CJ on Mathematics and Science

towards understanding by critical constructive inquiry

tisdag 22 september 2026

No Longer Any Mission for Theoretical Physicists?

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Swedish theoretical physics (string theory) Ulf Danielson today in Swedish mainstream media (SvD) concludes that with now AI writing article...
lördag 19 september 2026

Smoothness vs Wellposedness vs Clay Problem vs Ghost Solutions

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The official Clay Navier-Stokes Prize Problem asks about existence of smooth solutions but does not mention uniqueness or  wellposedness as ...
fredag 18 september 2026

Clay Math Institute Response to Criticism of Navier Stokes Problem Formulation

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Response from Martin Briden President Clay Mathematics Institute: Dear Prof Johnson I am familiar with the objections that you raise concern...

Letter to Clay Math Institute on Navier-Stokes Problem

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I have today sent the  following letter to Clay Mathematics Institute including this analysis of the OpenAI solution.   Copies to Terence Ta...
torsdag 17 september 2026

Meaningless OpenAI Solution to Clay Navier-Stokes Problem

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Here is a post composed by Claude from my prompts about the Clay Navier-Stokes Millennium Problem.  A Meaningless Solution to a Meaningless ...
söndag 13 september 2026

Mathematics Education vs AI vs BodyandSoul vs John Dewey

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Recent posts on the OpenAI solution to the Clay Navier-Stokes Millennium Problem reflect on the monumental challenge to professional mathema...
fredag 11 september 2026

Two Forms of LLM for Mathematics: Words and Numbers

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We have identified two forms of mathematics, (S) symbolic performed with symbols/words and (N) numerical performed by computation with numbe...
torsdag 10 september 2026

Difference between Analytical and Numerical Mathematics: Capital vs Labour

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The recent announcement by OpenAI of a solution to the Clay Navier-Stokes Millennium Problem exhibits a fundamental difference between analy...
onsdag 9 september 2026

AI Solution of Clay Problem Sends Shock Waves into Analytical Mathematics

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The Open AI solution (see previous post) to the Clay Navier-Stokes problems sends shock waves into the world of analytical (pure) mathematic...

Meaningless Clay Navier-Stokes Problem Solved by AI

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OpenAI announces  a proof of existence of a solution to the Navier-Stokes equations (but not its numerical values), which starting from zero...
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Claes Johnson
Professor of Applied Mathematics KTH
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