I'm surprised some people think this is a matter of checking whether formal sentences match some English sentences lol
It is a matter of checking whether formal sentences match mathematical statements, which are written in natural language.
Imagine someone saying "just write good English lol eventually you can do good math". I'm aware you're not quite saying this but you seem really distracted by the human language representation of math, connecting doing math proofs to generating English sentences from some probability distribution is ridiculous. Of course it is possible LLMs can do math, if it's matter of having nonzero chance, there's also a nonzero chance we are all brains in vats. More rationally if someone says something is possible they should produce some evidence that it is possible. And then we decide whether that evidence is good enough.
Writing well in any human language is not good enough, since it is entirely different from being able to tell whether a set of formal axioms capture certain ideas about a mathematical structure. This is a model theoretic issue. Neural network theorem provers deal with proof theoretic issue.
The best LLM-Lean provers right now are tackling the very challenging problem of how to generate the right sequence of tactics for infinite search space, all relying on, excuse me, undergrad students to formalize proofs and statements for them.
Would you trust a brand new assistant to write up an email for you without proof reading it? How much training would they require before you didn't need that step? How much training / fine-tuning would an LLM need? What about the next gen LLM?
Remember, we're not talking about a static target here, and the post I replied to set no qualifications on the claim that a human will always be needed to check that a mathematical definitions in the proof match the English equivalents. That's a long timeline on a rapidly moving target that is, as I said, already seems to be better than most humans at understanding and writing English.
> Would you trust a brand new assistant to write up an email for you without proof reading it?
Depends on the complexity, but for the simpler things I think I could get confident in a day or so. For more complex things, it might take longer to assess their ability.
But I'm not going to trust LLM blindly for anything.
> I replied to set no qualifications on the claim that a human will always be needed to check that a mathematical definitions in the proof match the English equivalents.
I don't defend this strong claim and limit my answer to LLMs (and mostly just state of the art). OTOH I believe that trust will continue to be a big topic for any future AI tech.
> But I'm not going to trust LLM blindly for anything.
Again, what does "blindly" mean? Suppose you went a month without finding a single issue. Or two months. Or a year. The probability of failure must literally be zero before you rely on it without checking? Are you applying the same low probability failure on the human equivalent? Does a zero probability of failure for a human really seem plausible?
Constructing a sentence is only the last step in writing, akin to pressing the shutter release on a camera.
LLMs can turn a phrase but they have nothing to say because they do not experience the world directly. They can only regurgitate and remix what others have said.
This doesn't seem to follow. Why kind computers get better at doing this (anticipating what humans want or whatever) than people? Some people are better at it than others and people are not magic, so I'd guess at some point computers will get it too.