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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

#61

Post by esikich »

yaqubroli wrote: post #43
raincole wrote: post #32

Earlier quoted context omitted.

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

The human provides the intention and the ability to appreciate the output. Tools do “heavy lifting” all the time, but we still primarily credit the humans who use them precisely because they made the choice to use them. Provability is just going the way of computation. John Napier had to manually compute logarithm tables over decades and was recognised for his work; now that same work could be performed by a 10 year…

What gives the intention and ability to the human?

Re: Ten advances in mathematics and theoretical computer science

#62

Post by traes »

lifeisstillgood wrote: post #47

On the token limits etc - one assumes that OpenAI et al are able to “hire expert in field, and let them spend the equivalent of a million dollars of tokens” because they are not actually selling their complete compute 24 hrs a day, so the cost internally is a negligible (ish) electricity bill. Which is very suggestive - if after everything they are not fully loaded then the next gazillion data centres being built loo…

Presumably it's a rounding error compared to their full output, and they're making sure they have enough compute set aside for research by limiting public models. The more datacenters they build the less they have to limit them.

Re: Ten advances in mathematics and theoretical computer science

#64

Post by zkmon »

raincole wrote: post #32
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…

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

When you use a crane to do the "heavy lifting" for construction work, do you give full credit to the cranes?

Re: Ten advances in mathematics and theoretical computer science

#65

Post by piker »

jibal wrote: post #46
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…

The chess analogy is awful. If you simply want to know the answer to a chess problem, give it to the engine. Chess only lives on because it's a competition between humans to test their skill (just like bicycles, cars, trains didn't eliminate foot races) ... the computer is largely factored out, but not entirely -- people train with the computer, use it to check whether they played correctly, ... and they cheat. A lot…

I’ve deleted it but no it’s not awful anymore than saying “we survived WWII, we can survive this.” The point was that change happens but humans find a way forward.

Re: Ten advances in mathematics and theoretical computer science

#66

Post by mathisfun123 »

raincole wrote: post #32
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…

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this:

> In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a complete nonexistence certificate are insufficient.

which is infact a very important part of the prompt.

Re: Ten advances in mathematics and theoretical computer science

#67

Post by raincole »

zkmon wrote: post #64
raincole wrote: post #32

Earlier quoted context omitted.

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

When you use a crane to do the "heavy lifting" for construction work, do you give full credit to the cranes?

Read the prompts in the PDF I link and see if your analogy makes sense in this context :)

Re: Ten advances in mathematics and theoretical computer science

#68

Post by traes »

energy123 wrote: post #50
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…

The old way of establishing career credibility is being destroyed, for better or worse. Accomplishments that used to be career-defining are hard to distinguish from AI, and correlate more with access to compute. Think about Bill Gates's math paper he wrote in college. That kind of thing is gone now as a path to credibility. There's still competitions and grades, but the diversity of paths is going away. Maybe new one…

If accomplishments can't be distinguished between talented people and untalented people with compute, is there really a point in trying? I suppose one can hope that talented people given compute will be more effective than untalented people with compute, but I despair that that may not be true for much longer.

Re: Ten advances in mathematics and theoretical computer science

#69

Post by ben_w »

raincole wrote: post #32
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…

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

> A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt.

I think you're over-estimating what a smarter highschooler could write.

A "finite loopless undirected multigraph" could have been explained to me at that age if we'd taken Discrete rather than Mechanics and Pure (and one module of Stats) in my two A-levels* in maths and further maths; but from what I saw of the Discrete module, neither:

  Every finite loopless multigraph with no bridge possesses a cycle double cover, without additional assumptions such as cubicity, planarity, connectivity, or higher edge-connectivity.
nor:

  repeated-edge closed trails masquerading as cycles
would have been something we'd have learned. But more importantly, we absolutely didn't have a feel for how much effort one needs to put into making sure the proof is right, so if one of us had been hypothetically asked to write a prompt it would've been no more than half that length, and missed most of the bullet points.

* For those not from the UK: A-levels are between secondary school and university, when aged 16-18. Functionally they are university entrance qualifications: https://en.wikipedia.org/wiki/A-level_(United_Kingdom)

Re: Ten advances in mathematics and theoretical computer science

#70

Post by esperent »

simianwords wrote: post #59
traes wrote: post #45

Earlier quoted context omitted.

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.

> deliberate misleading “lack of transparency” etc

It's a marketing post from a huge company. Only the naive would view it uncritically without assuming it's been written carefully to present the results in the best possible light while skirting the boundaries of outright lying.

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