The Navier-Stokes equations are supercritical, meaning that at smaller scales, the transport terms dominate over the viscosity terms, leading to unpredictable and turbulent behavior.

The Navier-Stokes equations are sophisticated nonlinear equations that are challenging to solve, particularly in three dimensions where singularities can form.

The Navier-Stokes equations govern fluid flow for incompressible fluids like water, and the Navier-Stokes regularity problem asks whether a smooth velocity field can ever concentrate to the point of becoming infinite, which would indicate a singularity.

The phenomenon of supercriticality versus criticality and subcriticality is a key qualitative feature that distinguishes equations that are predictable from those that are not, such as in fluid dynamics.

The Clay Foundation offers a million-dollar prize for solving one of the seven Millennium Prize Problems, one of which is the Navier-Stokes problem, and only one of these problems has been solved so far.

While the Fields Medal can inspire young mathematicians, it's important to respect those like Grigori Perelman, who prioritize their principles over recognition and awards.

Mathematicians care about whether something holds true 100% of the time, unlike most fields where 99.99% suffices. This is crucial in fluid dynamics, where we need to understand if there are special initial states that could lead to blow-up scenarios.

The point conjecture, a significant problem in mathematics, involves determining whether a three-dimensional space with certain properties can be continuously deformed into a sphere.

The concept of twistors introduces a new kind of curved twistor, which is essential for understanding complex solutions in physics, but it also leads to inherent confusion in the theory.