Who Taught the Machines Mathematics?

I'm reading this paragraph with the precedent of AlphaGo in mind, where none of the Go players would have expected that databases of human games would be valuable training material for machines instead of humans:

> I learned mathematics because others gave their time and knowledge freely, and I wanted to do the same for the next generation. The possibility that a student would go on to do something I could not do was part of the point. But I had imagined this as a continuation of a human activity. [...] I could not imagine treating this knowledge as something to be guarded.

But soon after, AlphaZero was trained purposefully without human games in the training data. The "extractive" training was sufficient to show that a certain machine learning model worked, but unnecessary to produce a machine that performs beyond the level of humans.

For coding agents I imagine it is similar: humans introduce so many subtle bugs, and they're only subtle relative to human cognitive capacity. I'm sure subtle mistakes pass peer review in mathematics too, even if it's generally more rigorous.

What I'm getting at is that labs have demonstrated that a certain model architecture is capable of producing mathematics at a (super)human level, and their extractive methodology was sufficient, but possibly not necessary. You can fight in court whether their methodology is against the law, but it would be naive not to look beyond that, which is my main gripe with the AHM statement the author refers to [1]

Fortunately the author of this article has a more nuanced view:

> I can understand the anger, but I am not sure that withdrawing from AI is the answer

[1] https://www.ahmath.org/statements

One thing I don't yet understand and would appreciate an opinion from a professional mathematician is: are we okay with mathematicians that outsource the discovery of new theorems to AI while providing verification services themselves?

For instance, imagine a mathematical institute that hires reasonably competent mathematicians who are amazing AI prompters but lack mathematical creativity or "genius". All they produce are mathematical papers with clear proofs and explanations. Very human readable stuff. But the catch is that they are not discovering any of it. All they are doing is "translating" full AI discoveries into a format others can understand.

Is that acceptable?

Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?

FWIW, it reads very similar to the woes of the SWEs previously, in the sense that it kinda appears like people assigned value to the wrong part of the work within the discipline?

The take-away of it being it being imperative to have open weights models accessible to all, instead of cloud-hosted models owned by few is of course true regardless of those specifics, but it gets a bit muddied by that, which is a shame, as that will be weaponized to dismiss it.

If you read any classic mathematics or computer science textbook, you get the sense that the author wants to impart the idea that this subject leads to an interesting and meaningful life. There are many famous quotes about being the architect or designer of an idea rather than just a technician holding a power tool following instructions someone else wrote. Now all of those adages have become effectively meaningless because so many involved in these careers are cool with the industry dying for some vague notion of progress due to a machine god. It’s a pathetic state of affairs that the elders aren’t speaking out more to protect the next generation of human thinking.

I say this as someone who uses LLMs in the physical sciences (one of the only areas where I would say it is ethical to use them).

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