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