--- title: "Meaning & Key Takeaway of: A mathematical idea should not be…" description: "\"A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.\" — James Joseph ..." image: "https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png" --- # A mathematical idea should not be petrified in a… ![“A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.” quote by James Joseph Sylvester](https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png) [Download](https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png) [Open image](https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png) > “A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.” [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical concepts thrive when they remain fluid and adaptable, not locked into rigid formalism. **In simple terms:** Ideas should stay flexible like a river. Key Takeaway Keep concepts adaptable. Themes creativity flexibility mathematics Mood inspired reflective Type philosophical educational When to use this quote - teaching - research - problem solving - interdisciplinary work Key Concepts fluidity formalism axioms Questions to Reflect On - How can you maintain flexibility in your work? - What benefits arise from fluid thinking? A Different Perspective Rigid formalism can stifle innovation. ★ ★ ★ ★ ★ No ratings yet [Axiomatic](https://sms4smile.com/quotes/about/axiomatic-312863/) [Axiomatic Setting](https://sms4smile.com/quotes/about/axiomatic-setting-5875866/) [Formalised](https://sms4smile.com/quotes/about/formalised-5875867/) [Formalised Axiomatic](https://sms4smile.com/quotes/about/formalised-axiomatic-5875865/) [Ideas](https://sms4smile.com/quotes/about/ideas/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematical Idea](https://sms4smile.com/quotes/about/mathematical-idea-4418140/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Rivers](https://sms4smile.com/quotes/about/rivers/) [Setting](https://sms4smile.com/quotes/about/setting/) [Settings](https://sms4smile.com/quotes/about/settings/) [Should](https://sms4smile.com/quotes/about/should/) ## Related quotes > [The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may…](https://sms4smile.com/quotes/benoit-mandelbrot/the-extraordinary-fact-is-that-the-first-idea-i-had-which-motivated/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [The axiomatic method has many advantages over honest work.](https://sms4smile.com/quotes/bertrand-russell/the-axiomatic-method-has-many-advantages-over-honest-work/) [Bertrand Russell](https://sms4smile.com/quotes/author/bertrand-russell/) > [it is axiomatic with most writing people that there are no such things as perfect conditions for work.](https://sms4smile.com/quotes/mary-roberts-rinehart/it-is-axiomatic-with-most-writing-people-that-there-are-no-such/) [Mary Roberts Rinehart](https://sms4smile.com/quotes/author/mary-roberts-rinehart/) > [An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). 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it is…](https://sms4smile.com/quotes/james-joseph-sylvester/mathematics-is-not-a-book-confined-within-a-cover-and-bound-between/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [ The object of pure Physic\[s\] is the unfolding of the laws of the intelligible world; the object of pure Mathematic\[s\] that of unfolding the… ](https://sms4smile.com/quotes/james-joseph-sylvester/the-object-of-pure-physic-s-is-the-unfolding-of-the-laws-of-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be…](https://sms4smile.com/quotes/james-joseph-sylvester/chemistry-has-the-same-quickening-and-suggestive-influence-upon-the/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these…](https://sms4smile.com/quotes/james-joseph-sylvester/the-theory-of-ramification-is-one-of-pure-colligation-for-it-takes-no/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [The object of pure Mathematic (is) that of unfolding the laws of human intelligence.](https://sms4smile.com/quotes/james-joseph-sylvester/the-object-of-pure-mathematic-is-that-of-unfolding-the-laws-of-human/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [May not music be described as the mathematics of the sense, mathematics as music of the reason?](https://sms4smile.com/quotes/james-joseph-sylvester/may-not-music-be-described-as-the-mathematics-of-the-sense/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting…](https://sms4smile.com/quotes/james-joseph-sylvester/so-long-as-a-man-remains-a-gregarious-and-sociable-being-he-cannot/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) [Explore all 25 James Joseph Sylvester quotes ](https://sms4smile.com/quotes/author/james-joseph-sylvester/) ## More Ideas quotes > [I think a new world will arise out of the religious mists when we approach our Bible with the idea that it is not…](https://sms4smile.com/quotes/aiden-wilson-tozer/i-think-a-new-world-will-arise-out-of-the-religious-mists-when-we/) [Aiden Wilson Tozer](https://sms4smile.com/quotes/author/aiden-wilson-tozer/) > [Companies with cultures that celebrate diverse opinions and encourage the exchange of ideas have an advantage when solving difficult problems. 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You treat ideas like cats: you make them follow you.](https://sms4smile.com/quotes/ray-bradbury/that-s-the-great-secret-of-creativity-you-treat-ideas-like-cats-you/) [Ray Bradbury](https://sms4smile.com/quotes/author/ray-bradbury/) > [I've always been fascinated by the idea that there's no such thing as evil; it's all in your point of view. To one group…](https://sms4smile.com/quotes/eli-roth/i-ve-always-been-fascinated-by-the-idea-that-there-s-no-such-thing-as/) [Eli Roth](https://sms4smile.com/quotes/author/eli-roth/) > [The image of blacks usually is one of people who are suffering from hunger, unemployment, and poverty. 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It means to know that one…](https://sms4smile.com/quotes/ernest-becker/what-does-it-mean-to-be-a-self-conscious-animal-the-idea-is-ludicrous/) [Ernest Becker](https://sms4smile.com/quotes/author/ernest-becker/) [Browse all 24,908 Ideas quotes ](https://sms4smile.com/quotes/about/ideas/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.", "creator": { "@type": "Person", "name": "James Joseph Sylvester" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/james-joseph-sylvester/a-mathematical-idea-should-not-be-petrified-in-a-formalised-axiomatic/", "about": { "@type": "Thing", "name": "Ideas" }, "@id": "https://sms4smile.com/quotes/james-joseph-sylvester/a-mathematical-idea-should-not-be-petrified-in-a-formalised-axiomatic/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png", "contentUrl": "https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png", "url": "https://sms4smile.com/quotes/i/783/james-joseph-sylvester-23602_ideas_a-mathematical-idea-should-not-be-petrif_1564348.png", "width": 1080, "height": 1080, "caption": "“A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered…” — James Joseph Sylvester", "creditText": "SMS4Smile Quotes", "creator": { "@id": "https://sms4smile.com/quotes/#organization" } } }, { "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://sms4smile.com/" }, { "@type": "ListItem", "position": 2, "name": "Quotes", "item": "https://sms4smile.com/quotes/" }, { "@type": "ListItem", "position": 3, "name": "James Joseph Sylvester", "item": "https://sms4smile.com/quotes/author/james-joseph-sylvester/" }, { "@type": "ListItem", "position": 4, "name": "A mathematical idea should not be...", "item": "https://sms4smile.com/quotes/james-joseph-sylvester/a-mathematical-idea-should-not-be-petrified-in-a-formalised-axiomatic/" } ], "@id": "https://sms4smile.com/quotes/james-joseph-sylvester/a-mathematical-idea-should-not-be-petrified-in-a-formalised-axiomatic/#breadcrumb" }, { "@type": "WebSite", "@id": "https://sms4smile.com/quotes/#website", "name": "SMS4Smile Quotes", "url": "https://sms4smile.com/quotes/", "publisher": { "@id": "https://sms4smile.com/quotes/#organization" } }, { "@type": "Organization", "@id": "https://sms4smile.com/quotes/#organization", "name": "SMS4Smile Quotes", "url": "https://sms4smile.com/quotes/", "logo": { "@type": "ImageObject", "url": "https://sms4smile.com/quotes/wp-content/themes/sq/assets/icons/icon-512.png", "width": 512, "height": 512 } } ] } ```