> we ask them to stop testing advanced mathematical problems on proprietary models.

Maybe I'm alone on this, but for some reason these sorts of requests strike me as akin to gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop.

Ensuring credit where credit is due? That's fine. If your model incorporates the efforts of many others, then it's reasonable to request acknowledgement of everyone who contributed (even indirectly). But that's not what the request states — presumably their ask subsumes any advanced ML model, including those that weren't trained on a giant corpus of text.

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.

For every important match problem solved by AI, without mathematicians we wouldn't know about the existence and importance of the problem.

Famous mathematical conjectures are social constructs, formed by decades of even centuries of attention given to them by members of the math community. Without it, the danger is that future math "progress" will be reduced to generating tables of Lean statements and a probable/unprovable bit generated by AI.

Either mathematical progress helps advance society, in which case progress is a good thing.

Or mathematics is more like a hobby, and while ai may spoil their fun, they need to move on like chess and go players.

I saw an interview (in French) of Cédric Villani, speaking on behalf of him and other Fiels medalists, who said that in order to advance mathematics we need three things:

- ideas

- students

- problems

Basically, students to bring original ideas to try and solve existing problems and this generates new ideas and possibly new problems for new students to try and solve with new ideas and so on.

And he continued to say that the issue with LLMs in mathematics, is that he's afraid they could run out of problems, and so students wouldn't bother trying, and this could hurt understanding of mathematics as a whole.

It's totally not my field so I'm not sure what to think of it but it seems important

As an answer to AI companies, this is so bad: instead of trying to find a path to a win-win-ish solution with some trade-offs, this says: sorry, we cannot think of any, so just stop making money, will you? Math needs better crisis managers.

But as an idea, this is even worse: does it mean to stop potential research to cold fusion, cancer and anything as long as it may touch some mathematician's interests, or does it mean math is so hopelessly irrelevant that this cannot be the case... Again, as a crisis manager, this is not how you pose it.

Makes me wonder, were they hired by Sam to sabotage?

> However, it is now the case that AI can output mathematical arguments in situations without the human who prompted it being able to understand the arguments, verify them, or take responsibility for them.

I read this as "anybody can prompt, few can understand". And "we need more who can understand". If we had more mathematicians (than we have today) all of them piloting advanced models, the pie would grow. The problem is that AI capabilities drain (by disincentivizing) the education pipeline that would get us those mathematicians, and if recent rumbles about what AI is doing to education are to be believed, it does so many years before students even get to grad school.

IMHO, it is not that bad. Not having any human who understands linear algebra after the Butlerian Jihad is a win :-) .

This paper wants AI companies to pay human mathematicians to understand AI-generated stuff. That's an unusual ask.

I applied to the caltech mathaton.

While applying, I looked at the current SoTA, (briefly) read through some of the papers, and realized that I am very far away from understanding them.

Understanding one of these proofs is the work of several months, years or lifetimes depending on whether or not something clicks. It requires a kind of stamina that I quite frankly don't have, but I would like to develop.

If the mathaton's organizers accept my team, I realized that I would spend the next few years working through the result.

So why apply to the Mathaton?

"Many years ago the great British explorer George Mallory, who was to die on Mount Everest, was asked why did he want to climb it. He said, 'Because it is there.'

Well, [theoretical math] is there, and we're going to climb it, and [topology] and [number theory] are there, and new hopes for knowledge and peace are there. And, therefore, as we set sail we ask God's blessing on the [~~most hazardous and dangerous and greatest adventure~~] on which [we have] ever embarked."

More seriously, I applied because I was hoping to get access to the models without the veil. I don't think people realize just how big the gap is between what exists behind the scenes at these entities, and what we get out here.

And it's frustrating. Because I think it's within the rights of frontier labs to decide whether or not to sell access to a product, but the labs aren't just doing that. They're trying to thumb the scale to make sure that none of us ever get access to these models at peak performance. Ever.

And I think humanity is worse off for that. I am worse off for that.

I have studied the shape and structure of historical technological revolutions (and I've written about it), and usually the world doesn't realize how big of a big deal the big deal is because the big deal is often flawed, broken, and under-delivers. In the short term.

In the long term...? The world changed in the past few months. I think mathematics is one small part of that.

For most of human history, higher mathematics would have been inaccessible to me, and other outsiders, no matter how well heeled. Mathematics is, or rather was, a living discipline that existed piecemeal in a handful of minds across the world. These people's time was finite and valuable. To just meet them, you'd have to jump through hoops, and spend years proving yourself.

There is no price for an hour of tutoring from Terence Tao. But now, with AI? You can have an entity with the capabilities of Terry Tao help you understand the subtleties of math.

AI has changed what mathematics is. And every prominent mathematician seems to know it. They feel like mathematics has been devalued, and in some ways it has. Mathematics has gone from being a living discipline kept alive by a chosen few to a wellspring everyone can sip from. For the first time in human existence, learning and accessing higher mathematics doesn't involve jumping through hoops and knowing the right people. You can just ask.

I can just ask.

Except I can't. Because that capability is being gate kept. And I want to know. I want to climb the mountain.

Honestly what is "AI generated math"?

Everything is WFFs all the way down

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I disagree with this.

OpenAI should be allowed to produce whatever it wants but it just can't claim that it has actually solved without the due process like peer review. If for example OpenAI solves a new conjecture, OpenAI should be free to publish it in their blog or arxiv in whatever way they desire. It can be slop, it can be non-slop. No one should police it.

Mathematicians are free to use it or discard it. They shouldn't externalise their concerns and restrict labs.

Mathematics is seen today as the noblest and most aristocratic of professions. Turns out, AI disrupts it because access to capital/compute now decides the results. Mathematicians don't like this corruption - understandable.

Its like guild of accountants opposing the calculator and require a responsible release. haha

Luddites are life-deniers and engage in extreme amounts of slave morality. Reject them with extreme prejudice in every context.