I have today sent the following letter to Clay Mathematics Institute including this analysis of the OpenAI solution. Copies to Terence Tao, Peter Constantin and Charles Fefferman (formulated the problem).
President
Clay Mathematics Institute
This is a follow up of my 2014 letter about the formulation of the Navier-Stokes problem motivated by the proposed OpenAI solution, which is expressed in the enclosed manuscript. I hope you will read and return with a comment after consulting with the experts.
In short, my analysis exhibits the unfortunate elimination of turbulent fluid flow, the essence of Navier-Stokes from both physical and mathematical point of view, from the official formulation of the problem, which now has triggered an AI solution without both physical and mathematical meaning. Clay Mathematics Institute is not served by announcing prize problem missing the essentials.
Sincerely
Claes Johnson
On Fri, 16 May 2014 at 16:50, Claes Johnson <claesjohnson@gmail.com> wrote:
PresidentClay Mathematics InstituteI want to convey the information that the formulation of the Clay Navier-Stokes problem is incorrect both mathematically and physically, because the fundamental aspects of (i) wellposedness and (ii) turbulence, are not included, as exposed in detail in the following sequence of blog posts:The result is that the problem cannot be given a meaningful solution and thus does not serve well as a Prize problem. Evidence is given by the fact that no progress towards a solution has been made.I have tried to engage Charles Fefferman, who has formulated the problem, Peter Constantin, who acts as a referee, and Terence Tao, who is working on the problem, into a discussion, but I get no response.I hope this way to stimulate discussion, which I think would be more constructive than no discussion.SincerelyClaes Johnsonprof of applied mathematicsRoyal Institute of Technology, Stockholm
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