Teaching is not about information. It's about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can't be real, then you have no right to inflict yourself upon innocent children.

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

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

To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion − not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to.

It is the story that matters, not just the ending.

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade?

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