The goal of mathematics has always been about human understanding of the ideas. When a mathematician solves a problem then they can explain to others the new concepts that lead them to this discovery, this proof, and how they came about it.

This is a great application of the study of epistemology – the philosophical discussion of knowing and understanding. It seeks to define the key points required to say we actually know something. In the case of this video – he is describing some of the things he believes are core principles of saying you actually understand a mathematical statement. This is a whole field of understanding and study – and one that I think is really coming to the forefront with the advent of AI.

This isn’t new, since 2010 there have been systems that can mathematically describe phenomenon. The Eureka machine was one of them that brought up this very same question over a decade ago.

The question soon becomes: computers can generate models for us that describe phenomenon; but to say we really know something as humans – we seem to desire more. We want to understand the underlying principles and even purpose. While physical sciences have increasingly stick to answering the ‘what’ without answering purpose/intent/meaning – we absolutely rely on that when deciding the guilt/innocence of human behavior.