Mathematics can help validate models by identifying weaknesses, such as systemic correlations in economic models that may lead to failures.

Mathematics allows you to change the rules of the problem, which is not possible in other fields like engineering, where fixed requirements exist.

When physicists need mathematics, they often rely on precursors developed by mathematicians, as seen when Einstein sought help from mathematicians for curved space.

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.

Mathematics has a theoretical and experimental component, with recent advancements allowing for more experimental approaches in the field.

In mathematics, we often start with hypotheses and explore their consequences, unlike other disciplines where conclusions drive the inquiry.

Einstein believed that if a measurement can be made without disturbing a system and gives a 100% certainty answer, then that measurement reveals an element of reality.

Mathematics is about finding connections between different fields, and this process has been ongoing throughout history, such as the unification of geometry and number theory.