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I dunno, I'm skeptical without proof. I've had the MAX+ plan for a while and I'm sorry, the quality between GPT vs Claude is night and day difference. Claude understands. GPT stumbles over every request I give it.
Weird thing to say about a report which literally has the attached mathematical proof.
Important note: this was not done with a special mathematics harness or specialized workflow.
Earlier quoted context omitted.
what basis do you have for assuming an LLM is fundamentally incapable of doing this?
Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)
As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.
However, this was not verified in Lean. This was purely plain language in and out. I think, in many ways, this is a quite exciting demonstration of exactly the opposite of the point you're making. Verification comes in when you want to offload checking proofs to computers as well. As it stands, this proof was hand-verified by a group of mathematicians in the field.
For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool…
One thing seems for certain is that OpenAI models hold a distinct lead in academics over Anthropic and Google models. For those in academics, is OpenAI the vendor of choice?
Gemini seems better trained for learning and I think Google has made a more deliberate effort to optimize for pedagoical best practices. (E.g. tutoring, formative feedback, cognitive load optimization) As far as academic research is concerned (e.g. this threads topic), I can't say.
Earlier quoted context omitted.
what basis do you have for assuming an LLM is fundamentally incapable of doing this?
Because by definition LLMs are permutation machines, not creativity machines. (My premise, which you may disagree with, is that creativity/imagination/artistry is not merely permutation.)
can we please put these ground breaking AIs to work on actual problems humans have?
To the “LLMs just interpolate their training data” crowd: Ayer, and in a different way early Wittgenstein, held that mathematical truths don’t report new facts about the world. Proofs unfold what is already implicit in axioms, definitions, symbols, and rules. I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. So either “recombining existing material” isn…
I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.
Said differently, what is prediction but composition projected forward through time/ideas?