Comment by freehorse

> That's not my site.

You brought the figure as an argument, so I assumed that was your argument? If not, what was your argument then? I see a (super)exponential fit, but I don't see why that's better than a logarithmic fit on these axes (which would imply linearity). For covid we know well about infection disease dynamics. We do not have good models for AI because we do not have prior experience. Even the data points here are obviously noisy (why is sol that higher than fable, which does not seem to reflect how people consider these models?).

> At what point did you predict the following? [...] explosion of AI-generated proofs [...]

My question is, who is gonna pause the questions that AI is gonna solve? Who is gonna decide which research directions are interesting to pursue? Who is gonna take a proof technique and generalise it into a theory and a new mathematical field and structures and associated questions? Who is gonna decide which such generalisations are interesting to pursue?

So there are 3 scenarios I see possible as to who will lead the research directions/questions:

1. Humans. If so, I don't see the explosion as a big issue, because the bottleneck for progress on mathematics is gonna stay on the human side and rhythms. There is gonna be an acceleration in getting new proofs faster, but a big part of mathematicians' job is not to write proofs but, essentially, pose interesting questions.

2. AI. The only way that I see this explosion as "human mathematicians losing control" is if AI can itself generate new questions and somehow dictate which paths are interesting. That would mean that AI has developed a "taste", which is not clear that this happens or will happen soon.

3. Nobody really. There is also the other option, that nobody does, and somehow the biggest part of theoretical mathematics stagnates and/or becomes a more superficial endeavour. Accompanied by associated budget cuts this scenario does not seem too unrealistic either.

Verifying solutions itself is the "easy" part when talking about automating proof generation, a proof will either be verified in lean or not be trusted. Lean will continue expanding to include more and more mathematics, and that's it. It will become more and more common to ask for lean verification at journal submission, depending on the field and how much it has been formalised in lean. The real question imo is "who is gonna understand the math produced and set new research directions".