The best representations of mathematics may not exist yet
Humility. It’s all I can feel after watching 3Blue1Brown’s latest maths video, in which Grant Sanderson and his team provide the most novel of approaches to solving 2D equations, using colour. It is the second time 3Blue1Brown has blown my mind to pieces in just a few weeks, following their earlier video that solved the Basel problem with light.
While I was familiar with the results/methods in both cases, the representations came as a complete surprise. The 3Blue1Brown videos are far from perfect (they proceed at a cadence that sometimes proves frustrating, lack interaction and, in the most recent example, may be of little use to the colour-blind), yet they remind us that our understanding of mathematics will never be complete. However well you think you understand a concept, there will always be new representations to deepen your thinking and force you to confront familiar truths in unfamiliar ways.
Mathematics is never a done deal. Believe it or not, we’re solving 2D equations on this image.