The theories that explain the universe often involve the same mathematical objects that solve mathematical problems, indicating a deep connection between the two fields.

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.

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.

The beauty of mathematics often lies in its simplicity, as seen in elegant equations like Euler's identity, which connects fundamental constants.

When you add more parameters and data, you capture more of the distribution, but it's unclear why it scales so smoothly with those parameters and data.

The strength of geometric algebra lies in its ability to unify various concepts in physics, including quantum mechanics and relativity, potentially offering new insights into quantum gravity.

General Relativity is based on two foundational pillars: general covariance, meaning physical laws don't depend on coordinate choices, and the principle of equivalence, which states that gravity is the same as local acceleration.

Maxwell's equations are conformally invariant, meaning they depend on the space-time structure independent of scaling.

The Riemann hypothesis, which concerns the distribution of prime numbers, is a fundamental problem in mathematics that remains unsolved, with significant implications for number theory.