Andrew Akbashev's post on X, curated on eChai

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The most careful summary written by anybody outside mathematics, and the only widely shared one that carries Buckmaster's own disclaimer rather than dropping it.

Andrew Akbashev 8 Sep 2026

1. The authors - Alpöge and Buckmaster - showed how to achieve a blowup with smooth forcing for 2D Boussinesq equation. Then they also worked it out for 3D incompressible Euler equations. These are Navier-Stokes but without viscosity.

Now, Tarrence Tao says that this approach may likely be extended to actual Navier-Stokes.

BUT there's a big drama behind it:

- OpenAI had learned about their progress before it was published and pushed their AI to quickly come up with a similar solution.

- However, OpenAI's solution was based on the same smooth-forcing approach that Buckmaster/Alpöge had quietly been developing. Buckmaster said that he does not know if their data was used, so he is “not accusing anyone of anything.”

- However, Sébastien Bubeck (a research lead at OpenAI) didn’t want to see Alpöge as the author because Alpöge works at Anthropic.

Bubeck from OpenAI called these allegations “false and inflammatory”. As of now, there are no further comments.

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Nadeem Jafri 1h

How do you pick the right consultant for your company?

Is it someone who speaks at your level? Someone who doesn’t hide behind jargon to impress, but takes the time to understand your business, your processes and, most importantly, your people?

In my 22+ years of entrepreneurship, I’ve worked with several coaches and consultants. Many brought expertise, but few were able to connect with my team or truly understand the ground realities of our business.

For me, a great consultant is not someone who sits on a pedestal and hands down ideas. It is someone who becomes a partner in the journey, who listens, participates, challenges, mentors and helps the team move forward.

Our team has been with us for over two decades. They are loyal, hardworking, grassroots employees who have built this business with us. The answer, therefore, isn’t to replace them. It is to equip them with the right technology, digital capabilities and confidence to evolve.

If we want to compete with the best, digitisation is no longer optional. We need to bring technology into our processes and use analytics to turn data into sharper business and market strategies.

When we discussed this with Shrijay Sheth and introduced him to our team, he immediately connected with them. He interacted as though he had known them for years. There was no jargon, just genuine curiosity, participation and an instinctive understanding of how to work with people.

We knew then that this was the kind of consultant we wanted alongside us: an expert who would partner us through our digital transformation, not simply advise us from the sidelines.

My mandate to Shrijay was simple:

“I have a team of Lagaan under Bhuven. Make them Team India under Dhoni.”

He picked up the challenge with a smile.

And today, Hire4Higher Consulting is an integral part of our think tank as we embark on this transformation journey.
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Curated from X →

By late morning this was the highest-engagement account of the day at 5,300 likes and 263,000 views, and it is the version most people will have read. Every line of it is in the statement. What is not in the statement is the conclusion a reader draws from the last two: Buckmaster asked about training and got no answer, and he is explicit that he does not know what the answer is.

NIK 5h

>math professor spends a year on one of the hardest unsolved problems in math
>"Navier-Stokes"
>his drafts for the whole project went through codex sessions
>openai had his logs in codex
>suddenly rumor leaks AI solved it
>he emails openai to ask what's going on
>openai calls within days
>"funny story, our model also solved it"
>using his exact approach
>asks openai: did you train on my sessions?
>no answer
Curated from X →

Bryan is an associate professor of strategy at Toronto's Rotman School and chief economist at CDL Toronto. By late morning the reading that OpenAI had trained on private Codex sessions had taken over X, and this is the most substantial public pushback on it: he accepts that OpenAI pursued the route after hearing the rumours and still calls the training insinuation unfair. It is the strongest version of the account that does not assume the worst, which is why it sits here rather than among the reactions.

Kevin A. Bryan 6h

1) Navier-Stokes result will be shown soon, by humans+AI. This is "Nobel-level" result. 2) OAI has an internal proof also. 3) They had AI pursue a path partly based on rumors of a strategy that might work. 4) OAI did not "train on the humans' GPT input"- insinuation is unfair

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