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Totally agreed that having rigorous engines that are able to provide synthetic training will massively help progress. But my sense is that the data they can generate is still of the type, "This works," "This doesn't work," or, "Here is a counterexample." Which can still be massively useful, but may still run into the context/problem definition/"elegance" concerns. Given that the back ends are getting good enough to provide the yes/no/counterexample results, I think it's highly likely that LLMs will become solidly good at translating human problems statements into rigorous problem statements for the back end to evaluate, which will be a huge help to the usefulness of those systems... but the jury is still out in my mind to what extent they'll be able to go further and add appropriate context. It's a lot harder to find data or synthetic data for that part.
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