Tech Impact of Solutions to both Millennium Physics Problems

[greswd]

Out of the 6 remaining Millennium Prize Problems, two concern physics, the Navier-Stokes smoothness problem and the Yang-Mills mass gap problem.

What I'm curious about is, if both problems were to be solved right now, what would be the immediate experimental and/or technological impacts of the solutions?

We can explore both scenarios (proven true/false) for each problem.

 

[mfb]

Everyone expects them to be true - I don't see technological advances that would come from a proof. The situation is similar for many other unsolved mathematical problems, e. g. the Riemann hypothesis: sure, a proof would be great, but mainly of mathematical interest, putting a checkbox after all proofs "assuming the Riemann hypthesis is true, then [...]".

Showing that one of them is false would be much more interesting. As an example, it would show that the Navier-Stokes equations for describing fluids have to be wrong in some situation. Can we reproduce this experimentally?

 

[greswd]

Everyone expects them to be true - I don't see technological advances that would come from a proof. The situation is similar for many other unsolved mathematical problems, e. g. the Riemann hypothesis: sure, a proof would be great, but mainly of mathematical interest, putting a checkbox after all proofs "assuming the Riemann hypthesis is true, then [...]".

Showing that one of them is false would be much more interesting. As an example, it would show that the Navier-Stokes equations for describing fluids have to be wrong in some situation. Can we reproduce this experimentally?

that sounds interesting. Maybe an experimenter could even find the answer before a mathematician.

what about for Yang Mills?