For the most part, physicists and mathematicians have settled on a fine division of labour in which the former complain about the finickiness of the latter, and the latter complain about the sloppiness of the former.

The main reason we use math in physics, however, is because we can.

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie.

If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.