--- title: "Meaning & Key Takeaway of: To many, mathematics is a collection of…" description: "\"To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examp..." image: "https://sms4smile.com/quotes/i/3da/john-b-conway-248931_collections_to-many-mathematics-is-a-collection-of-t_3171560.jpg" --- # To many, mathematics is a collection of theorems. For me… ![“To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples...” quote by John B. Conway](https://sms4smile.com/quotes/i/3da/john-b-conway-248931_collections_to-many-mathematics-is-a-collection-of-t_3171560.jpg) [Download](https://sms4smile.com/quotes/i/3da/john-b-conway-248931_collections_to-many-mathematics-is-a-collection-of-t_3171560.jpg) [Open image](https://sms4smile.com/quotes/i/3da/john-b-conway-248931_collections_to-many-mathematics-is-a-collection-of-t_3171560.jpg) > “To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples...” John B. Conway ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics is best understood through concrete examples, with theorems serving to organize and explain them. **In simple terms:** Examples illustrate concepts; theorems organize them. Key Takeaway Study examples, then seek theorems that connect them. Themes mathematics examples theorems classification explanation Mood analytical curious reflective Type aphilosophical educational When to use this quote - teaching - research - self‑study - problem solving - academic writing Key Concepts conceptual understanding classification explanatory frameworks Questions to Reflect On - How do examples shape your intuition? - When does a theorem fail to explain an example? A Different Perspective A theorem alone may not capture the richness of all examples. ★ ★ ★ ★ ★ No ratings yet [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Purpose](https://sms4smile.com/quotes/about/purpose/) [Theorems](https://sms4smile.com/quotes/about/theorems/) ## Related quotes > [Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when…](https://sms4smile.com/quotes/ross-honsberger/paul-erdos-has-a-theory-that-god-has-a-book-containing-all-the/) Ross Honsberger > [Theorems are not to mathematics what successful courses are to a meal.](https://sms4smile.com/quotes/gian-carlo-rota/theorems-are-not-to-mathematics-what-successful-courses-are-to-a-meal/) [Gian-Carlo Rota](https://sms4smile.com/quotes/author/gian-carlo-rota/) > [The story does what no theorem can quite do. It may not be "like real life" in the superficial sense: but it sets before…](https://sms4smile.com/quotes/c-s-lewis/the-story-does-what-no-theorem-can-quite-do-it-may-not-be-like-real/) [C. S. Lewis](https://sms4smile.com/quotes/author/c-s-lewis/) > [Those who have more power are liable to sin more; no theorem in geometry is more certain than this.](https://sms4smile.com/quotes/lord-acton/those-who-have-more-power-are-liable-to-sin-more-no-theorem-in/) [Lord Acton](https://sms4smile.com/quotes/author/lord-acton/) > [Any good theorem should have several proofs, the more the better.](https://sms4smile.com/quotes/michael-atiyah/any-good-theorem-should-have-several-proofs-the-more-the-better/) [Michael Atiyah](https://sms4smile.com/quotes/author/michael-atiyah/) > [What philosophy worthy of the name has truly been able to avoid the link between poem and theorem?](https://sms4smile.com/quotes/michel-serres/what-philosophy-worthy-of-the-name-has-truly-been-able-to-avoid-the/) [Michel Serres](https://sms4smile.com/quotes/author/michel-serres/) > [It is not so much whether a theorem is useful that matters, but how elegant it is.](https://sms4smile.com/quotes/stanislaw-ulam/it-is-not-so-much-whether-a-theorem-is-useful-that-matters-but-how/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Bells theorem dealt a shattering blow to Einsteins position by showing that the conception of reality as consisting of separate parts, joined by local…](https://sms4smile.com/quotes/fritjof-capra/bells-theorem-dealt-a-shattering-blow-to-einsteins-position-by/) [Fritjof Capra](https://sms4smile.com/quotes/author/fritjof-capra/) > [A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.](https://sms4smile.com/quotes/richard-arnold-epstein/a-proven-theorem-of-game-theory-states-that-every-game-with-complete/) [Richard Arnold Epstein](https://sms4smile.com/quotes/author/richard-arnold-epstein/) > [There's no answer for my offense, just like the polythagorean theorem.](https://sms4smile.com/quotes/shaquille-o-neal/there-s-no-answer-for-my-offense-just-like-the-polythagorean-theorem/) [Shaquille O'Neal](https://sms4smile.com/quotes/author/shaquille-o-neal/) > [A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions.](https://sms4smile.com/quotes/anatol-rapoport/a-theorem-is-a-proposition-which-is-a-strict-logical-consequence-of/) [Anatol Rapoport](https://sms4smile.com/quotes/author/anatol-rapoport/) > [Murphy's Law, that brash proletarian restatement of Godel's Theorem ...](https://sms4smile.com/quotes/thomas-pynchon/murphy-s-law-that-brash-proletarian-restatement-of-godel-s-theorem/) [Thomas Pynchon](https://sms4smile.com/quotes/author/thomas-pynchon/) > [The Limbaugh Theorem is the way Obama gets away with no accountability for anything he's done is he never was perceived as governing. He…](https://sms4smile.com/quotes/rush-limbaugh/the-limbaugh-theorem-is-the-way-obama-gets-away-with-no/) [Rush Limbaugh](https://sms4smile.com/quotes/author/rush-limbaugh/) > [It gives me the same pleasure when someone else proves a good theorem as when I do it myself.](https://sms4smile.com/quotes/edmund-landau/it-gives-me-the-same-pleasure-when-someone-else-proves-a-good-theorem/) Edmund Landau > [I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever…](https://sms4smile.com/quotes/andrew-wiles/i-loved-doing-problems-in-school-i-d-take-them-home-and-make-up-new/) [Andrew Wiles](https://sms4smile.com/quotes/author/andrew-wiles/) ## More Collections quotes > [Life is a collection of moments. Mindfulness is beautification of the moments.](https://sms4smile.com/quotes/amit-ray/life-is-a-collection-of-moments-mindfulness-is-beautification-of-the/) [Amit Ray](https://sms4smile.com/quotes/author/amit-ray/) > [Hercules used noise! Brass bells! He scared them away with the most horrible sound he could-" said Percy "Percy... Chiron's collection!](https://sms4smile.com/quotes/rick-riordan/hercules-used-noise-brass-bells-he-scared-them-away-with-the-most/) [Rick Riordan](https://sms4smile.com/quotes/author/rick-riordan/) > [MAC allowed me to have complete freedom on the collaborations—from the shades, the look-and-feel, to the campaign visuals. I have to admit that the…](https://sms4smile.com/quotes/philip-treacy/mac-allowed-me-to-have-complete-freedom-on-the-collaborations-from/) [Philip Treacy](https://sms4smile.com/quotes/author/philip-treacy/) > [I took a wrong turn on the way to the bathroom and found myself in a beautifully proportioned room I had never seen before,…](https://sms4smile.com/quotes/anonymous/i-took-a-wrong-turn-on-the-way-to-the-bathroom-and-found-myself-in-a/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Whatever we may say against collections, which present authors in a disjointed form, they nevertheless bring about many excellent results. We are not always…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/whatever-we-may-say-against-collections-which-present-authors-in-a/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [This is an extraordinary illustrated collection of Chinese herbsaccompanied by concise and expert comments. Jing-Nuan Wu has succeeded incompiling this most unique and informative…](https://sms4smile.com/quotes/koji-nakanishi/this-is-an-extraordinary-illustrated-collection-of-chinese/) Koji Nakanishi > [I have a large watch collection, and classic watches are especially important to me. I had a silver Rolex, and I actually gave it…](https://sms4smile.com/quotes/nate-berkus/i-have-a-large-watch-collection-and-classic-watches-are-especially/) [Nate Berkus](https://sms4smile.com/quotes/author/nate-berkus/) > [By calling it a memoir, I meant is as a collection of memories. I thought it was (a more) artful (title) than documentary.](https://sms4smile.com/quotes/natalie-merchant/by-calling-it-a-memoir-i-meant-is-as-a-collection-of-memories-i/) [Natalie Merchant](https://sms4smile.com/quotes/author/natalie-merchant/) > [Who wrote the Bible? Current scholarship, to my knowledge, assumes that the material that constitutes the Old Testament was put together from various oral…](https://sms4smile.com/quotes/noam-chomsky/who-wrote-the-bible-current-scholarship-to-my-knowledge-assumes-that/) [Noam Chomsky](https://sms4smile.com/quotes/author/noam-chomsky/) > [I've had plenty of jo-jobs. Nothing I'd call a career. Let me put it this way. I have an extensive collection of name tags…](https://sms4smile.com/quotes/wayne-campbell/i-ve-had-plenty-of-jo-jobs-nothing-i-d-call-a-career-let-me-put-it/) [Wayne Campbell](https://sms4smile.com/quotes/author/wayne-campbell/) > [The benefit of writing a collection - as opposed to a novel - is that I'm able to have some version of the war…](https://sms4smile.com/quotes/said-sayrafiezadeh/the-benefit-of-writing-a-collection-as-opposed-to-a-novel-is-that-i-m/) [Said Sayrafiezadeh](https://sms4smile.com/quotes/author/said-sayrafiezadeh/) > [Museums do not share their collections with other museums unless they get something in exchange. The Metropolitan will deal with the Louvre, but will…](https://sms4smile.com/quotes/eli-broad/museums-do-not-share-their-collections-with-other-museums-unless-they/) [Eli Broad](https://sms4smile.com/quotes/author/eli-broad/) > [I didn't grow up in one of those restrictive Christian households where you couldn't do this or that. We were brought up with a…](https://sms4smile.com/quotes/yolanda-adams/i-didn-t-grow-up-in-one-of-those-restrictive-christian-households/) [Yolanda Adams](https://sms4smile.com/quotes/author/yolanda-adams/) > [People give me money and I don't know why, my real collection plate is an empty cup held by a homeless guy.](https://sms4smile.com/quotes/bo-burnham/people-give-me-money-and-i-don-t-know-why-my-real-collection-plate-is/) [Bo Burnham](https://sms4smile.com/quotes/author/bo-burnham/) > [A good collection is more than just the sum of its parts.](https://sms4smile.com/quotes/tom-peters/a-good-collection-is-more-than-just-the-sum-of-its-parts/) [Tom Peters](https://sms4smile.com/quotes/author/tom-peters/) Browse all 1,148 Collections quotes ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "To many, mathematics is a collection of theorems. 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