A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity.

Mathematics is not a language, it's an adventure

Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

I don't see how it's doing society any good to have so many members walking around with vague memories of algebraic formulas and geometric diagrams and clear memories of hating them.

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.

[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.