--- title: "Meaning & Key Takeaway of: ...the source of all great mathematics is…" description: "\"...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of see..." image: "https://sms4smile.com/quotes/i/8f2/paul-halmos-19455_cases_the-source-of-all-great-mathematics-is-t_585819.png" --- # ...the source of all great mathematics is the special… ![“...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.” quote by Paul Halmos](https://sms4smile.com/quotes/i/8f2/paul-halmos-19455_cases_the-source-of-all-great-mathematics-is-t_585819.png) [Download](https://sms4smile.com/quotes/i/8f2/paul-halmos-19455_cases_the-source-of-all-great-mathematics-is-t_585819.png) [Open image](https://sms4smile.com/quotes/i/8f2/paul-halmos-19455_cases_the-source-of-all-great-mathematics-is-t_585819.png) > “...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.” [Paul Halmos](https://sms4smile.com/quotes/author/paul-halmos/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. General ideas are best understood through specific, concrete examples that reveal their true nature. **In simple terms:** Use concrete examples to grasp abstract concepts. Key Takeaway Apply specific cases to learn general principles. Themes learning mathematics abstraction Mood inquisitive motivated Type educational inspirational When to use this quote - teaching - research - problem solving - education Key Concepts examples concrete cases Questions to Reflect On - What concrete example helped you understand a complex idea? - How can you find the right example for a new concept? A Different Perspective Abstract concepts may still be elusive without proper context. ★ ★ ★ ★ ★ No ratings yet [Cases](https://sms4smile.com/quotes/about/cases/) [Concepts](https://sms4smile.com/quotes/about/concepts/) [Concrete](https://sms4smile.com/quotes/about/concrete/) [Concrete Example](https://sms4smile.com/quotes/about/concrete-example-4806210/) [Essence](https://sms4smile.com/quotes/about/essence/) [Example](https://sms4smile.com/quotes/about/example/) [Generalities](https://sms4smile.com/quotes/about/generalities/) [Generality](https://sms4smile.com/quotes/about/generality/) [Great Mathematics](https://sms4smile.com/quotes/about/great-mathematics-1133167/) [Instance](https://sms4smile.com/quotes/about/instance/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Mathematics Special](https://sms4smile.com/quotes/about/mathematics-special-4806209/) [Science](https://sms4smile.com/quotes/about/science/) [Source](https://sms4smile.com/quotes/about/source/) [Special](https://sms4smile.com/quotes/about/special/) [Special Case](https://sms4smile.com/quotes/about/special-case-2615576/) ## Related quotes > [The art of doing mathematics consists in finding that special case which contains all the germs of generality](https://sms4smile.com/quotes/david-hilbert/the-art-of-doing-mathematics-consists-in-finding-that-special-case/) [David Hilbert](https://sms4smile.com/quotes/author/david-hilbert/) > [ Euclid avoids it \[the treatment of the infinite\]; in modern mathematics it is systematically introduced, for only then is generality obtained. ](https://sms4smile.com/quotes/arthur-cayley/euclid-avoids-it-the-treatment-of-the-infinite-in-modern-mathematics/) [Arthur Cayley](https://sms4smile.com/quotes/author/arthur-cayley/) > [The generality of men are so accustomed to judge of things by their senses that, because the air is indivisible, they ascribe but little…](https://sms4smile.com/quotes/robert-boyle/the-generality-of-men-are-so-accustomed-to-judge-of-things-by-their/) [Robert Boyle](https://sms4smile.com/quotes/author/robert-boyle/) > [It is certain that the easy and obvious philosophy will always, with the generality of mankind, have preference above the accurate.](https://sms4smile.com/quotes/david-hume/it-is-certain-that-the-easy-and-obvious-philosophy-will-always-with/) [David Hume](https://sms4smile.com/quotes/author/david-hume/) > [No generality has any weight whatever. It is like saying "how do you do?" When you have no intention of inquiring about ones health.…](https://sms4smile.com/quotes/claude-c-hopkins/no-generality-has-any-weight-whatever-it-is-like-saying-how-do-you-do/) [Claude C. Hopkins](https://sms4smile.com/quotes/author/claude-c-hopkins/) > [All that is alive tends toward color, individuality, specificity, effectiveness and opacity. 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Boulding](https://sms4smile.com/quotes/author/kenneth-e-boulding/) > [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/) ## More by Paul Halmos > [Applied mathematics will always need pure mathematics just as anteaters will always need ants.](https://sms4smile.com/quotes/paul-halmos/applied-mathematics-will-always-need-pure-mathematics-just-as/) [Paul Halmos](https://sms4smile.com/quotes/author/paul-halmos/) > [When a student comes and asks, "Should I become a mathematician?" the answer should be no. 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The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom…](https://sms4smile.com/quotes/paul-halmos/the-mathematical-fraternity-is-a-little-like-a-self-perpetuating/) [Paul Halmos](https://sms4smile.com/quotes/author/paul-halmos/) > [Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork.](https://sms4smile.com/quotes/paul-halmos/mathematics-is-not-a-deductive-science-that-s-a-clich-what-you-do-is/) [Paul Halmos](https://sms4smile.com/quotes/author/paul-halmos/) > [I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. 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