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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#51
post #11

> claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system’s contribution and the nature of genuine human intellectual work. AI has no self-awareness. It's a tool. When you assemble a furniture using a screw driver, the torque force interacts with the molecular forces inside the metal and miraculously it transfers the force to the screw though a clever geometry desig…

> AI has no self-awareness What is your mechanistic model of self awareness that yields this conclusion? > It's a tool Does your model suggest that tools can't have self awareness?

Dunno about the parent commenter, but I personally interpret the concept as having a hidden representation of self that is continually tended to, and influences future choices. This implies statefulness, which models are intentionally not at inference time (*).

(*) Even if we hack around this and just do the usual trick of simply laundering statefulness to a higher level, in this case the context window being fed in, I fail to identify (**) a representation of its own state in these bodies of text that it'd be meticulously maintaining. I further fail to identify how it could be hidden or maintained, considering I control like half of it. The best you could ascribe it is a meticulous maintenance of a persona the user is talking to, but then that doesn't necessarily represent the model's internal state, the same way my own words here aren't doing so either. Difference being, I actually have one (I'm "on-line").

You'll sometimes catch models mixing up who's who and how many who-s there even are for example.

(**) I did wish for something hidden though, so maybe it's just concealed? The same way people can encode a lot more of their emotional and mental state than normal into text if they read and write a lot of it, I'm aware of research that suggested the same for LLMs, albeit I cannot cite it. Maybe those phrasing signatures are just alien to me and will never pop out. Either way, I'd expect researchers to stumble upon this during interpretability studies, and either they haven't, they have but it wasn't popsci adopted, or they're keeping awfully tight lipped about it. If you know of anything like this, your turn now, would be happy to learn.

I do wonder how reasonable it is to expect e.g. a single maintained identity though. Maybe it isn't?

(*) Another way to hack around this of course is to just precompute some internal "self-awareness states" and hop around between them. Probably the closest to what the models are actually "doing".

Re: Ten advances in mathematics and theoretical computer science

#52
post #5

I wonder what the total cost of this research was, including the salary for their mathematicians and engineers.

Given that OpenAI pays their employees with stock surely a breathtaking number, but not a very meaningful number now that the infrastructure is in place and the models are trained. AI could never get better and it would still be incredibly disruptive.

Re: Ten advances in mathematics and theoretical computer science

#53
post #49
post #5

I wonder what the total cost of this research was, including the salary for their mathematicians and engineers.

> The cost of generating the proofs for all 10 of these breakthroughs combined was under $2,000 at Sol API prices. https://x.com/polynoamial/status/2083470822258467194

That's clearly just for the tokens, this doesn't really answer OP's question.

Re: Ten advances in mathematics and theoretical computer science

#54
post #11

> claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system’s contribution and the nature of genuine human intellectual work. AI has no self-awareness. It's a tool. When you assemble a furniture using a screw driver, the torque force interacts with the molecular forces inside the metal and miraculously it transfers the force to the screw though a clever geometry desig…

> Do you attribute the build to the tool? The "system's contribution" is helped by many other things all the way down to chips, datacenters and power generation. If the authorship requires attributing to a tool, then it should happen all the way down.

When the tool is a 3D printer, or any CNC system really, you bet I attribute a build to it.

I could also attribute the operator; there is no contradiction, it's a free choice, just like saying "I am in Berlin" does not contradict "I am in Germany".

Re: Ten advances in mathematics and theoretical computer science

#55
post #26
post #10

Earlier quoted context omitted.

Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess,…

Another noteworthy difference is that Stockfish is also gpl.

If there was any real money in it Stockfish would not be the best chess engine.

Re: Ten advances in mathematics and theoretical computer science

#57
post #42

Earlier quoted context omitted.

The level of conspiracy theory is nuts

I would say the lack of skepticism is nuts, honestly.

Capabilities of this sort have already been demonstrated by independent parties, and models have consistently gotten better at this. Yes, insinuating that mathematicians and scientists are secretly solving decades-old problems on OpenAI's behalf is an insane conspiracy theory.

Re: Ten advances in mathematics and theoretical computer science

#58
post #25

Earlier quoted context omitted.

A better analogy would be a manufactured object, say 3d printed for simplicity. The 3d printer is given an input, and an object manifests itself after some time. We say that the creator of the object is the person turning on the machine, sending the data, and collecting the object. Not the machine itself.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

I would say „I made this gadget with my 3d printer, but the designer is someone else (I found the model online)“. The intent, the drive, the action comes from the human

Re: Ten advances in mathematics and theoretical computer science

#59
post #45

Earlier quoted context omitted.

[flagged]

It's a very important clarification if it took $2000/problem on 20 problem attempts or on 1,000 problem attempts for each successful one. That may be the deciding factor on whether or not it's economically viable to replace a mathematician with a ChatGPT subscription.

Yeah fair I concede that this is somewhat crucial information. The parent seems to write it in a tone that suggests deliberate misleading “lack of transparency” etc.

Re: Ten advances in mathematics and theoretical computer science

#60
post #58
post #25

Earlier quoted context omitted.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

I would say „I made this gadget with my 3d printer, but the designer is someone else (I found the model online)“. The intent, the drive, the action comes from the human

"I made this proof myself, but the designer is someone else" is an extremely unconvincing claim to ownership.
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