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> Because the core of the issue is that it may well not have solved it, but instead plagiarised the significant step of the result from other researchers It's

by sho_hn 16d ago

> Because the core of the issue is that it may well not have solved it, but instead plagiarised the significant step of the result from other researchers It's also true however that I haven't seen a single write up trying to discern what did more of the work in those AI chats - the prompts or the responses - bubble to the surface, also since we don't have access to them. For example, if I prompt Codex with "Make me a website about strawberry cake" and nothing else, and OpenAI announces they have the best strawberry cake minutes before I launch, I'm not sure they plagiarized anything. We just don't know if this is quibbling over "who prompted first" or if the researchers came up with anything strikingly original by themselves.

20k 16d ago
The researchers apparently spend a year or so working on this, and it builds off significant previous work, so it seems like it was a pretty significant amount of work that OpenAI may have trained on I'd love to see an in depth analysis of how much OpenAI actually did, but I suspect we'll never see that because it would indicate at least some plagiarism which undermines a lot of what OpenAI is putting out in public
- felipeerias 15d ago
  The American Mathematical Society credits the Spanish researchers Diego Córdoba and Luis Martínez‑Zoroa with the breakthroughs that eventually led to this solution, and which were published from ~2023 onwards. This is a good summary: > In broad outline, the pair’s technique relies on creating an infinite sequence of “layers,” each of which is a non-singular solution to the equation they are studying. (They’ve applied similar techniques to both the Euler and Navier-Stokes equations, as well as to other related systems.) They then combine those solutions in what Martínez-Zoroa calls an “infinite cascade” to produce a new solution. > > That new solution, they showed, contains the desired singularity. However, even though each individual layer relies on a smooth forcing function, combining them together can cause the forcing function to have undesirable mathematical properties. That’s why their solution fell short of satisfying the Millennium Prize criteria. The remaining hurdle was to figure out how to create a similar infinite cascade that resulted not only in a singularity, but also in a smooth forcing function. > > That’s the step that both competing AI groups appear to have had success with. https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-... The question is whether OpenAI started out from that published and well known research exclusively, or they also had some insight into the ongoing work of Tristan Buckmaster and Levent Alpöge. On the one hand, OpenAI have already admitted that they only launched their massive effort after hearing rumours that this particular problem had been solved. On the other, progress in mathematics research has accelerated significantly over the past months thanks to the availability of newer and more capable AI models. Alpöge himself presented a counterexample to the Jacobian conjecture on July, found with Claude Fable. So if model capability was a bottleneck, that gives credibility to the idea that an even more powerful unreleased model with massive compute would be able to make even faster progress.
Hardwired8976 16d ago
The conversation was about using the chat to check the draft, the novel ideas came from the researcher.
TZubiri 15d ago
It's worth noting that the case is that your input is being used to train their AI, and that's more important than whether it materially contributed, it cannot be denied or attributed accurately, it cannot be said with certainty which way it happened, and that's what's important.
ImPostingOnHN 15d ago
The truth is likely that without the tool or the humans using it, the process would have taken longer
- airstrike 15d ago
  Without the humans, no tool would ever have done it. Without the tool, humans would have done it.

by sho_hn 16d ago

20k 16d ago

The researchers apparently spend a year or so working on this, and it builds off significant previous work, so it seems like it was a pretty significant amount of work that OpenAI may have trained on I'd love to see an in depth analysis of how much OpenAI actually did, but I suspect we'll never see that because it would indicate at least some plagiarism which undermines a lot of what OpenAI is putting out in public

felipeerias 15d ago
The American Mathematical Society credits the Spanish researchers Diego Córdoba and Luis Martínez‑Zoroa with the breakthroughs that eventually led to this solution, and which were published from ~2023 onwards. This is a good summary: > In broad outline, the pair’s technique relies on creating an infinite sequence of “layers,” each of which is a non-singular solution to the equation they are studying. (They’ve applied similar techniques to both the Euler and Navier-Stokes equations, as well as to other related systems.) They then combine those solutions in what Martínez-Zoroa calls an “infinite cascade” to produce a new solution. > > That new solution, they showed, contains the desired singularity. However, even though each individual layer relies on a smooth forcing function, combining them together can cause the forcing function to have undesirable mathematical properties. That’s why their solution fell short of satisfying the Millennium Prize criteria. The remaining hurdle was to figure out how to create a similar infinite cascade that resulted not only in a singularity, but also in a smooth forcing function. > > That’s the step that both competing AI groups appear to have had success with. https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-million-millennium-prize-problems-20260908/ https://www.quantamagazine.org/ai-has-solved-one-of-maths-1-... The question is whether OpenAI started out from that published and well known research exclusively, or they also had some insight into the ongoing work of Tristan Buckmaster and Levent Alpöge. On the one hand, OpenAI have already admitted that they only launched their massive effort after hearing rumours that this particular problem had been solved. On the other, progress in mathematics research has accelerated significantly over the past months thanks to the availability of newer and more capable AI models. Alpöge himself presented a counterexample to the Jacobian conjecture on July, found with Claude Fable. So if model capability was a bottleneck, that gives credibility to the idea that an even more powerful unreleased model with massive compute would be able to make even faster progress.

Hardwired8976 16d ago

The conversation was about using the chat to check the draft, the novel ideas came from the researcher.

TZubiri 15d ago

It's worth noting that the case is that your input is being used to train their AI, and that's more important than whether it materially contributed, it cannot be denied or attributed accurately, it cannot be said with certainty which way it happened, and that's what's important.

ImPostingOnHN 15d ago

The truth is likely that without the tool or the humans using it, the process would have taken longer

airstrike 15d ago
Without the humans, no tool would ever have done it. Without the tool, humans would have done it.