Paul Lockhart said this quote

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.

~ Paul Lockhart

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?

~ Paul Lockhart

Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.

~ Paul Lockhart

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

~ Paul Lockhart