For reasoning a manually-curated dataset is too small; you need to be able to automatically generate vast volumes of synthetic reasoning data with provably corr

For reasoning a manually-curated dataset is too small; you need to be able to automatically generate vast volumes of synthetic reasoning data with provably correct answers. That's presumably why Claude and GPT are so good at using Lean (the theorem prover), because they get fed a bunch of synthetic, verifiably correct training data.