281–290 of 1001 posts
Is there a reason why we only hear of Erdos problems being solved? I would imagine there are a myriad of other unsolved problems in math, but every single ChatGPT "breakthrough in math" I come across on r/singularity and r/accelerate are Erdos problems.
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I'd hope most functional adults understand that the Fields Medal and basically every other annual "prize" out there is awarded to both "recombinant" innovations and "new-dimensional thinking" innovations. Humans aren't going to come up with "new-dimensional" innovations in every field, every single year. I'd say yes, LLMs "just" recombine things. I still don't think if you trained an LLM with every pre-Newton/Liebniz…
> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) The experiment is feasible. If it were performed and produced a positive result, what would it imply/change about how you see LLMs?
This is impressive, no question. Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain origi…
Seems like a very tin-foil-hat-take to me
I like how everyone laughed when OpenAI said their models will have "PhD-Level Intelligence" and now the goalpost has been moved to if AI can create new math (i.e., not PhD-Level, but Leibniz/Euler/Galois level.)
What was discovered were numerous mistakes in the published literature on the subject. “New math! AI!” No, just mechanical application of rules, human mistakes.
There were things that were theorized, but couldn’t be exhaustively checked until computers were bigger.
Once again, a tool is applied, it has the AI label - its progress! But it isn’t something new. It’s just an LLM.
There’s a consistent under appreciation of AI (and math, honestly), but watching soulless AI mongers declare that their toy has created the new is something of a new low; uninspired, failed creatives, without rhyme or context; this is a bigger version of declaring that your spell checker has created new words.
The result is more impressive than what was done with tables of integrals and SAINT in 1961, sure.
Apparently if you add a “temperature” knob to a text predictor, otherwise sane individuals piss themselves and call it new.
Then again I thought NFTs, crypto, and the Metaverse were stupid, so what do I know.
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> I think that idea is deeply fascinating, AND have no problem that we still credit mathematicians with discoveries. Most discoveries are indeed implied from axioms, but every now and then, new mathematics is (for lack of a better word) "created"—and you have people like Descartes, Newton, Leibniz, Gauss, Euler, Ramanujan, Galois, etc. that treat math more like an art than a science. For example, many belive that to…
Creation is done by humans who have been trained on the data of their life experiences. Nothing new is being created, just changing forms. A scientist has to extract the "Creation" from an abstract dimension using the tools of "human knowledge". The creativity is often selecting the best set of tools or recombining tools to access the platonic space. For instance a "telescope" is not a new creation, it is recombinati…
Humans and animals have intuitive notions of space and motion since they can obviously move. But, symbolizing such intuitions into forms and communicating that via language is the creative act. Birds can fly, but can they symbolize that intuitive intelligence to create a theory of flight and then use that to build a plane ?
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I feel this is the case whenever I "problem solve". I'm not really being creative, I'm pruning a graph of a conceptual space that already exists . The more possibilities I see, the easier it is to run more towards an optimal route between the nodes, but I didn't "create" those nodes or edges, they are just causal inevitabilities.
I dont know this sort of just seems like youre really stretching the meaning of "creative". The conceptual space of the graph already exists, but the act of discovering it or whatever you want to call that is itself creative. Unless youre following a pre-defined algorithm(certainly sometimes, arguably always I suppose) seeing the possibilities has to involve some creativity.
I would claim the graph exists, and seeing it is more of an knowledge problem. Creativity, to me, is the ability to reject existing edges and add nodes to the graph AND mentally test them to some sufficient confidence that a practical attempt will probably work (this is what differentiates it from random guessing).
But, as you become more of an expert on certain problem space (graph), that happens less frequently, and everything trends towards "obvious", or the "creative jumps" are super slight, with a node obviously already there. If you extended that to the max, an oracle can't be creative.
My day job does not include sparse graphs.
This is impressive, no question. Without knowing all this model has been trained on though, it is pretty hard to ascertain the extent to which it arrived to this "on its own". The entire AI industry has been (not so secretly) paying a lot of experts in many fields to generate large amounts of novel training data. Novel training data that isn't found anywhere else--they hoard it--and which could actually contain origi…
Seems like a very tin-foil-hat-take to me
edit: >> https://techcrunch.com/2025/10/19/openais-embarrassing-math/
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> I still don't think if you trained an LLM with every pre-Newton/Liebniz algebra/geometry/trig text available, it could create calculus. (I'm open to being proven wrong.) The experiment is feasible. If it were performed and produced a positive result, what would it imply/change about how you see LLMs?
How are you going to train a frontier level llm with no references to post 1700 mathematics?
There are people working on this.