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 Copy Share Image
The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come… — Paul Lockhart Copy Share Image
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them. — Paul Lockhart Copy Share Image
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems,… — Paul Lockhart Copy Share Image
Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it… — Paul Lockhart Copy Share Image
So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people;… — Paul Lockhart Copy Share Image
[Math is] not at all like science. There's no experiment I can do with test tubes and equipment and whatnot that will tell me… — Paul Lockhart Copy Share Image
“Mathematics is the music of reason . To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to… — Paul Lockhart Copy Share Image
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… — Paul Lockhart Copy Share Image
The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along… — Paul Lockhart Copy Share Image
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?… — Paul Lockhart Copy Share Image
There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. — Paul Lockhart Copy Share Image
To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion −… — Paul Lockhart Copy Share Image
“And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music - is… — Paul Lockhart Copy Share Image
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 Copy Share Image
“[Students] are being trained to ape arguments, not to intend them.” — Paul Lockhart Copy Share Image
“Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being… — Paul Lockhart Copy Share Image
![“[Math is] not at all like science. There's no experiment I can do with test tubes and equipment and whatnot that will tell me the truth about a figment of my imagination. The only way to get at the truth about our imaginations is to use our imaginations...” quote by Paul Lockhart](https://sms4smile.com/quotes/img-quotes/3e0/paul-lockhart-18353_can-do_math-is-not-at-all-like-science-there-s_140084.jpg)
![“[Students] are being trained to ape arguments, not to intend them.” quote by Paul Lockhart](https://sms4smile.com/quotes/img-quotes/125/paul-lockhart-18353_quote_students-are-being-trained-to-ape-argume_1064702.jpg)
![“Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to…” quote by Paul Lockhart](https://sms4smile.com/quotes/img-quotes/e5b/paul-lockhart-18353_geometry_be-honest-did-you-actually-read-the-abov_1114656.jpg)