--- title: "Meaning & Key Takeaway of: The certainty of mathematics depends on…" description: "\"“The certainty of mathematics depends on its complete abstract generality.”\" — Alfred North Whitehead" image: "https://sms4smile.com/quotes/i/f0e/alfred-north-whitehead-836_abstract_the-certainty-of-mathematics-depends-on_871832.png" --- # The certainty of mathematics depends on its complete… ![“The certainty of mathematics depends on its complete abstract generality.” quote by Alfred North Whitehead](https://sms4smile.com/quotes/i/f0e/alfred-north-whitehead-836_abstract_the-certainty-of-mathematics-depends-on_871832.png) [Download](https://sms4smile.com/quotes/i/f0e/alfred-north-whitehead-836_abstract_the-certainty-of-mathematics-depends-on_871832.png) [Open image](https://sms4smile.com/quotes/i/f0e/alfred-north-whitehead-836_abstract_the-certainty-of-mathematics-depends-on_871832.png) > ““The certainty of mathematics depends on its complete abstract generality.”” [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics' reliability stems from its abstract, universal nature that abstracts away specifics, ensuring consistency across contexts. **In simple terms:** Math works because it’s completely abstract and general. Key Takeaway Value abstraction for reliable reasoning. Themes abstraction reliability universality Mood analytical thoughtful Type philosophical educational When to use this quote - teaching - research - engineering - policy making Key Concepts logic foundations of mathematics Questions to Reflect On - When does abstraction hinder problem solving? - How can we balance abstraction with concrete relevance? A Different Perspective Over‑abstraction may detach math from practical problems, limiting applicability. ★ ★ ★ ★ ★ No ratings yet [Abstract](https://sms4smile.com/quotes/about/abstract/) [Abstract Generality](https://sms4smile.com/quotes/about/abstract-generality-960964/) [Certainty](https://sms4smile.com/quotes/about/certainty/) [Certainty Mathematics](https://sms4smile.com/quotes/about/certainty-mathematics-960965/) [Generality](https://sms4smile.com/quotes/about/generality/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Mathematics Depends](https://sms4smile.com/quotes/about/mathematics-depends-960966/) ## Related quotes > [He who does not understand the supreme certainty of mathematics is wallowing in confusion.](https://sms4smile.com/quotes/leonardo-da-vinci/he-who-does-not-understand-the-supreme-certainty-of-mathematics-is/) [Leonardo da Vinci](https://sms4smile.com/quotes/author/leonardo-da-vinci/) > [It is this union of passionate interest in the detailed facts with equal devotion to abstract generalisation which forms the novelty in our present…](https://sms4smile.com/quotes/alfred-north-whitehead/it-is-this-union-of-passionate-interest-in-the-detailed-facts-with/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from…](https://sms4smile.com/quotes/alfred-north-whitehead/it-is-natural-to-think-that-an-abstract-science-cannot-be-of-much/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure…](https://sms4smile.com/quotes/charles-sanders-peirce/generality-is-indeed-an-indispensable-ingredient-of-reality-for-mere/) [Charles Sanders Peirce](https://sms4smile.com/quotes/author/charles-sanders-peirce/) > [“When we choose a generality, an idea, a cause, instead of a person, when this becomes the accepted, the required thing to do, then…](https://sms4smile.com/quotes/madeleine-l-engle/when-we-choose-a-generality-an-idea-a-cause-instead-of-a-person-when/) [Madeleine L'Engle](https://sms4smile.com/quotes/author/madeleine-l-engle/) > [The generality of men have, like plants, latent properties, which chance brings to light.](https://sms4smile.com/quotes/francois-de-la-rochefoucauld/the-generality-of-men-have-like-plants-latent-properties-which-chance/) [Francois de La Rochefoucauld](https://sms4smile.com/quotes/author/francois-de-la-rochefoucauld/) > [The opinion I have of the generality of women--who appear to me as children to whom I would rather give a sugar plum than…](https://sms4smile.com/quotes/john-keats/the-opinion-i-have-of-the-generality-of-women-who-appear-to-me-as/) [John Keats](https://sms4smile.com/quotes/author/john-keats/) > [Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity…](https://sms4smile.com/quotes/kenneth-e-boulding/conventions-of-generality-and-mathematical-elegance-may-be-just-as/) [Kenneth E. Boulding](https://sms4smile.com/quotes/author/kenneth-e-boulding/) > [This idea that there is generality in the specific is of far-reaching importance.](https://sms4smile.com/quotes/anonymous/this-idea-that-there-is-generality-in-the-specific-is-of-far-reaching/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Since the generality of persons act from impulse, much more than from principle, men are neither so good nor so bad as we are…](https://sms4smile.com/quotes/augustus-hare/since-the-generality-of-persons-act-from-impulse-much-more-than-from/) [Augustus Hare](https://sms4smile.com/quotes/author/augustus-hare/) > [Don’t become a wandering generality. Be a meaningful specific.](https://sms4smile.com/quotes/zig-ziglar/don-t-become-a-wandering-generality-be-a-meaningful-specific/) [Zig Ziglar](https://sms4smile.com/quotes/author/zig-ziglar/) > [God is basic Fact. He must not be thought of as a featureless generality. He is the most concrete thing there is.](https://sms4smile.com/quotes/c-s-lewis/god-is-basic-fact-he-must-not-be-thought-of-as-a-featureless/) [C. S. Lewis](https://sms4smile.com/quotes/author/c-s-lewis/) > [To the generality of men you cannot give a stronger hint for them to impose upon you than by imposing upon yourself.](https://sms4smile.com/quotes/henry-fielding/to-the-generality-of-men-you-cannot-give-a-stronger-hint-for-them-to/) [Henry Fielding](https://sms4smile.com/quotes/author/henry-fielding/) > [It is good sense applied with diligence to what was at first a mere accident, and which by great application grew to be called,…](https://sms4smile.com/quotes/samuel-johnson/it-is-good-sense-applied-with-diligence-to-what-was-at-first-a-mere/) [Samuel Johnson](https://sms4smile.com/quotes/author/samuel-johnson/) > [...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept…](https://sms4smile.com/quotes/paul-halmos/the-source-of-all-great-mathematics-is-the-special-case-the-concrete/) [Paul Halmos](https://sms4smile.com/quotes/author/paul-halmos/) ## More by Alfred North Whitehead > [For successful education there must always be a certain freshness in the knowledge dealt with. It must be either new in itself or invested…](https://sms4smile.com/quotes/alfred-north-whitehead/for-successful-education-there-must-always-be-a-certain-freshness-in/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Philosophy begins in wonder. And, at the end, when philosophic thought has done its best, the wonder remains.](https://sms4smile.com/quotes/alfred-north-whitehead/philosophy-begins-in-wonder-and-at-the-end-when-philosophic-thought/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [The pursuit of mathematics is a divine madness of the human spirit.](https://sms4smile.com/quotes/alfred-north-whitehead/the-pursuit-of-mathematics-is-a-divine-madness-of-the-human-spirit/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Without adventure all civilization is full of decay. Adventure rarely reaches its predetermined end. Columbus never reached China.](https://sms4smile.com/quotes/alfred-north-whitehead/without-adventure-all-civilization-is-full-of-decay-adventure-rarely/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Aristotle discovered all the half-truths which were necessary to the creation of science.](https://sms4smile.com/quotes/alfred-north-whitehead/aristotle-discovered-all-the-half-truths-which-were-necessary-to-the/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [On the ostensible exactitude of certain branches of human knowledge, including mathematics. The exactness is a fake.](https://sms4smile.com/quotes/alfred-north-whitehead/on-the-ostensible-exactitude-of-certain-branches-of-human-knowledge/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [It is this union of passionate interest in the detailed facts with equal devotion to abstract generalisation which forms the novelty in our present…](https://sms4smile.com/quotes/alfred-north-whitehead/it-is-this-union-of-passionate-interest-in-the-detailed-facts-with/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Our minds are finite, and yet even in these circumstances of infinitude we are surrounded by possibilities that are infinite, and the purpose of…](https://sms4smile.com/quotes/alfred-north-whitehead/our-minds-are-finite-and-yet-even-in-these-circumstances-of/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [The many become one and are increased by one.](https://sms4smile.com/quotes/alfred-north-whitehead/the-many-become-one-and-are-increased-by-one/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.](https://sms4smile.com/quotes/alfred-north-whitehead/art-is-the-imposing-of-a-pattern-on-experience-and-our-aesthetic/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [The future belongs to those who can rise above the confines of the earth.](https://sms4smile.com/quotes/alfred-north-whitehead/the-future-belongs-to-those-who-can-rise-above-the-confines-of-the/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Common sense is genius in homespun.](https://sms4smile.com/quotes/alfred-north-whitehead/common-sense-is-genius-in-homespun/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Everyone is a philosopher. Not everyone is good at it.](https://sms4smile.com/quotes/alfred-north-whitehead/everyone-is-a-philosopher-not-everyone-is-good-at-it/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Do not teach too many subjects and what you teach, teach thoroughly.](https://sms4smile.com/quotes/alfred-north-whitehead/do-not-teach-too-many-subjects-and-what-you-teach-teach-thoroughly/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are cavalry charges in…](https://sms4smile.com/quotes/alfred-north-whitehead/civilization-advances-by-extending-the-number-of-important-operations/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) [Explore all 356 Alfred North Whitehead quotes ](https://sms4smile.com/quotes/author/alfred-north-whitehead/) ## More Abstract quotes > [Love is like that, fragile and light. 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It's sort of an abstract silliness, that sometimes the joke isn't the star.](https://sms4smile.com/quotes/dana-carvey/describing-comic-sensibility-is-near-impossible-it-s-sort-of-an/) [Dana Carvey](https://sms4smile.com/quotes/author/dana-carvey/) > [For people of color - especially African Americans - the idea that racist cops might frame members of their community is no abstract notion,…](https://sms4smile.com/quotes/tim-wise/for-people-of-color-especially-african-americans-the-idea-that-racist/) [Tim Wise](https://sms4smile.com/quotes/author/tim-wise/) > [The word of the Lord never comes to us as an opinion, no attempt is made to support it by argument, it comes as…](https://sms4smile.com/quotes/anthony-w-ivins/the-word-of-the-lord-never-comes-to-us-as-an-opinion-no-attempt-is/) [Anthony W. Ivins](https://sms4smile.com/quotes/author/anthony-w-ivins/) > [A mobile is an abstract sculpture made chiefly out of sheet metal, steel rods, wire and wood. Some or all of these elements move,…](https://sms4smile.com/quotes/alexander-calder/a-mobile-is-an-abstract-sculpture-made-chiefly-out-of-sheet-metal/) [Alexander Calder](https://sms4smile.com/quotes/author/alexander-calder/) > [I'm this superphilosophical kind of person. 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