1) OpenAI and Buckmaster did not solve the same problem. Per https://x.com/IlinVasily29521/status/2097554700321329393 , here is a breakdown of who solved what.

  Tristan + Levent: 3D incompressible Euler with forcing
  OpenAI: 3D incompressible Euler without forcing
  OpenAI: Navier-Stokes with forcing
  No one: Navier-Stokes without forcing

Euler equations = Navier-Stokes without viscosity. Forcing means external force. Absence of viscosity and presence of external force make blowup easier to construct.

Tristan+Levent ticked the weakest case, OpenAI ticked the two next weakest, then the final case is unsolved. Only the last two are eligible for the Millennium Prize. The Navier-Stokes general case remains unsolved.

Navier-Stokes has an extra viscosity term compared to Euler, which makes the problem noticeably harder to find a blowup. They are not the same problem.

2) The approach both chose to use (by Luis and Diego) was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same route as Luis and Diego, without access to Buckmaster's work.

3) You mischaracterized OpenAI's statement. They issued a blanket denial on using Buckmaster's Codex data from after July 3.

"We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training. After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

July 3 was the training cutoff date for the model that solved Navier-Stokes. No user data after that date influenced the model.

4) Buckmaster and Alpöge found their blow-up for 3D incompressible Euler with forcing on August 15 https://cims.nyu.edu/~tristanb/statement.pdf , over a month after the model training cutoff point. They stated they did not have real progress prior to this point.

This is what Terence Tao said of Buckmaster’s and Alpolge approach:

“There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task…”

Pouring infinite AI resources into it is exactly what OpenAI did.

For your point 2. It is of course possible, but it is highly unlikely if I understood Buckmaster's statements correctly.

Not when you have 10,000 concurrent agents attacking the problem. OpenAI brute-forced their way to a solution. They likely tried every approach in published literature, which includes the 2023 approach by Luis and Diego.

Everyone involved with openAI will flat out lie to your face and will fund media campaigns to promote their lies. OpenAI made personal threats. That is a sign that they were doing something wrong and are desperate to control the narrative.

It is laughable to claim they are not datamining users when datamining users is their strongest advantage over open models.

In the end, there is no reason to care about openAI or credit them with anything. Tools are not attributed, people are.

The best solution is for universities to be universities and provide llms for students and staff to use. Any university allowing students to use cloud based AI has failed.

> Altman and Bubeck claim that because the proof used different scaling parameters and analytical steps, it's not related,

Is Altman even mathematican these days?