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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

#11

Post by zkmon »

> 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 design, communicating the force to the screw to turn it in a certain way.

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.

Re: Ten advances in mathematics and theoretical computer science

#12

Post by danielrmay »

emil-lp wrote: post #7
danielrmay wrote: post #4

I'm enjoying learning about these hard problems, but this line about credit made me chuckle: > We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness Offering to take responsibility for the correctness of a proof written in Lean feels like volunteering to be the fall guy in case someone finds a flaw in basic arithmetic, no?

No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.

I see. It still feels like a bit of an oddly solemn way of saying "this is the part we admit responsibility for"

Re: Ten advances in mathematics and theoretical computer science

#13

Post by emil-lp »

danielrmay wrote: post #12
emil-lp wrote: post #7

Earlier quoted context omitted.

No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.

I see. It still feels like a bit of an oddly solemn way of saying "this is the part we admit responsibility for"

Well, to be fair, with Lean proofs, that's the only thing there is (unless I'm missing something).

Re: Ten advances in mathematics and theoretical computer science

#14

Post by einpoklum »

aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar?

Another question I have is whether or not OpenAI 'simply' hired capable combinatorics researchers to work on problems, and they have, and the use of the model is incidental / secondary to their work.

Re: Ten advances in mathematics and theoretical computer science

#15

Post by NitpickLawyer »

zkmon wrote: 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…

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.

Re: Ten advances in mathematics and theoretical computer science

#16

Post by traes »

0x5FC3 wrote: post #9

How much do you all think it would cost to "buy" these advances from PhDs, practicing scientists?

This isn't really a productive way to think about these things, IMO. It's quite possible it would take hundreds of years for any specific group of PhDs to solve them. Or one individual PhD could have the correct flash of insight and solve it in a month. There's absolutely no way to predict this, besides trying to gauge the apparent simplicity of the proof or counterexample (which is likely to be misleading). Until someone actually runs an experiment like this it's not a viable metric.

Re: Ten advances in mathematics and theoretical computer science

#17

Post by baq »

piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

As in chess and go and also coding for the past ~year there are two groups of people: the disappointed and the enthusiastic. The disappointed are sad that they lost their advantage and that the craft they honed for years or decades has rapidly lost its value; the enthusiastic are excited about the future and what computers can bring to their domain and how it will evolve. I’m a bit of both if it comes to programming, more enthusiastic than disappointed, but also more than a bit terrified about the pace of it all. I imagine that’s how Kasparov felt back then, that’s how Lee Sedol felt and now that’s how Terry Tao feels.

The most disappointed folks will simply drop out, but the enthusiastic ones will keep going and with luck make up for the ones who decided to quit. Chess and go certainly went this way.

Re: Ten advances in mathematics and theoretical computer science

#18

Post by esikich »

zkmon wrote: 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…

Your brain also is physical. Electrochemical gradients flow between physical molecular constructs. Isn't it just chemistry? Do you attribute it to physics or some whole-is-greater-than-the-parts idea?

Re: Ten advances in mathematics and theoretical computer science

#19

Post by naasking »

zkmon wrote: 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?

Re: Ten advances in mathematics and theoretical computer science

#20

Post by anematode »

traes wrote: post #10
piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

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,…

Fully agreed. As someone who both loves chess and works on chess engines... these comparisons to chess needs to stop.
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