The 10 Most Important Lessons 20 Years of Mathematics Taught Me

#5. There are no shortcuts to mastery.

One. Breaking the rules is often the best course of action.

I can’t even count the number of math-breaking ideas that propelled science forward by light years.

We have set theory because Bertrand Russell broke the notion that “sets are just collections of things.” We have complex numbers because Gerolamo Cardano kept the computations going when encountering √−1, refusing to acknowledge that it doesn’t exist. We have non-Euclidean spaces because János Bolyai did not accept that given a line and an external point, there’s only one parallel line that intersects the point.

A triangle of three right angles breaks one space, but creates another.

No assumption should be set in stone, and I’m not afraid to challenge them. You shouldn’t be afraid either.