CJ on Mathematics and Science

towards understanding by critical constructive inquiry

torsdag 28 februari 2019

Planck's Desperate Mad Ugly Ad Hoc Trick: The Quantum

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Planck's reasoning was mad, but his madness has that divine quality that only the greatest transitional figures can bring to science. (A...
fredag 22 februari 2019

Boltzmann 175 vs 2nd Law by Finite Precision Computation

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Ludwig Boltzmann 1844-1906 Lubos on the Reference Frame  recalls the 175th birthday of Ludwig Boltzmann: Yesterday, Ludwig Eduard Bol...
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torsdag 21 februari 2019

Hamming and Tartar on Clay Navier Stokes Problem

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Richard Hamming (1915-98) The mathematician  Richard Hamming said: Mathematics is an interesting intellectual sport but it should no...
onsdag 20 februari 2019

From Equation to Solution

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This is a continuation of the previous post on the role of functional analysis, more precisely the role of the finite element method as a f...
tisdag 19 februari 2019

Banach and DFS and Clay Navier-Stokes Problem

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This is an exercise in preparation for participation in a film about the Polish mathematician Stefan Banach who advanced functional anal...
tisdag 12 februari 2019

Kolmogorov/Onsager: Turbulent Velocity 1/3 Hölder Continuous

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Let me here recall the derivation by a scaling argument of the law of Kolmogorov/Onsager stating that fully developed turbulent velocities a...
lördag 9 februari 2019

Is Digital Computation a Form of Mathematics?

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In the last two posts a resolution of the Clay Navier-Stokes Prize Problem is presented, a resolution based on digital computation. I have t...
onsdag 6 februari 2019

Wellposedness of Navier-Stokes/Euler: Clay Problem

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This is a continuation of the previous post proposing a resolution of the Clay Navier-Stokes Millennium Problem with further remarks on the ...
måndag 28 januari 2019

Solution of the Clay Navier-Stokes Problem by Computer-Assisted Proof

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This is a reminder of the resolution of the Clay Navier-Stokes Millennium Problem which I have presented together with Johan Hoffman and Jo...
söndag 11 november 2018

Turbulence Riddle Solved by AI as Automated Computational Mathematical Modeling ACMM

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The (super)human intellect of Euler (1707-83) formulated Euler's equation for fluid flow. The information society is based on compu...
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Claes Johnson
Professor of Applied Mathematics KTH
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