--- title: "Meaning & Key Takeaway of: What exactly is mathematics? Many have…" description: "\"What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, pe..." image: "https://sms4smile.com/quotes/i/298/stanislaw-ulam-16765_axioms_what-exactly-is-mathematics-many-have-tr_1872280.jpg" --- # What exactly is mathematics? Many have tried but nobody… ![“What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas…” quote by Stanislaw Ulam](https://sms4smile.com/quotes/i/298/stanislaw-ulam-16765_axioms_what-exactly-is-mathematics-many-have-tr_1872280.jpg) [Download](https://sms4smile.com/quotes/i/298/stanislaw-ulam-16765_axioms_what-exactly-is-mathematics-many-have-tr_1872280.jpg) [Open image](https://sms4smile.com/quotes/i/298/stanislaw-ulam-16765_axioms_what-exactly-is-mathematics-many-have-tr_1872280.jpg) > “What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes.” [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics resists a single definition, constantly evolving beyond fixed concepts. **In simple terms:** Math is ever-changing and hard to define. Key Takeaway Accept mathematics as evolving. Themes philosophy mathematics knowledge Mood curious intellectual Type academic philosophical When to use this quote - Teaching curricula - research methodology Key Concepts Epistemology conceptual fluidity Questions to Reflect On - How does this fluidity affect learning? - What defines mathematical progress? A Different Perspective May seem abstract. ★ ★ ★ ★ ★ No ratings yet [Axioms](https://sms4smile.com/quotes/about/axioms/) [Changed](https://sms4smile.com/quotes/about/changed/) [Deals](https://sms4smile.com/quotes/about/deals/) [Defining](https://sms4smile.com/quotes/about/defining/) [Defining Mathematics](https://sms4smile.com/quotes/about/defining-mathematics-2364521/) [Exactly is](https://sms4smile.com/quotes/about/exactly-is/) [Exactly Mathematics](https://sms4smile.com/quotes/about/exactly-mathematics-2364523/) [Figures](https://sms4smile.com/quotes/about/figures/) [Formal](https://sms4smile.com/quotes/about/formal/) [Involving](https://sms4smile.com/quotes/about/involving/) [Involving Axioms](https://sms4smile.com/quotes/about/involving-axioms-2591063/) [Knows](https://sms4smile.com/quotes/about/knows/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Mathematics Tried](https://sms4smile.com/quotes/about/mathematics-tried-2364522/) [Numbers](https://sms4smile.com/quotes/about/numbers/) [Operations](https://sms4smile.com/quotes/about/operations/) [People](https://sms4smile.com/quotes/about/people/) [Procedures](https://sms4smile.com/quotes/about/procedures/) [Proof](https://sms4smile.com/quotes/about/proof/) [Relation](https://sms4smile.com/quotes/about/relation/) [Theorems](https://sms4smile.com/quotes/about/theorems/) ## Related quotes > [What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.](https://sms4smile.com/quotes/stanislaw-ulam/what-exactly-is-mathematics-many-have-tried-but-nobody-has-really/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [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/) > [What exactly is 'viewer discretion'? If viewers had discretion, most television shows would not be on the air.](https://sms4smile.com/quotes/george-carlin/what-exactly-is-viewer-discretion-if-viewers-had-discretion-most/) [George Carlin](https://sms4smile.com/quotes/author/george-carlin/) > [I come from an improvisational background so I'm used to playing. I'm used to not knowing what exactly is going to come out.](https://sms4smile.com/quotes/naomi-grossman/i-come-from-an-improvisational-background-so-i-m-used-to-playing-i-m/) [Naomi Grossman](https://sms4smile.com/quotes/author/naomi-grossman/) > [And the pressure to clarify what exactly is happening to Christians and other minorities in the Middle East is certain to intensify in the…](https://sms4smile.com/quotes/tom-gjelten/and-the-pressure-to-clarify-what-exactly-is-happening-to-christians/) [Tom Gjelten](https://sms4smile.com/quotes/author/tom-gjelten/) > [The ability to speak exactly is intimately related to the ability to know exactly.](https://sms4smile.com/quotes/wendell-berry/the-ability-to-speak-exactly-is-intimately-related-to-the-ability-to/) [Wendell Berry](https://sms4smile.com/quotes/author/wendell-berry/) > [There are some filmmakers like the Coen brothers that are very precise. They make shooting boards, they do it shot by shot, and they…](https://sms4smile.com/quotes/pablo-larrain/there-are-some-filmmakers-like-the-coen-brothers-that-are-very/) [Pablo Larrain](https://sms4smile.com/quotes/author/pablo-larrain/) > [I get very frustrated by this term 'genre exercise.' I mean, what exactly is that? Genre is not really relevant when you are writing…](https://sms4smile.com/quotes/elvis-costello/i-get-very-frustrated-by-this-term-genre-exercise-i-mean-what-exactly/) [Elvis Costello](https://sms4smile.com/quotes/author/elvis-costello/) > [What exactly is your 'fair share' of what 'someone else' has worked for?](https://sms4smile.com/quotes/thomas-sowell/what-exactly-is-your-fair-share-of-what-someone-else-has-worked-for/) [Thomas Sowell](https://sms4smile.com/quotes/author/thomas-sowell/) > [What exactly is "midair"? 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Fifteen seconds of the purported therapeutic effort, followed by about 45 seconds of a rapidly…](https://sms4smile.com/quotes/charles-krauthammer/consider-the-oddity-of-those-drug-commercials-on-television-fifteen/) [Charles Krauthammer](https://sms4smile.com/quotes/author/charles-krauthammer/) > [Let's not even talking about chain migration, immigration, which is another trick, but all of these things are designed to penetrate the heart exactly…](https://sms4smile.com/quotes/rush-limbaugh/let-s-not-even-talking-about-chain-migration-immigration-which-is/) [Rush Limbaugh](https://sms4smile.com/quotes/author/rush-limbaugh/) > [If you choose to lead your life just like everyone else, then what exactly is it that you have to offer?](https://sms4smile.com/quotes/wayne-dyer/if-you-choose-to-lead-your-life-just-like-everyone-else-then-what/) [Wayne Dyer](https://sms4smile.com/quotes/author/wayne-dyer/) > [Congratulations to Obama! He's now increased the debt more in three years than George W. Bush did his entire eight year presidency. But all…](https://sms4smile.com/quotes/frank-j-fleming/congratulations-to-obama-he-s-now-increased-the-debt-more-in-three/) [Frank J. Fleming](https://sms4smile.com/quotes/author/frank-j-fleming/) > [What exactly is success? For me it is to be found not in applause, but in the satisfaction of feeling that one is realizing…](https://sms4smile.com/quotes/anna-pavlova/what-exactly-is-success-for-me-it-is-to-be-found-not-in-applause-but/) [Anna Pavlova](https://sms4smile.com/quotes/author/anna-pavlova/) ## More by Stanislaw Ulam > [According to recent studies, at least one star out of three is multiple.](https://sms4smile.com/quotes/stanislaw-ulam/according-to-recent-studies-at-least-one-star-out-of-three-is-multiple/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [In mathematics, as in physics, so much depends on chance, on a propitious moment.](https://sms4smile.com/quotes/stanislaw-ulam/in-mathematics-as-in-physics-so-much-depends-on-chance-on-a/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from…](https://sms4smile.com/quotes/stanislaw-ulam/in-many-cases-mathematics-is-an-escape-from-reality-the-mathematician/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Mathematics may be a way of developing physically, that is anatomically, new connections in the brain.](https://sms4smile.com/quotes/stanislaw-ulam/mathematics-may-be-a-way-of-developing-physically-that-is/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from…](https://sms4smile.com/quotes/stanislaw-ulam/in-many-cases-mathematics-is-an-escape-from-reality-the-mathematician-2/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [ He \[John von Neumann\] had the invaluable faculty of being able to take the most difficult problem and separate it into its components, whereupon… ](https://sms4smile.com/quotes/stanislaw-ulam/he-john-von-neumann-had-the-invaluable-faculty-of-being-able-to-take/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can…](https://sms4smile.com/quotes/stanislaw-ulam/it-is-still-an-unending-source-of-surprise-for-me-how-a-few-scribbles/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Mathematics is an escape from reality.](https://sms4smile.com/quotes/stanislaw-ulam/mathematics-is-an-escape-from-reality/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching…](https://sms4smile.com/quotes/stanislaw-ulam/one-conversation-centered-on-the-ever-accelerating-progress-of/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Whatever is worth saying, can be stated in fifty words or less.](https://sms4smile.com/quotes/stanislaw-ulam/whatever-is-worth-saying-can-be-stated-in-fifty-words-or-less/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years…](https://sms4smile.com/quotes/stanislaw-ulam/sometimes-i-feel-that-a-more-rational-explanation-for-all-that-has/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Thinking very hard about the same problem for several hours can produce a severe fatigue, close to a breakdown. I never really experienced a…](https://sms4smile.com/quotes/stanislaw-ulam/thinking-very-hard-about-the-same-problem-for-several-hours-can/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.](https://sms4smile.com/quotes/stanislaw-ulam/what-exactly-is-mathematics-many-have-tried-but-nobody-has-really/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [Very soon I discovered that if one gets a feeling for no more than a dozen other radiation and nuclear constants, one can imagine…](https://sms4smile.com/quotes/stanislaw-ulam/very-soon-i-discovered-that-if-one-gets-a-feeling-for-no-more-than-a/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) > [As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his…](https://sms4smile.com/quotes/stanislaw-ulam/as-a-mathematician-von-neumann-was-quick-brilliant-efficient-and/) [Stanislaw Ulam](https://sms4smile.com/quotes/author/stanislaw-ulam/) [Explore all 39 Stanislaw Ulam quotes ](https://sms4smile.com/quotes/author/stanislaw-ulam/) ## More Axioms quotes > [As a leader... 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Buckminster Fuller](https://sms4smile.com/quotes/author/r-buckminster-fuller/) > [It was an axiom of "containment" that no part of the known world could be considered neutral. 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