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It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality.", "language": "en", "author": { "name": "Henri Poincaré", "slug": "henri-poincare", "url": "https://www.leafyquotes.com/henri-poincare" }, "book": { "title": "Science and Method", "slug": "science-and-method", "url": "https://www.leafyquotes.com/henri-poincare/science-and-method" }, "character": null, "chapter": null, "chapter_parent": null, "page": 128, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "intuition", "slug": "intuition", "url": "https://www.leafyquotes.com/topics/intuition" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Henri_Poincar%C3%A9#Science_and_Method_(1908)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-26T07:49:02" }, { "id": "698f64f3-90bf-4ec5-9db4-707e6d8dee45", "slug": "mighty-is-the", "url": "https://www.leafyquotes.com/william-wordsworth/the-prelude/mighty-is-the", "text": "Mighty is the charm Of those abstractions to a mind beset With images, and haunted by herself, And specially delightful unto me Was that clear synthesis built up aloft So gracefully; even then when it appeared Not more than a mere plaything, or a toy To sense embodied: not the thing it is In verity, an independent world, Created out of pure intelligence.", "language": "en", "author": { "name": "William Wordsworth", "slug": "william-wordsworth", "url": "https://www.leafyquotes.com/william-wordsworth" }, "book": { "title": "The Prelude", "slug": "the-prelude", "url": "https://www.leafyquotes.com/william-wordsworth/the-prelude" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/The_Prelude#Book_VI", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:05:54" }, { "id": "ed1f3424-831e-4d45-9a58-dead469a739e", "slug": "the-natural-world", "url": "https://www.leafyquotes.com/william-boyd/brazzaville-beach/the-natural-world", "text": "The natural world is full of irregularity and random alteration, but in the antiseptic, dust-free, shadowless, brightly lit, abstract realm of the mathematicians they like their cabbages spherical, please.", "language": "en", "author": { "name": "William Boyd", "slug": "william-boyd", "url": "https://www.leafyquotes.com/william-boyd" }, "book": { "title": "Brazzaville Beach", "slug": "brazzaville-beach", "url": "https://www.leafyquotes.com/william-boyd/brazzaville-beach" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "nature", "slug": "nature", "url": "https://www.leafyquotes.com/topics/nature" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/William_Boyd_(writer)#Brazzaville_Beach_(1990)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:05:26" }, { "id": "b27c4be8-eca4-4447-9e64-3932aee4cf09", "slug": "my-hero-was", "url": "https://www.leafyquotes.com/jeffrey-ford/the-empire-of-ice-cream/my-hero-was", "text": "My hero was J. S. Bach. It was from his works that I came to understand mathematics and, through a greater understanding of math, came to a greater understanding of Bach—the golden ratio, the rise of complexity through the reiteration of simple elements, the presence of the cosmic in the common.", "language": "en", "author": { "name": "Jeffrey Ford", "slug": "jeffrey-ford", "url": "https://www.leafyquotes.com/jeffrey-ford" }, "book": { "title": "The Empire of Ice Cream", "slug": "the-empire-of-ice-cream", "url": "https://www.leafyquotes.com/jeffrey-ford/the-empire-of-ice-cream" }, "character": null, "chapter": null, "chapter_parent": null, "page": 58, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "music", "slug": "music", "url": "https://www.leafyquotes.com/topics/music" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Jeffrey_Ford#The_Empire_of_Ice_Cream_(2006)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:04:57" }, { "id": "9821d9dd-a1c1-4a8a-b809-8915adf84a0b", "slug": "tao-i-dont", "url": "https://www.leafyquotes.com/wesley-chu/the-rebirths-of-tao/tao-i-dont", "text": "“Tao, I don’t understand why I need to know this.” Advanced mathematics opens doors to many fields of study. More importantly, it expands the way you think.", "language": "en", "author": { "name": "Wesley Chu", "slug": "wesley-chu", "url": "https://www.leafyquotes.com/wesley-chu" }, "book": { "title": "The Rebirths of Tao", "slug": "the-rebirths-of-tao", "url": "https://www.leafyquotes.com/wesley-chu/the-rebirths-of-tao" }, "character": null, "chapter": null, "chapter_parent": null, "page": 112, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "thinking", "slug": "thinking", "url": "https://www.leafyquotes.com/topics/thinking" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Wesley_Chu#The_Rebirths_of_Tao_(2015)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:04:48" }, { "id": "85e08b66-8a85-4f2b-bfe2-fc6f08b6ebf8", "slug": "its-not-for", "url": "https://www.leafyquotes.com/terry-pratchett/pyramids/its-not-for", "text": "It's not for nothing that advanced mathematics tends to be invented in hot countries. It's because of the morphic resonance of all the camels, who have that disdainful expression and famous curled lip as a natural result of an ability to do quadratic equations. (p. 171)", "language": "en", "author": { "name": "Terry Pratchett", "slug": "terry-pratchett", "url": "https://www.leafyquotes.com/terry-pratchett" }, "book": { "title": "Pyramids", "slug": "pyramids", "url": "https://www.leafyquotes.com/terry-pratchett/pyramids" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "humor", "slug": "humor", "url": "https://www.leafyquotes.com/topics/humor" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Pyramids_(novel)#Quotes", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:04:12" }, { "id": "4cfb59c1-e39a-4bb6-9da5-90ea7c1ffd20", "slug": "a-mathematical-argument", "url": "https://www.leafyquotes.com/david-berlinski/a-tour-of-the-calculus/a-mathematical-argument", "text": "A mathematical argument, once understood, is in its capacity to compel belief a miracle of enlightened life.", "language": "en", "author": { "name": "David Berlinski", "slug": "david-berlinski", "url": "https://www.leafyquotes.com/david-berlinski" }, "book": { "title": "A Tour of the Calculus", "slug": "a-tour-of-the-calculus", "url": "https://www.leafyquotes.com/david-berlinski/a-tour-of-the-calculus" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Berlinski#A_Tour_of_the_Calculus_(1995)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:04:01" }, { "id": "3274b074-82ef-4d80-98f0-4ec6adfc7594", "slug": "any-idiot-he-said", "url": "https://www.leafyquotes.com/david-berlinski/a-tour-of-the-calculus/any-idiot-he-said", "text": "“Any idiot,” he said calmly but with immense conviction, “can learn anything in mathematics. It requires only patience.”", "language": "en", "author": { "name": "David Berlinski", "slug": "david-berlinski", "url": "https://www.leafyquotes.com/david-berlinski" }, "book": { "title": "A Tour of the Calculus", "slug": "a-tour-of-the-calculus", "url": "https://www.leafyquotes.com/david-berlinski/a-tour-of-the-calculus" }, "character": null, "chapter": null, "chapter_parent": null, "page": 281, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "patience", "slug": "patience", "url": "https://www.leafyquotes.com/topics/patience" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Berlinski#A_Tour_of_the_Calculus_(1995)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:04:01" }, { "id": "2545ed37-2222-4930-b691-fc16a4f3bb46", "slug": "hungary-severed-from", "url": "https://www.leafyquotes.com/neal-stephenson/reamde/hungary-severed-from", "text": "Hungary, severed from half of the population and most of the natural resources that it had once claimed, had now to practice a sort of economic acupuncture, striving to know the magic nodes in the global energy flow where a pinprick could alter the workings of a major organ. Mathematics was one of the few disciplines where it was possible to exert that degree of leverage, and so the Hungarians had become phenomenally good at teaching it to their children.", "language": "en", "author": { "name": "Neal Stephenson", "slug": "neal-stephenson", "url": "https://www.leafyquotes.com/neal-stephenson" }, "book": { "title": "Reamde", "slug": "reamde", "url": "https://www.leafyquotes.com/neal-stephenson/reamde" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Reamde#Day_4", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:03:46" }, { "id": "47e7f867-8f77-4d65-ac8c-25985cceecbb", "slug": "mathematics-gave-tengo", "url": "https://www.leafyquotes.com/haruki-murakami/1q84/mathematics-gave-tengo", "text": "Mathematics gave Tengo an effective means of retreat. By fleeing into a world of numerical expression, he was able to escape from the troublesome cage of reality.", "language": "en", "author": { "name": "Haruki Murakami", "slug": "haruki-murakami", "url": "https://www.leafyquotes.com/haruki-murakami" }, "book": { "title": "1Q84", "slug": "1q84", "url": "https://www.leafyquotes.com/haruki-murakami/1q84" }, "character": null, "chapter": null, "chapter_parent": null, "page": 221, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/1Q84#Book_1_(April-June)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:03:38" }, { "id": "425545a6-1b8a-42c6-a393-34622a5cbb65", "slug": "i-began-to-study", "url": "https://www.leafyquotes.com/tara-westover/educated/i-began-to-study", "text": "I began to study trigonometry. There was solace in its strange formulas and equations. I was drawn to the Pythagorean theorem and its promise of a universal—the ability to predict the nature of any three points containing a right angle, anywhere, always. What I knew of physics I had learned in the junkyard, where the physical world often seemed unstable, capricious. But here was a principal through which the dimensions of life could be defined, captured. Perhaps reality was not wholly volatile. Perhaps it could be explained, predicted. Perhaps it could be made to make sense.", "language": "en", "author": { "name": "Tara Westover", "slug": "tara-westover", "url": "https://www.leafyquotes.com/tara-westover" }, "book": { "title": "Educated", "slug": "educated", "url": "https://www.leafyquotes.com/tara-westover/educated" }, "character": null, "chapter": null, "chapter_parent": null, "page": 124, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Tara_Westover#Educated_(2018)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:02:37" }, { "id": "c6b9a230-7d92-4e4f-a6cb-e0b9e4a568c8", "slug": "mathematics-is-universal", "url": "https://www.leafyquotes.com/charles-sheffield/summertide/mathematics-is-universal", "text": "Mathematics is universal. But very little else is.", "language": "en", "author": { "name": "Charles Sheffield", "slug": "charles-sheffield", "url": "https://www.leafyquotes.com/charles-sheffield" }, "book": { "title": "Summertide", "slug": "summertide", "url": "https://www.leafyquotes.com/charles-sheffield/summertide" }, "character": null, "chapter": null, "chapter_parent": null, "page": 119, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Charles_Sheffield#Summertide_(1990)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:02:32" }, { "id": "2cd1ea2f-d70d-4d0b-8155-ba0bb2e61f16", "slug": "you-are-lucky", "url": "https://www.leafyquotes.com/robert-l-forward/dragons-egg/you-are-lucky", "text": "You are lucky. Very few theoretical scientists ever see their mathematical equations turned into working hardware in their lifetime.", "language": "en", "author": { "name": "Robert L. Forward", "slug": "robert-l-forward", "url": "https://www.leafyquotes.com/robert-l-forward" }, "book": { "title": "Dragon's Egg", "slug": "dragons-egg", "url": "https://www.leafyquotes.com/robert-l-forward/dragons-egg" }, "character": null, "chapter": null, "chapter_parent": null, "page": 255, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "science", "slug": "science", "url": "https://www.leafyquotes.com/topics/science" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Robert_L._Forward#Dragon's_Egg_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:02:15" }, { "id": "a217c92f-06ef-40ad-a568-ad1a9dbff329", "slug": "its-time-to-let", "url": "https://www.leafyquotes.com/john-allen-paulos/a-mathematician-reads-the-newspaper/its-time-to-let", "text": "It’s time to let the secret out: mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us.", "language": "en", "author": { "name": "John Allen Paulos", "slug": "john-allen-paulos", "url": "https://www.leafyquotes.com/john-allen-paulos" }, "book": { "title": "A Mathematician Reads the Newspaper", "slug": "a-mathematician-reads-the-newspaper", "url": "https://www.leafyquotes.com/john-allen-paulos/a-mathematician-reads-the-newspaper" }, "character": null, "chapter": null, "chapter_parent": null, "page": 3, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "thinking", "slug": "thinking", "url": "https://www.leafyquotes.com/topics/thinking" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/John_Allen_Paulos#A_Mathematician_Reads_the_Newspaper_(1995)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:01:59" }, { "id": "0535c14f-b38a-4162-bf28-3f1618e46361", "slug": "i-remember-thinking", "url": "https://www.leafyquotes.com/john-allen-paulos/innumeracy/i-remember-thinking", "text": "I remember thinking of mathematics as a kind of omnipotent protector. You could prove things to people and they would have to believe you whether they liked you or not.", "language": "en", "author": { "name": "John Allen Paulos", "slug": "john-allen-paulos", "url": "https://www.leafyquotes.com/john-allen-paulos" }, "book": { "title": "Innumeracy", "slug": "innumeracy", "url": "https://www.leafyquotes.com/john-allen-paulos/innumeracy" }, "character": null, "chapter": null, "chapter_parent": null, "page": 99, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "evidence", "slug": "evidence", "url": "https://www.leafyquotes.com/topics/evidence" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/John_Allen_Paulos#Innumeracy:_Mathematical_Illiteracy_and_its_Consequences_(1988)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:01:58" }, { "id": "98ba8fa6-b3c8-4374-b217-349da45f22a0", "slug": "we-should-all", "url": "https://www.leafyquotes.com/edward-frenkel/love-and-math/we-should-all", "text": "We should all have access to the mathematical knowledge and tools needed to protect us from arbitrary decisions made by the powerful few in an increasingly math-driven world. Where there is no mathematics, there is no freedom.", "language": "en", "author": { "name": "Edward Frenkel", "slug": "edward-frenkel", "url": "https://www.leafyquotes.com/edward-frenkel" }, "book": { "title": "Love and Math", "slug": "love-and-math", "url": "https://www.leafyquotes.com/edward-frenkel/love-and-math" }, "character": null, "chapter": null, "chapter_parent": null, "page": 5, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "freedom", "slug": "freedom", "url": "https://www.leafyquotes.com/topics/freedom" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Edward_Frenkel#Love_and_Math,_2013", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:01:17" }, { "id": "bd6ccb30-686e-40d9-8d34-4dc5cd271506", "slug": "in-the-history", "url": "https://www.leafyquotes.com/tobias-dantzig/number/in-the-history", "text": "In the history of mathematics, the \"how\" always preceded the \"why,\" the technique of the subject preceded its philosophy.", "language": "en", "author": { "name": "Tobias Dantzig", "slug": "tobias-dantzig", "url": "https://www.leafyquotes.com/tobias-dantzig" }, "book": { "title": "Number", "slug": "number", "url": "https://www.leafyquotes.com/tobias-dantzig/number" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Tobias_Dantzig#Number:_The_Language_of_Science_(1930)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:00:53" }, { "id": "ac0398fc-0c07-4d0b-946b-d9ba09bc5d65", "slug": "the-progress-of-mathematics", "url": "https://www.leafyquotes.com/tobias-dantzig/number/the-progress-of-mathematics", "text": "The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it. ...It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth in had no part. ...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.", "language": "en", "author": { "name": "Tobias Dantzig", "slug": "tobias-dantzig", "url": "https://www.leafyquotes.com/tobias-dantzig" }, "book": { "title": "Number", "slug": "number", "url": "https://www.leafyquotes.com/tobias-dantzig/number" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "intuition", "slug": "intuition", "url": "https://www.leafyquotes.com/topics/intuition" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Tobias_Dantzig#Number:_The_Language_of_Science_(1930)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:00:53" }, { "id": "4112b654-1294-43d6-9426-1a42514aea7e", "slug": "between-the-philosophers", "url": "https://www.leafyquotes.com/tobias-dantzig/number/between-the-philosophers", "text": "Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic.", "language": "en", "author": { "name": "Tobias Dantzig", "slug": "tobias-dantzig", "url": "https://www.leafyquotes.com/tobias-dantzig" }, "book": { "title": "Number", "slug": "number", "url": "https://www.leafyquotes.com/tobias-dantzig/number" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "reality", "slug": "reality", "url": "https://www.leafyquotes.com/topics/reality" }, { "name": "philosophy", "slug": "philosophy", "url": "https://www.leafyquotes.com/topics/philosophy" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Tobias_Dantzig#Number:_The_Language_of_Science_(1930)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:00:53" }, { "id": "ff00a031-b26f-412d-8c66-f0d32514172f", "slug": "the-existence-theorem", "url": "https://www.leafyquotes.com/alastair-reynolds/pushing-ice/the-existence-theorem", "text": "The existence theorem says that it is always much easier to find a solution when you can be confident that one exists.", "language": "en", "author": { "name": "Alastair Reynolds", "slug": "alastair-reynolds", "url": "https://www.leafyquotes.com/alastair-reynolds" }, "book": { "title": "Pushing Ice", "slug": "pushing-ice", "url": "https://www.leafyquotes.com/alastair-reynolds/pushing-ice" }, "character": null, "chapter": null, "chapter_parent": null, "page": 444, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Alastair_Reynolds#Pushing_Ice_(2005)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:00:40" }, { "id": "ba2a1e13-a7f3-4e71-a06b-957fb0095f3a", "slug": "i-had-never", "url": "https://www.leafyquotes.com/alastair-reynolds/diamond-dogs-turquoise-days/i-had-never", "text": "I had never understood mathematics with any great agility, but now I sensed it as a hard grid of truth underlying everything: bones shining through the thin flesh of the world.", "language": "en", "author": { "name": "Alastair Reynolds", "slug": "alastair-reynolds", "url": "https://www.leafyquotes.com/alastair-reynolds" }, "book": { "title": "Diamond Dogs, Turquoise Days", "slug": "diamond-dogs-turquoise-days", "url": "https://www.leafyquotes.com/alastair-reynolds/diamond-dogs-turquoise-days" }, "character": null, "chapter": null, "chapter_parent": null, "page": 135, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "truth", "slug": "truth", "url": "https://www.leafyquotes.com/topics/truth" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Alastair_Reynolds#Diamond_Dogs,_Turquoise_Days_(2003)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T23:00:36" }, { "id": "d17d4ef0-732c-40a7-ac43-b3df4ceba05f", "slug": "the-laws-of-mathematics", "url": "https://www.leafyquotes.com/john-twelve-hawks/spark/the-laws-of-mathematics", "text": "The laws of mathematics are stronger than the laws of man.", "language": "en", "author": { "name": "John Twelve Hawks", "slug": "john-twelve-hawks", "url": "https://www.leafyquotes.com/john-twelve-hawks" }, "book": { "title": "Spark", "slug": "spark", "url": "https://www.leafyquotes.com/john-twelve-hawks/spark" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/John_Twelve_Hawks#Spark_(2014)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:59:59" }, { "id": "d2eba6e9-5520-49de-81c3-3279b1c9043b", "slug": "although-mathematics-originates", "url": "https://www.leafyquotes.com/nick-herbert/quantum-reality/although-mathematics-originates", "text": "Although mathematics originates in the human mind, its remarkable effectiveness in explaining the world does not extend to the mind itself. Psychology has proved unusually resistant to the mathematization that works so well in physics.", "language": "en", "author": { "name": "Nick Herbert", "slug": "nick-herbert", "url": "https://www.leafyquotes.com/nick-herbert" }, "book": { "title": "Quantum Reality", "slug": "quantum-reality", "url": "https://www.leafyquotes.com/nick-herbert/quantum-reality" }, "character": null, "chapter": null, "chapter_parent": null, "page": 2, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "psychology", "slug": "psychology", "url": "https://www.leafyquotes.com/topics/psychology" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Nick_Herbert_(physicist)#Quantum_Reality_-_Beyond_The_New_Physics", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:58:56" }, { "id": "bee8fec6-9b66-436e-8338-3e155a524c00", "slug": "that-logic-as-a-science", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought/that-logic-as-a-science", "text": "That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.", "language": "en", "author": { "name": "George Boole", "slug": "george-boole", "url": "https://www.leafyquotes.com/george-boole" }, "book": { "title": "An Investigation of the Laws of Thought", "slug": "an-investigation-of-the-laws-of-thought", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought" }, "character": null, "chapter": null, "chapter_parent": null, "page": 12, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "logic", "slug": "logic", "url": "https://www.leafyquotes.com/topics/logic" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/George_Boole#An_Investigation_of_the_Laws_of_Thought_(1854)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:56:56" }, { "id": "7b429978-16bb-4cf0-bf24-1f7f82fe1001", "slug": "it-is-not", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought/it-is-not", "text": "It is not of the essence of mathematics to be conversant with the ideas of number and quantity.", "language": "en", "author": { "name": "George Boole", "slug": "george-boole", "url": "https://www.leafyquotes.com/george-boole" }, "book": { "title": "An Investigation of the Laws of Thought", "slug": "an-investigation-of-the-laws-of-thought", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought" }, "character": null, "chapter": null, "chapter_parent": null, "page": 12, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/George_Boole#An_Investigation_of_the_Laws_of_Thought_(1854)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:56:56" }, { "id": "4686cc3f-179e-4067-b794-568d0116664b", "slug": "there-is-not", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought/there-is-not", "text": "There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted.", "language": "en", "author": { "name": "George Boole", "slug": "george-boole", "url": "https://www.leafyquotes.com/george-boole" }, "book": { "title": "An Investigation of the Laws of Thought", "slug": "an-investigation-of-the-laws-of-thought", "url": "https://www.leafyquotes.com/george-boole/an-investigation-of-the-laws-of-thought" }, "character": null, "chapter": null, "chapter_parent": null, "page": 6, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "logic", "slug": "logic", "url": "https://www.leafyquotes.com/topics/logic" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/George_Boole#An_Investigation_of_the_Laws_of_Thought_(1854)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:56:56" }, { "id": "b6c2ef16-3052-4271-9650-fe7f358f6ebd", "slug": "mathematics-thought-that", "url": "https://www.leafyquotes.com/brandon-sanderson/rhythm-of-war/mathematics-thought-that", "text": "Mathematics thought that there were numbers associated with tones—frequencies, wavelengths. Music, at its most fundamental level, was math.", "language": "en", "author": { "name": "Brandon Sanderson", "slug": "brandon-sanderson", "url": "https://www.leafyquotes.com/brandon-sanderson" }, "book": { "title": "Rhythm of War", "slug": "rhythm-of-war", "url": "https://www.leafyquotes.com/brandon-sanderson/rhythm-of-war" }, "character": null, "chapter": null, "chapter_parent": null, "page": 1040, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "music", "slug": "music", "url": "https://www.leafyquotes.com/topics/music" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Brandon_Sanderson#Rhythm_of_War_(2020)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:56:40" }, { "id": "e8a57a79-8e8e-4b87-bd47-89f8a61532dc", "slug": "there-is-terror", "url": "https://www.leafyquotes.com/darrell-huff/how-to-lie-with-statistics/there-is-terror", "text": "There is terror in numbers. [...] Perhaps we suffer from a trauma induced by grade-school arithmetic.", "language": "en", "author": { "name": "Darrell Huff", "slug": "darrell-huff", "url": "https://www.leafyquotes.com/darrell-huff" }, "book": { "title": "How to Lie with Statistics", "slug": "how-to-lie-with-statistics", "url": "https://www.leafyquotes.com/darrell-huff/how-to-lie-with-statistics" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "fear", "slug": "fear", "url": "https://www.leafyquotes.com/topics/fear" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/How_to_Lie_with_Statistics#Chapter_5:_The_Gee-Whiz_Graph", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:58" }, { "id": "e1e092b2-0a3d-42d1-9cbf-e3f06f8747e5", "slug": "we-need-heuristic", "url": "https://www.leafyquotes.com/george-polya/how-to-solve-it/we-need-heuristic", "text": "We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.", "language": "en", "author": { "name": "George Pólya", "slug": "george-polya", "url": "https://www.leafyquotes.com/george-polya" }, "book": { "title": "How to Solve It", "slug": "how-to-solve-it", "url": "https://www.leafyquotes.com/george-polya/how-to-solve-it" }, "character": null, "chapter": null, "chapter_parent": null, "page": 113, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/George_P%C3%B3lya#How_to_Solve_It_(1945)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:52" }, { "id": "7f31a202-d306-468a-b63d-7da61f6a4b23", "slug": "the-cookbook-gives", "url": "https://www.leafyquotes.com/george-polya/how-to-solve-it/the-cookbook-gives", "text": "The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. … Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.", "language": "en", "author": { "name": "George Pólya", "slug": "george-polya", "url": "https://www.leafyquotes.com/george-polya" }, "book": { "title": "How to Solve It", "slug": "how-to-solve-it", "url": "https://www.leafyquotes.com/george-polya/how-to-solve-it" }, "character": null, "chapter": null, "chapter_parent": null, "page": 219, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/George_P%C3%B3lya#How_to_Solve_It_(1945)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:52" }, { "id": "f66111dc-d37c-4c9a-afbe-183054f02ee0", "slug": "to-peer-through", "url": "https://www.leafyquotes.com/gregory-benford/cosm/to-peer-through", "text": "To peer through the quick stubble of mathematics and see the wonders lurking behind was to momentarily live in the infinite, beyond the press of the ordinary world where everyone else dwelled in ignorance.", "language": "en", "author": { "name": "Gregory Benford", "slug": "gregory-benford", "url": "https://www.leafyquotes.com/gregory-benford" }, "book": { "title": "Cosm", "slug": "cosm", "url": "https://www.leafyquotes.com/gregory-benford/cosm" }, "character": null, "chapter": null, "chapter_parent": null, "page": 335, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "beauty", "slug": "beauty", "url": "https://www.leafyquotes.com/topics/beauty" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Gregory_Benford#Cosm_(1998)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:24" }, { "id": "764531dd-2a05-4ce8-a3a2-5c5634fd5566", "slug": "that-was-what", "url": "https://www.leafyquotes.com/gregory-benford/artifact/that-was-what", "text": "That was what drew him to mathematics. Not because it was rarefied, but because it probed to the subtle, deeper reality. People said that mathematicians were unworldly, and yammered on about how Einstein couldn’t make correct change. Nonsense. Einstein just didn’t give a damn. It was the subtle, the beautiful that concerned him.", "language": "en", "author": { "name": "Gregory Benford", "slug": "gregory-benford", "url": "https://www.leafyquotes.com/gregory-benford" }, "book": { "title": "Artifact", "slug": "artifact", "url": "https://www.leafyquotes.com/gregory-benford/artifact" }, "character": null, "chapter": null, "chapter_parent": null, "page": 76, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "beauty", "slug": "beauty", "url": "https://www.leafyquotes.com/topics/beauty" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Gregory_Benford#Artifact_(1985)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:23" }, { "id": "4e5bcc59-7a9e-4017-b680-0346068e3fec", "slug": "one-of-the", "url": "https://www.leafyquotes.com/gregory-benford/timescape/one-of-the", "text": "“One of the laws of nature,” Gordon said, “is that half the people have got to be below average.” ”For a Gaussian distribution, yeah,” Cooper said. “Sad, though.”", "language": "en", "author": { "name": "Gregory Benford", "slug": "gregory-benford", "url": "https://www.leafyquotes.com/gregory-benford" }, "book": { "title": "Timescape", "slug": "timescape", "url": "https://www.leafyquotes.com/gregory-benford/timescape" }, "character": null, "chapter": null, "chapter_parent": null, "page": 234, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "humor", "slug": "humor", "url": "https://www.leafyquotes.com/topics/humor" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Gregory_Benford#Timescape_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:22" }, { "id": "ea4da2af-29e2-4ac2-bd2e-1c845f520c03", "slug": "as-far-as-the", "url": "https://www.leafyquotes.com/neal-stephenson/the-diamond-age/as-far-as-the", "text": "As far as the laws of probability, my lady, these cannot be broken, any more than any other mathematical principle. But laws of physics and mathematics are like a coordinate system that runs in only one dimension. Perhaps there is another dimension perpendicular to it, invisible to those laws of physics, describing the same things with different rules, and those rules are written in our hearts, in a deep place where we cannot go and read them except in our dreams.", "language": "en", "author": { "name": "Neal Stephenson", "slug": "neal-stephenson", "url": "https://www.leafyquotes.com/neal-stephenson" }, "book": { "title": "The Diamond Age", "slug": "the-diamond-age", "url": "https://www.leafyquotes.com/neal-stephenson/the-diamond-age" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "dreams", "slug": "dreams", "url": "https://www.leafyquotes.com/topics/dreams" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/The_Diamond_Age#Part_the_Second", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:55:12" }, { "id": "a0c940bf-1800-4881-b275-21a5cf8b20aa", "slug": "the-entire-physical", "url": "https://www.leafyquotes.com/roger-penrose/the-road-to-reality/the-entire-physical", "text": "...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles.", "language": "en", "author": { "name": "Roger Penrose", "slug": "roger-penrose", "url": "https://www.leafyquotes.com/roger-penrose" }, "book": { "title": "The Road to Reality", "slug": "the-road-to-reality", "url": "https://www.leafyquotes.com/roger-penrose/the-road-to-reality" }, "character": null, "chapter": null, "chapter_parent": null, "page": 18, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "physics", "slug": "physics", "url": "https://www.leafyquotes.com/topics/physics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Roger_Penrose#The_Road_to_Reality_(2004)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:54:37" }, { "id": "a24dc250-8d80-4628-8af6-e92cadb04def", "slug": "the-mathematical-forms", "url": "https://www.leafyquotes.com/marie-louise-von-franz/psyche-and-matter/the-mathematical-forms", "text": "The mathematical forms of order which the mind of a physicist manipulates coincides \"miraculously\" with experimental measurements.", "language": "en", "author": { "name": "Marie-Louise von Franz", "slug": "marie-louise-von-franz", "url": "https://www.leafyquotes.com/marie-louise-von-franz" }, "book": { "title": "Psyche and Matter", "slug": "psyche-and-matter", "url": "https://www.leafyquotes.com/marie-louise-von-franz/psyche-and-matter" }, "character": null, "chapter": null, "chapter_parent": null, "page": 269, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "science", "slug": "science", "url": "https://www.leafyquotes.com/topics/science" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Marie-Louise_von_Franz#Psyche_and_Matter_(1992)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:53:07" }, { "id": "bfab6c4c-3210-4108-b310-a1dbdf19a9f3", "slug": "if-mathematical-objects", "url": "https://www.leafyquotes.com/cormac-mccarthy/stella-maris/if-mathematical-objects", "text": "If mathematical objects exist independently of human thought what else are they independent of? The universe, I suppose.", "language": "en", "author": { "name": "Cormac McCarthy", "slug": "cormac-mccarthy", "url": "https://www.leafyquotes.com/cormac-mccarthy" }, "book": { "title": "Stella Maris", "slug": "stella-maris", "url": "https://www.leafyquotes.com/cormac-mccarthy/stella-maris" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Cormac_McCarthy#Stella_Maris_(2022)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:52:31" }, { "id": "9ec36aa5-db74-4379-bae6-3345475f4bc7", "slug": "i-have-asked", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms/i-have-asked", "text": "I have asked many teachers and parents what they thought mathematics to be and why it was important to learn it. Few held a view of mathematics that was sufficiently coherent to justify devoting several thousand hours of a child's life to learning it, and children sense this. When a teacher tells a student that the reason for those many hours of arithmetic is to be able to check the change at the supermarket, the teacher is simply not believed. Children see such \"reasons\" as one more example of adult double talk. The same effect is produced when children are told school math is \"fun\" when they are pretty sure that teachers who say so spend their leisure hours on anything except this allegedly fun-filled activity. Nor does it help to tell them that they need math to become scientists---most children don't have such a plan. The children can see perfectly well that the teacher does not enjoy math any more than they do and that the reason for doing it is simply that it has been inscribed into the curriculum. All of this erodes children's confidence in the adult world and the process of education. And I think it introduces a deep element of dishonestly into the education relationship.", "language": "en", "author": { "name": "Seymour A. Papert", "slug": "seymour-a-papert", "url": "https://www.leafyquotes.com/seymour-a-papert" }, "book": { "title": "Mindstorms", "slug": "mindstorms", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "honesty", "slug": "honesty", "url": "https://www.leafyquotes.com/topics/honesty" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Seymour_Papert#Mindstorms:_Children,_Computers,_and_Powerful_Ideas_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:51:17" }, { "id": "5313ecab-e712-44ae-aca5-33edce0dd5c7", "slug": "it-is-not", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms/it-is-not", "text": "It is not uncommon for intelligent adults to turn into passive observers of their own incompetence in anything but the most elementary mathematics. Individuals may see the direct consequences of this intellectual paralysis in terms of limiting job possibilities. But the indirect, secondary consequences are even more serious. One of the main lessons learned by most people in math class is a sense of having rigid limitations. They learn a balkanized image of human knowledge which they come to see as a patchwork of territories separated by impassable iron curtains.", "language": "en", "author": { "name": "Seymour A. Papert", "slug": "seymour-a-papert", "url": "https://www.leafyquotes.com/seymour-a-papert" }, "book": { "title": "Mindstorms", "slug": "mindstorms", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Seymour_Papert#Mindstorms:_Children,_Computers,_and_Powerful_Ideas_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:51:17" }, { "id": "3ed75fdc-1cf1-443d-8b93-0b084367ca44", "slug": "the-kind-of-mathematics", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms/the-kind-of-mathematics", "text": "The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it.", "language": "en", "author": { "name": "Seymour A. Papert", "slug": "seymour-a-papert", "url": "https://www.leafyquotes.com/seymour-a-papert" }, "book": { "title": "Mindstorms", "slug": "mindstorms", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "children", "slug": "children", "url": "https://www.leafyquotes.com/topics/children" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Seymour_Papert#Mindstorms:_Children,_Computers,_and_Powerful_Ideas_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:51:17" }, { "id": "278a520b-f009-404e-a9e4-d88d44a8d6aa", "slug": "our-children-grow", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms/our-children-grow", "text": "Our children grow up in a culture permeated with the idea that there are \"smart people\" and \"dumb people\". The social construction of the individual is as a bundle of aptitudes. There are people who are \"good at math\" and people who \"can't do math.\" Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. As a result, children perceive failure as relegating them either to the group of \"dumb people\" or, more often, to a group of people \"dumb at x\" (where, as we have pointed out, x often equals mathematics). Within this framework children will define themselves in terms of their limitations, and this definition will be consolidated and reinforced throughout their lives. Only rarely does some exceptional event lead people to reorganize their intellectual self-image in such a way as to open up new perspectives on what is learnable.", "language": "en", "author": { "name": "Seymour A. Papert", "slug": "seymour-a-papert", "url": "https://www.leafyquotes.com/seymour-a-papert" }, "book": { "title": "Mindstorms", "slug": "mindstorms", "url": "https://www.leafyquotes.com/seymour-a-papert/mindstorms" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "children", "slug": "children", "url": "https://www.leafyquotes.com/topics/children" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Seymour_Papert#Mindstorms:_Children,_Computers,_and_Powerful_Ideas_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:51:17" }, { "id": "bd7ca4ca-2c33-46d2-88b3-fcb508fab079", "slug": "the-notions-she", "url": "https://www.leafyquotes.com/david-brin/glory-season/the-notions-she", "text": "The notions she fought with needed more than the simple algebra she’d been grudgingly taught at Lamai Hold. More and more she resented how they had robbed her of this, arguably her one talent, driving her from math and other abstractions by the simple expedient of making them seem boring.", "language": "en", "author": { "name": "David Brin", "slug": "david-brin", "url": "https://www.leafyquotes.com/david-brin" }, "book": { "title": "Glory Season", "slug": "glory-season", "url": "https://www.leafyquotes.com/david-brin/glory-season" }, "character": null, "chapter": null, "chapter_parent": null, "page": 337, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "education", "slug": "education", "url": "https://www.leafyquotes.com/topics/education" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Brin#Glory_Season_(1993)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:50:45" }, { "id": "7e4bbdc1-d760-4642-86e4-fd8ec09c9aa8", "slug": "its-magic-the", "url": "https://www.leafyquotes.com/david-brin/glory-season/its-magic-the", "text": "“It’s magic,” the chief cook concluded, in awe. ”No, not magic,” the ship’s doctor replied. “It’s much more. It’s mathematics.”", "language": "en", "author": { "name": "David Brin", "slug": "david-brin", "url": "https://www.leafyquotes.com/david-brin" }, "book": { "title": "Glory Season", "slug": "glory-season", "url": "https://www.leafyquotes.com/david-brin/glory-season" }, "character": null, "chapter": null, "chapter_parent": null, "page": 466, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Brin#Glory_Season_(1993)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:50:45" }, { "id": "7332acb2-8d6d-4a70-9db6-13165ff20871", "slug": "about-drafting-all", "url": "https://www.leafyquotes.com/samuel-r-delany/out-of-the-dead-city/about-drafting-all", "text": "About drafting all the scientific students into the war effort. Maybe the war is good, but, Tomar, I’m working on my own project. All at once, the thing I want most in the world is to be left alone to work on it. And I want you, and I want to have a picnic. I’m nearly at the solution, and to have to stop and work on bomb sightings and missile trajectories…Tomar, there’s a beauty in abstract mathematics that shouldn’t be dulled with that sort of thing.", "language": "en", "author": { "name": "Samuel R. Delany", "slug": "samuel-r-delany", "url": "https://www.leafyquotes.com/samuel-r-delany" }, "book": { "title": "Out of the Dead City", "slug": "out-of-the-dead-city", "url": "https://www.leafyquotes.com/samuel-r-delany/out-of-the-dead-city" }, "character": null, "chapter": null, "chapter_parent": null, "page": 64, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "war", "slug": "war", "url": "https://www.leafyquotes.com/topics/war" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Samuel_R._Delany#Out_of_the_Dead_City_(1963)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:48:16" }, { "id": "46347026-1a5b-4b79-b9dd-4910b7a29787", "slug": "e-ven-in-the", "url": "https://www.leafyquotes.com/werner-heisenberg/physics-and-philosophy/e-ven-in-the", "text": "[E]ven in the most precise part of science, in mathematics, we cannot avoid using concepts that involve contradictions. ...[I]t is well known that the concept of infinity leads to contradictions... but it would be practically impossible to construct... mathematics without this concept.", "language": "en", "author": { "name": "Werner Heisenberg", "slug": "werner-heisenberg", "url": "https://www.leafyquotes.com/werner-heisenberg" }, "book": { "title": "Physics and Philosophy", "slug": "physics-and-philosophy", "url": "https://www.leafyquotes.com/werner-heisenberg/physics-and-philosophy" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "science", "slug": "science", "url": "https://www.leafyquotes.com/topics/science" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Werner_Heisenberg#Physics_and_Philosophy_(1958)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:48:06" }, { "id": "6445a343-515c-4aea-836d-6c04af7d8560", "slug": "mathematics-is-the", "url": "https://www.leafyquotes.com/michio-kaku/hyperspace/mathematics-is-the", "text": "Mathematics... is the set of all possible self-consistent structures, and there are vastly more logical structures than physical principles.", "language": "en", "author": { "name": "Michio Kaku", "slug": "michio-kaku", "url": "https://www.leafyquotes.com/michio-kaku" }, "book": { "title": "Hyperspace", "slug": "hyperspace", "url": "https://www.leafyquotes.com/michio-kaku/hyperspace" }, "character": null, "chapter": null, "chapter_parent": null, "page": 328, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Michio_Kaku#Hyperspace_(1995)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:46:34" }, { "id": "76e473be-344b-46c1-92a4-7abd1e90c9ff", "slug": "beauty-cannot-be-defined", "url": "https://www.leafyquotes.com/carl-von-clausewitz/on-war/beauty-cannot-be-defined", "text": "Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their geometrical formulas.", "language": "en", "author": { "name": "Carl von Clausewitz", "slug": "carl-von-clausewitz", "url": "https://www.leafyquotes.com/carl-von-clausewitz" }, "book": { "title": "On War", "slug": "on-war", "url": "https://www.leafyquotes.com/carl-von-clausewitz/on-war" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "beauty", "slug": "beauty", "url": "https://www.leafyquotes.com/topics/beauty" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Carl_von_Clausewitz#Book_3", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:45:37" }, { "id": "36f84fd5-da85-41db-a561-a734a7868303", "slug": "galileo-wrote-that", "url": "https://www.leafyquotes.com/steven-pinker/how-the-mind-works/galileo-wrote-that", "text": "Galileo wrote that 'the book of nature is written in the language of mathematics; without its help it is impossible to comprehend a single word of it.'", "language": "en", "author": { "name": "Steven Pinker", "slug": "steven-pinker", "url": "https://www.leafyquotes.com/steven-pinker" }, "book": { "title": "How the Mind Works", "slug": "how-the-mind-works", "url": "https://www.leafyquotes.com/steven-pinker/how-the-mind-works" }, "character": null, "chapter": null, "chapter_parent": null, "page": 359, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "nature", "slug": "nature", "url": "https://www.leafyquotes.com/topics/nature" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Steven_Pinker#How_the_Mind_Works_(1997)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:49" }, { "id": "7ab62bbd-6f6f-4b2d-b85f-b71d80c59e22", "slug": "yes-god-makes", "url": "https://www.leafyquotes.com/kim-stanley-robinson/galileos-dream/yes-god-makes", "text": "Yes. God makes the world using mathematics, and he has given us minds that can see it. We can discover the laws He used! It is a most beautiful thing to witness and understand! It's prayer. It's more than prayer, it's a sacrament, a kind of communion. An apprehension—an epiphany—it's seeing God, while still in this body and in this world! How blessed we are, to be able to experience God like that! Who would not devote their time to understanding more, to seeing deeper in God's manner of thinking about these things?", "language": "en", "author": { "name": "Kim Stanley Robinson", "slug": "kim-stanley-robinson", "url": "https://www.leafyquotes.com/kim-stanley-robinson" }, "book": { "title": "Galileo's Dream", "slug": "galileos-dream", "url": "https://www.leafyquotes.com/kim-stanley-robinson/galileos-dream" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "science", "slug": "science", "url": "https://www.leafyquotes.com/topics/science" }, { "name": "god", "slug": "god", "url": "https://www.leafyquotes.com/topics/god" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Kim_Stanley_Robinson#Galileo's_Dream_(2009)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:47" }, { "id": "6a5fcd90-5e74-4e79-98b1-17e6aaaf063d", "slug": "the-world-operates", "url": "https://www.leafyquotes.com/kim-stanley-robinson/the-years-of-rice-and-salt/the-world-operates", "text": "The world operates by number, by physical laws, expressed mathematically. If you know these, you will have a better grasp of things. And some possible job skills.", "language": "en", "author": { "name": "Kim Stanley Robinson", "slug": "kim-stanley-robinson", "url": "https://www.leafyquotes.com/kim-stanley-robinson" }, "book": { "title": "The Years of Rice and Salt", "slug": "the-years-of-rice-and-salt", "url": "https://www.leafyquotes.com/kim-stanley-robinson/the-years-of-rice-and-salt" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Kim_Stanley_Robinson#The_Years_of_Rice_and_Salt_(2002)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:46" }, { "id": "1b13050d-7936-4108-9dc4-d3ee5cd3d2f1", "slug": "and-so-he-struggled", "url": "https://www.leafyquotes.com/kim-stanley-robinson/blue-mars/and-so-he-struggled", "text": "And so he struggled on. As he did he saw it anew, as fresh as in his undergraduate days: the structure of science was so beautiful. It was surely one of the greatest achievements of the human spirit, a kind of stupendous parthenon of the mind, constantly a work in progress, like a symphonic epic poem of thousands of stanzas, being composed by them all in a giant ongoing collaboration. The language of the poem was mathematics, because this appeared to be the language of nature itself; there was no other way to explain the startling adherence of natural phenomena to mathematical expressions of great difficulty and subtlety. And so in this marvelous family of languages their songs explored the various manifestations of reality, in different fields of science, and each science worked up its standard model to explain things, all constellating at some distance around the basics of particle physics, depending on what level or scale was being investigated, so that all the standard models hopefully interlocked in a coherent larger structure.", "language": "en", "author": { "name": "Kim Stanley Robinson", "slug": "kim-stanley-robinson", "url": "https://www.leafyquotes.com/kim-stanley-robinson" }, "book": { "title": "Blue Mars", "slug": "blue-mars", "url": "https://www.leafyquotes.com/kim-stanley-robinson/blue-mars" }, "character": null, "chapter": null, "chapter_parent": null, "page": 656, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "science", "slug": "science", "url": "https://www.leafyquotes.com/topics/science" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Kim_Stanley_Robinson#Blue_Mars_(1996)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:46" }, { "id": "6a38ad76-d924-4214-8dda-38be803d5aa3", "slug": "waves-striking-the", "url": "https://www.leafyquotes.com/kim-stanley-robinson/blue-mars/waves-striking-the", "text": "Waves striking the sea cliffs bounced back outward, creating interference patterns with the incoming waves that could have come right out of a physics wave tank: so beautiful. And so strange, that the world should conform so well to mathematical formulation. The unreasonable effectiveness of math; it was at the heart of the great unexplainable.", "language": "en", "author": { "name": "Kim Stanley Robinson", "slug": "kim-stanley-robinson", "url": "https://www.leafyquotes.com/kim-stanley-robinson" }, "book": { "title": "Blue Mars", "slug": "blue-mars", "url": "https://www.leafyquotes.com/kim-stanley-robinson/blue-mars" }, "character": null, "chapter": null, "chapter_parent": null, "page": 439, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "nature", "slug": "nature", "url": "https://www.leafyquotes.com/topics/nature" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Kim_Stanley_Robinson#Blue_Mars_(1996)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:45" }, { "id": "cf8105d1-a0d8-4582-8d6d-8be55f6cb2cb", "slug": "anyone-who-cannot", "url": "https://www.leafyquotes.com/robert-a-heinlein/time-enough-for-love/anyone-who-cannot", "text": "Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.", "language": "en", "author": { "name": "Robert A. Heinlein", "slug": "robert-a-heinlein", "url": "https://www.leafyquotes.com/robert-a-heinlein" }, "book": { "title": "Time Enough For Love", "slug": "time-enough-for-love", "url": "https://www.leafyquotes.com/robert-a-heinlein/time-enough-for-love" }, "character": null, "chapter": null, "chapter_parent": null, "page": 247, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Time_Enough_for_Love#Quotes", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:44:01" }, { "id": "c37fe971-5412-4b3e-bb5d-9e14c8a316a8", "slug": "necessary-truth-is-merely", "url": "https://www.leafyquotes.com/david-deutsch/the-fabric-of-reality/necessary-truth-is-merely", "text": "Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.", "language": "en", "author": { "name": "David Deutsch", "slug": "david-deutsch", "url": "https://www.leafyquotes.com/david-deutsch" }, "book": { "title": "The Fabric of Reality", "slug": "the-fabric-of-reality", "url": "https://www.leafyquotes.com/david-deutsch/the-fabric-of-reality" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Deutsch#The_Fabric_of_Reality_(1997)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:43:51" }, { "id": "4aedb268-ea63-4436-afdb-cfc94728a8b7", "slug": "mathematical-knowledge-may", "url": "https://www.leafyquotes.com/david-deutsch/the-fabric-of-reality/mathematical-knowledge-may", "text": "Mathematical knowledge may, just like our scientific knowledge, be deep and broad, it may be subtle and wonderfully explanatory, it may be uncontroversially accepted; but it cannot be certain.", "language": "en", "author": { "name": "David Deutsch", "slug": "david-deutsch", "url": "https://www.leafyquotes.com/david-deutsch" }, "book": { "title": "The Fabric of Reality", "slug": "the-fabric-of-reality", "url": "https://www.leafyquotes.com/david-deutsch/the-fabric-of-reality" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "knowledge", "slug": "knowledge", "url": "https://www.leafyquotes.com/topics/knowledge" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/David_Deutsch#The_Fabric_of_Reality_(1997)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:43:51" }, { "id": "454fa816-c4ac-482b-9d3e-82d59103eb9d", "slug": "godels-theorem-shows", "url": "https://www.leafyquotes.com/freeman-dyson/the-scientist-as-rebel/godels-theorem-shows", "text": "Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.", "language": "en", "author": { "name": "Freeman Dyson", "slug": "freeman-dyson", "url": "https://www.leafyquotes.com/freeman-dyson" }, "book": { "title": "The Scientist as Rebel", "slug": "the-scientist-as-rebel", "url": "https://www.leafyquotes.com/freeman-dyson/the-scientist-as-rebel" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "truth", "slug": "truth", "url": "https://www.leafyquotes.com/topics/truth" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Freeman_Dyson#The_Scientist_As_Rebel_(2006)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:43:13" }, { "id": "a62dbd52-5531-4bbb-a683-33d68155cc1f", "slug": "i-doubt-not", "url": "https://www.leafyquotes.com/john-locke/an-essay-concerning-human-understanding/i-doubt-not", "text": "I doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out.", "language": "en", "author": { "name": "John Locke", "slug": "john-locke", "url": "https://www.leafyquotes.com/john-locke" }, "book": { "title": "An Essay Concerning Human Understanding", "slug": "an-essay-concerning-human-understanding", "url": "https://www.leafyquotes.com/john-locke/an-essay-concerning-human-understanding" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "morality", "slug": "morality", "url": "https://www.leafyquotes.com/topics/morality" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/John_Locke#An_Essay_Concerning_Human_Understanding_(1689)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:42:07" }, { "id": "e72ee7e8-33e6-46a9-a1c6-df64bbb3e79c", "slug": "i-dont-believe", "url": "https://www.leafyquotes.com/richard-p-feynman/the-pleasure-of-finding-things-out/i-dont-believe", "text": "...I don't believe in the idea that there are a few peculiar people capable of understanding math and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, \"What one fool can do, another fool can.\" What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it all deep and profound...", "language": "en", "author": { "name": "Richard P. Feynman", "slug": "richard-p-feynman", "url": "https://www.leafyquotes.com/richard-p-feynman" }, "book": { "title": "The Pleasure of Finding Things Out", "slug": "the-pleasure-of-finding-things-out", "url": "https://www.leafyquotes.com/richard-p-feynman/the-pleasure-of-finding-things-out" }, "character": null, "chapter": null, "chapter_parent": null, "page": 194, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Richard_Feynman#The_Pleasure_of_Finding_Things_Out_(1999)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:41:01" }, { "id": "ba1aab3a-9046-4eca-b2f8-38d25601347f", "slug": "mathematics-is-not", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law/mathematics-is-not", "text": "Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.", "language": "en", "author": { "name": "Richard P. Feynman", "slug": "richard-p-feynman", "url": "https://www.leafyquotes.com/richard-p-feynman" }, "book": { "title": "The Character of Physical Law", "slug": "the-character-of-physical-law", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "logic", "slug": "logic", "url": "https://www.leafyquotes.com/topics/logic" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Richard_Feynman#The_Character_of_Physical_Law_(1965)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:59" }, { "id": "aaaa6926-c98d-479a-b500-248ee72b54c2", "slug": "dirac-discovered-the", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law/dirac-discovered-the", "text": "...Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way. ...It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.", "language": "en", "author": { "name": "Richard P. Feynman", "slug": "richard-p-feynman", "url": "https://www.leafyquotes.com/richard-p-feynman" }, "book": { "title": "The Character of Physical Law", "slug": "the-character-of-physical-law", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" }, { "name": "physics", "slug": "physics", "url": "https://www.leafyquotes.com/topics/physics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Richard_Feynman#The_Character_of_Physical_Law_(1965)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:59" }, { "id": "883d6322-6daf-4399-a56a-aaac115219d1", "slug": "to-those-who", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law/to-those-who", "text": "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.", "language": "en", "author": { "name": "Richard P. Feynman", "slug": "richard-p-feynman", "url": "https://www.leafyquotes.com/richard-p-feynman" }, "book": { "title": "The Character of Physical Law", "slug": "the-character-of-physical-law", "url": "https://www.leafyquotes.com/richard-p-feynman/the-character-of-physical-law" }, "character": null, "chapter": null, "chapter_parent": null, "page": 58, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "nature", "slug": "nature", "url": "https://www.leafyquotes.com/topics/nature" }, { "name": "beauty", "slug": "beauty", "url": "https://www.leafyquotes.com/topics/beauty" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Richard_Feynman#The_Character_of_Physical_Law_(1965)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:59" }, { "id": "c29652aa-b1b2-41a8-b2cb-6353b943cfed", "slug": "someone-told-me-that", "url": "https://www.leafyquotes.com/stephen-w-hawking/a-brief-history-of-time/someone-told-me-that", "text": "Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, . I hope that this will not scare off half of my potential readers.", "language": "en", "author": { "name": "Stephen W. 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It is also an end in itself, and as such, it has, over the centuries, affected our worldview in its own right.", "language": "en", "author": { "name": "Stephen W. Hawking", "slug": "stephen-w-hawking", "url": "https://www.leafyquotes.com/stephen-w-hawking" }, "book": { "title": "God Created the Integers", "slug": "god-created-the-integers", "url": "https://www.leafyquotes.com/stephen-w-hawking/god-created-the-integers" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Stephen_Hawking#God_Created_the_Integers_(2007)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:31" }, { "id": "36e51a83-2c19-45a0-a13f-5ad45b7085ee", "slug": "the-universe-was", "url": "https://www.leafyquotes.com/carl-sagan/contact/the-universe-was", "text": "The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn't matter what you look like, or what you're made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you'll find it. It's already here. It's inside everything. You don't have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist's signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.", "language": "en", "author": { "name": "Carl Sagan", "slug": "carl-sagan", "url": "https://www.leafyquotes.com/carl-sagan" }, "book": { "title": "Contact", "slug": "contact", "url": "https://www.leafyquotes.com/carl-sagan/contact" }, "character": null, "chapter": null, "chapter_parent": null, "page": 431, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "god", "slug": "god", "url": "https://www.leafyquotes.com/topics/god" }, { "name": "the universe", "slug": "the-universe", "url": "https://www.leafyquotes.com/topics/the-universe" }, { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Carl_Sagan#Contact_(1985)", "license": { "label": "CC BY-SA 4.0", "url": 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{ "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:27" }, { "id": "5e4cf065-542a-4461-9cf8-80ad026d6039", "slug": "a-googolplex-is-precisely", "url": "https://www.leafyquotes.com/carl-sagan/cosmos/a-googolplex-is-precisely", "text": "A googolplex is precisely as far from infinity as is the number 1... no matter what number you have in mind, infinity is larger still.", "language": "en", "author": { "name": "Carl Sagan", "slug": "carl-sagan", "url": "https://www.leafyquotes.com/carl-sagan" }, "book": { "title": "Cosmos", "slug": "cosmos", "url": "https://www.leafyquotes.com/carl-sagan/cosmos" }, "character": null, "chapter": null, "chapter_parent": null, "page": 220, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], "source": { "name": "Wikiquote", "url": "https://en.wikiquote.org/wiki/Carl_Sagan#Cosmos_(1980)", "license": { "label": "CC BY-SA 4.0", "url": "https://creativecommons.org/licenses/by-sa/4.0/" } }, "added_at": "2026-09-25T22:40:27" }, { "id": "1ca9a454-c4b3-4e91-ad85-2eaf7ee3ebce", "slug": "angling-may-be-said", "url": "https://www.leafyquotes.com/izaak-walton/the-compleat-angler/angling-may-be-said", "text": "Angling may be said to be so like the mathematics that it can never be fully learnt.", "language": "en", "author": { "name": "Izaak Walton", "slug": "izaak-walton", "url": "https://www.leafyquotes.com/izaak-walton" }, "book": { "title": "The Compleat Angler", "slug": "the-compleat-angler", "url": "https://www.leafyquotes.com/izaak-walton/the-compleat-angler" }, "character": null, "chapter": null, "chapter_parent": null, "page": null, "verified": false, "original": null, "other_languages": [], "topics": [ { "name": "mathematics", "slug": "mathematics", "url": "https://www.leafyquotes.com/topics/mathematics" } ], 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