"A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity."
"Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them."
"[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on."
"The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there"all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods."
"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?"
"Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?"