> They're clearly cost effective for frontier AI firms

It's not obvious that this is a given. "Cost-effective" implies a comparison between cost and output. OAI spent millions to race human researchers on Navier Stokes, and that doesn't even account for the training cost. And how does one value the output? OAI is for some reason still hiring armies of humans instead of automating roles like "AI support engineer" or "Product Designer" (https://openai.com/careers/search/).

Calling the proofs a "side-product" is also rather dubious when OAI employs a team of mathematicians specifically to train its theorem proving capabilities.

Yeah, right now the juice isn’t only about the progress of math - it’s also the advancement of the LLM tech and the marketing benefit to the AI companies which feeds back into developing the tech. Those each have a different juice to squeeze ROI.