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

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

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

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

“I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

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

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

“no hay nada tan onírico y poético, nada tan radical, subversivo y psicodélico como las matemáticas. Es tan impresionante como la cosmología o la física (los matemáticos concibieron los agujeros negros mucho antes de que los astrónomos encontrasen uno), y permite más libertad de expresión que la poesía, el arte o la música (que dependen mucho en las propiedades físicas del universo). Las matemáticas son el arte más puro, así como el más incomprendido.”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“having an honest intellectual relationship with our students and our subject.”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

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

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

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

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

“The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

“Qué irónico que la gente descarte las matemáticas como la antítesis de la creatividad. Están desperdiciando una forma de arte más antigua que cualquier libro, más profunda que cualquier poema, y más abstracta que cualquier otra cosa.”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

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

“all the education degrees in the world won’t help you, and”
― Paul Lockhart, quote from A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

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“Then what in your opinion is a good story?'

'What it's always been, monkey,' Ganesha said. 'One dhansu conflict. Some chaka-chak song and dance. Grief. Love. Love for the lover, love for the mother. Love for the land. Comedy. Terror. One tremendous villain whom we must love also. All the elements properly balanced and mixed together, item after item, like a perfect meal with a dance of tastes. There you have it.”
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“يقول سبينوزا: وعندما يبدو لنا أي شيء في الطبيعة مضحكاً أو سخيفاً، غامضاً أو شراً فذلك لأننا ليست لدينا سوى معرفة قليلة بالأشياء، وأننا جاهلون بنظام الطبيعة وتماسكها ككل واحد، ولأننا نريد أن تجري الأشياء وفقاً لتفكيرنا وآرائنا، مع أن ما يعتبره عقلنا سيئاً أو شراً ليس شراً أو سيئاً بالنسبة إلى نظام الطبيعة وقوانينها الشاملة الكلية. بل بالنسبة إلى قوانين طبيعتنا الخاصة المنفصلة. أما بالنسبة إلى كلمة الخير والشر فإنها لا تدل على شيء إيجابي في حد ذاتها، لأن الشيء الواحد نفسه قد يكون في وقت واحد خيراً أو شراً، أو لا هذا ولا ذاك كالموسيقى مثلاً فإنها خير بالنسبة إلى المنقبض النفس وشر بالنسبة إلى النائح الحزين الذي فقد شخصاً عزيزاً عليه. وهي ليست خيراً أو شراً بالنسبة إلى الميت”
― Will Durant, quote from The Story of Philosophy: The Lives and Opinions of the World's Greatest Philosophers

“I was amazed as people must be who are seized and kidnapped, and who realize that in the strange world of their captors they have a value absolutely unconnected with anything they know about themselves.”
― Alice Munro, quote from Lives of Girls and Women

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