Paul Lockhart Quotes & Sayings

The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems. — Paul Lockhart

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

Worse, the perpetuation of this "pseudo-mathematics," this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values. Those — Paul Lockhart

There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood. — Paul Lockhart

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

Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work. — Paul Lockhart

Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. — Paul Lockhart

Mathematics is the art of explanation. — Paul Lockhart

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

[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

The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many — Paul Lockhart

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations. — Paul Lockhart

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

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

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

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

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

... 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

SIMPLICIO: ... You have to [learn to] walk before you can run.
SALVIATI: No, you have to have something you want to run toward. — Paul Lockhart

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

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 diagrams and clear memories of hating them. — Paul Lockhart

... That little narrative is an example of the mathematician's art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it's fascinating, it's fun, and it's free! — 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

Mathematics is not a language, it's an adventure — Paul Lockhart

Efficiency and economy simply do not make good pedagogy. — Paul Lockhart

If teaching is reduced to mere data transmission, if there is no sharing or excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students? — Paul Lockhart

Teaching is not about information. It's about having an honest intellectual relationship with your students. — 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

It is the story that matters not just the ending. — Paul Lockhart

The only thing I am interested in using mathematics for is to have a good time and to help others do the same. — Paul Lockhart

And I'll go even further and say that mathematics, this art of abstract pattern-making - even more than storytelling, painting, or music - is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are. — Paul Lockhart

[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 ... — Paul Lockhart

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

If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done-I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. — Paul Lockhart