Math is broken, writes Bret Victor:

When most people speak of Math, what they have in mind is more its mechanism than its essence. This “Math” consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots.

This mechanism of math evolved for a reason: it was the most efficient means of modeling quantitative systems given the constraints of pencil and paper. Unfortunately, most people are not comfortable with bundling up meaning into abstract symbols and making them dance. Thus, the power of math beyond arithmetic is generally reserved for a clergy of scientists and engineers (many of whom struggle with symbolic abstractions more than they’ll actually admit).

We are no longer constrained by pencil and paper. The symbolic shuffle should no longer be taken for granted as the fundamental mechanism for understanding quantity and change. Math needs a new interface.

Now this is thinking outside the box, outside the constraints and definitions we never think to question.

It’s the responsibility of our tools to adapt inaccessible things to our human limitations, to translate into forms we can feel. Microscopes adapt tiny things so they can be seen with our plain old eyes. Tweezers adapt tiny things so they can be manipulated with our plain old fingers. Calculators adapt huge numbers so they can be manipulated with our plain old brain. And I’m imagining a tool that adapts complex situations so they can be seen, experienced, and reasoned about with our plain old brain.

Bret’s full essay, complete with animated visual aids, is here, on his unconventional but visually stunning website.