Math is definitely just a language. It is a combination of symbols and a grammar about how they go together. It’s what you come up with when you maximally abstract away the real world, and the part about not needing any grounding was specifically about abstract math, where there is no real world.
Verifiable is obviously important for training (since we could give effectively infinite training data), but the reason it is verifiable so easily is because it doesn’t rely on the world. Also, note that programming languages are also just that, languages (and quite simple ones) but abstract math is even less dependent on the real world than programming.
Math is definitely just a language. It is a combination of symbols and a grammar about how they go together. It’s what you come up with when you maximally abstract away the real world, and the part about not needing any grounding was specifically about abstract math, where there is no real world.
Verifiable is obviously important for training (since we could give effectively infinite training data), but the reason it is verifiable so easily is because it doesn’t rely on the world. Also, note that programming languages are also just that, languages (and quite simple ones) but abstract math is even less dependent on the real world than programming.