates the new understanding to the broader community.
The insane part is placing the burden on AI labs to advance mathematical understanding. Why should this be their responsibility?
If they want to simply generate theorems and proofs and post them on the internet, why not? Does doing that really inflict "substantial negative externalities ... on the mathematical community"?
If math is a "burden" on AI labs, why do they willingly spend tens of millions of dollars for a purely theoretical and unphysical result? What's the ROI for that when the frontier labs are already notoriously cash-strapped? Their motives pervade the entire discussion and cannot be ignored here.
...Could you not ask this of anyone who works on pure math problems? What on Earth are you talking about??
"Academics are paid paltry salaries, university departments are cash-strapped, why are they studying these abstruse math problems instead of building rockets?"
Successfully advancing fields of math and science is a good thing. Why would they not do it. Why would they not want to prove their increasingly intelligent computers are able to solve unsolved, complex math problems humans have failed to solve for centuries and then release the solutions to the public. What do you want them to do, not try to solve them?
They are not advancing the field. At least they didn't in the case of the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.
kingstnap · · focus · HN ↗
I think the spicy take is definitely this stance that longstanding mathematical problems shouldn't be used as benchmarks for (specifically proprietary) models. Stated right at the very top.
The justification is pretty clear.
> The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline.
It is all fun and games (for non mathematicians) when mathematicians can't compete with AI labs but I think the more dangerous direction is when this starts being true for the rest of everything. For example cybersecurity or whatnot. Hence why I think Anthropics whole stance of being completely against open anything is actually *extremely* dangerous due to the centralization of power which they completely ignore as a risk factor.
The most discussable thing in this is certainly the idea that labs should fund mathematicians to do expositions.
> One of our principles is that AI labs have a responsibility to provide support, including funding, for the development of human understanding of the AI mathematical output that they release.
Obviously this directionally sounds like the role of mathematicians would be shifting towards interpreting AI results instead of making proofs. I'm not sure who would should really be billed for that. Plus how would you decide who gets the grant?
An interesting thing is that by stating that that the lab that dropped the result provide the funding, this is *directly* proposing an example of taxing AI labs for displacing knowledge workers.
meowface · · focus · HN ↗
"The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline."
Are mathematicians' private brains unfair if they're way better at solving open math problems than anyone else? Are they required to share everything they're working on, as they're working on it?
Should Andrew Wiles have been condemned? Wouldn't these arguments all have applied to him? Besides him working at more human speeds.
emil-lp · · focus · HN ↗
The goal is to expand and extend our understanding.
When an LLM produces a proof, nobody (including the LLM) gained new understanding ... Unless, of course, a human being sits down and understands it, and communicates the new understanding to the broader community.
Calazon · · focus · HN ↗
If they want to simply generate theorems and proofs and post them on the internet, why not? Does doing that really inflict "substantial negative externalities ... on the mathematical community"?
curt15 · · focus · HN ↗
meowface · · focus · HN ↗
"Academics are paid paltry salaries, university departments are cash-strapped, why are they studying these abstruse math problems instead of building rockets?"
Successfully advancing fields of math and science is a good thing. Why would they not do it. Why would they not want to prove their increasingly intelligent computers are able to solve unsolved, complex math problems humans have failed to solve for centuries and then release the solutions to the public. What do you want them to do, not try to solve them?
pegasus · · focus · HN ↗