Paul Lockhart > Quotes

“It is the story that matters not just the ending.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Mathematics is the music of reason. 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; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.”
― Paul Lockhart , A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Mathematics is the art of explanation.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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 say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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?”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Teaching is not about information. It's about having an honest intellectual relationship with your students.”
― Paul Lockhart

“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; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“To say that math is important because it is useful is like saying that children are important because we can train them to do spiritually meaningless labor in order to increase corporate profits. Or is that in fact what we are saying?”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“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.”
― Paul Lockhart

“Efficiency and economy simply do not make good pedagogy.”
― Paul Lockhart

“Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“People don't do mathematics because it's useful. They do it because it's interesting.”
― Paul Lockhart, Measurement

“What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty.”
― Paul Lockhart, Measurement

“The solution to a math problem is not a number: it's an argument, a proof. We're trying to create these little poems of pure reason. Of course, like any other form of poetry, we want our work to be beautiful as well as meaningful. Mathematics is the art of explanation, and consequently, it is difficult, frustrating, and deeply satisfying.”
― Paul Lockhart, Measurement

“[Students] are being trained to ape arguments, not to intend them.”
― Paul Lockhart

“It is an aesthetic principle almost universally acknowledged among mathematicians that the best way to solve a problem is to find an ingenious way not to have to solve it at all.”
― Paul Lockhart, Measurement

“... This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.

On the other hand, once you have made your choices then your new creations do what they do, whether you like it or not. This is the amazing thing about making imaginary patterns: they talk back!”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“In my mind's eye, there is a universe where beautiful shapes and patterns float by and do curious and surprising things that keep me amused and entertained. It's an amazing place, and I really love it.”
― Paul Lockhart, Measurement

“So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.”
― Paul Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic as mathematics”
― Paul Lockhart

“it doesn’t matter so much what is true. It matters why it’s true.”
― Paul Lockhart, Measurement