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.

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.

Grigori Perelman transformed the supercritical Navier-Stokes problem into a critical problem by introducing concepts like reduced volume and permanence entropy, which simplified the analysis of singularities.

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.

In the subatomic world, the rules are consistent with the observable world, and understanding how our perceived reality emerges from subatomic behavior is crucial.

Emerging phenomena, like temperature, arise from the collective behavior of many particles, indicating that such properties are not fundamental but rather emergent.

The principle of equivalence in general relativity conflicts with the principle of superposition in quantum mechanics, highlighting a fundamental tension between these two theories.

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

The interplay between theory and experiment is crucial in science, as observations can guide theoretical models and vice versa.