--- title: "Meaning & Key Takeaway of: Probably no branch of mathematics has…" description: "\"Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subjec..." image: "https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png" --- # Probably no branch of mathematics has experienced a more… ![“Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.” quote by Raymond Louis Wilder](https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png) [Download](https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png) [Open image](https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png) > “Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today \[1938\] an indispensable equipment for the investigation of modern mathematical theories.” [Raymond Louis Wilder](https://sms4smile.com/quotes/author/raymond-louis-wilder/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Topology evolved from abstract theory to essential tool for modern mathematics, showing how pure ideas can become practical foundations. **In simple terms:** Abstract math became vital. Key Takeaway Study foundational concepts. Themes mathematics evolution utility Mood inquisitive optimistic Type educational inspirational When to use this quote - education - research - technology development Key Concepts abstract theory practical application Questions to Reflect On - How does abstract theory become useful? - What other fields might benefit from topology? A Different Perspective Rapid growth may outpace understanding for newcomers. ★ ★ ★ ★ ★ No ratings yet [Abstract](https://sms4smile.com/quotes/about/abstract/) [Branches](https://sms4smile.com/quotes/about/branches/) [Equipment](https://sms4smile.com/quotes/about/equipment/) [Experience](https://sms4smile.com/quotes/about/experience/) [Growth](https://sms4smile.com/quotes/about/growth/) [Growth Topology](https://sms4smile.com/quotes/about/growth-topology-1412310/) [Indispensable](https://sms4smile.com/quotes/about/indispensable/) [Investigation](https://sms4smile.com/quotes/about/investigation/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Mathematics Experienced](https://sms4smile.com/quotes/about/mathematics-experienced-1412311/) [Modern](https://sms4smile.com/quotes/about/modern/) [Modern Mathematical](https://sms4smile.com/quotes/about/modern-mathematical-1412309/) [Subjects](https://sms4smile.com/quotes/about/subjects/) [Surprising](https://sms4smile.com/quotes/about/surprising/) [Theory](https://sms4smile.com/quotes/about/theory/) [Today](https://sms4smile.com/quotes/about/today/) [Topology](https://sms4smile.com/quotes/about/topology/) [Topology Considered](https://sms4smile.com/quotes/about/topology-considered-1412308/) ## Related quotes > [A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and…](https://sms4smile.com/quotes/hermann-weyl/a-modern-mathematical-proof-is-not-very-different-from-a-modern/) [Hermann Weyl](https://sms4smile.com/quotes/author/hermann-weyl/) > [“Topology is that branch of mathematics which is interested in the forms of things aside from their size and shape, Two things are said…](https://sms4smile.com/quotes/john-d-barrow/topology-is-that-branch-of-mathematics-which-is-interested-in-the/) [John D. Barrow](https://sms4smile.com/quotes/author/john-d-barrow/) > [A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one…](https://sms4smile.com/quotes/jacques-lacan/a-geometry-implies-the-heterogeneity-of-locus-namely-that-there-is-a/) [Jacques Lacan](https://sms4smile.com/quotes/author/jacques-lacan/) > [Topology and number theory are my faves.](https://sms4smile.com/quotes/janna-levin/topology-and-number-theory-are-my-faves/) [Janna Levin](https://sms4smile.com/quotes/author/janna-levin/) > [Point set topology is a disease from which the human race will soon recover.](https://sms4smile.com/quotes/henri-poincare/point-set-topology-is-a-disease-from-which-the-human-race-will-soon/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Topology is the science of fundamental pattern and structural relationships of event constellations.](https://sms4smile.com/quotes/r-buckminster-fuller/topology-is-the-science-of-fundamental-pattern-and-structural/) [R. Buckminster Fuller](https://sms4smile.com/quotes/author/r-buckminster-fuller/) > [ \[Mathematics\] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one… ](https://sms4smile.com/quotes/anonymous/mathematics-is-security-certainty-truth-beauty-insight-structure/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.](https://sms4smile.com/quotes/vladimir-arnold/celestial-mechanics-is-the-origin-of-dynamical-systems-linear-algebra/) [Vladimir Arnold](https://sms4smile.com/quotes/author/vladimir-arnold/) > [Poetry and code - and mathematics - make us read differently from other forms of writing. Written poetry makes the silent reader read three…](https://sms4smile.com/quotes/stephanie-strickland/poetry-and-code-and-mathematics-make-us-read-differently-from-other/) [Stephanie Strickland](https://sms4smile.com/quotes/author/stephanie-strickland/) > [“Topology is destiny,' he said, and put the drawers on. One leg at a time.”](https://sms4smile.com/quotes/neal-stephenson/topology-is-destiny-he-said-and-put-the-drawers-on-one-leg-at-a-time/) [Neal Stephenson](https://sms4smile.com/quotes/author/neal-stephenson/) > [In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when…](https://sms4smile.com/quotes/edward-witten/in-einstein-s-general-relativity-the-structure-of-space-can-change/) [Edward Witten](https://sms4smile.com/quotes/author/edward-witten/) > [ I would have private conversations with \[Buckminster Fuller\]. I once had an argument, for four hours, about the existence of the Mobius strip. Because… ](https://sms4smile.com/quotes/paul-laffoley/i-would-have-private-conversations-with-buckminster-fuller-i-once-had/) [Paul Laffoley](https://sms4smile.com/quotes/author/paul-laffoley/) > [“Topology is destiny,”](https://sms4smile.com/quotes/neal-stephenson/topology-is-destiny/) [Neal Stephenson](https://sms4smile.com/quotes/author/neal-stephenson/) > [“Time and space were, from Death's point of view, merely things that he'd heard described. When it came to Death, they ticked the box…](https://sms4smile.com/quotes/terry-pratchett/time-and-space-were-from-death-s-point-of-view-merely-things-that-he/) [Terry Pratchett](https://sms4smile.com/quotes/author/terry-pratchett/) > [Topology is precisely the mathematical discipline that allows the passage from local to global...](https://sms4smile.com/quotes/rene-thom/topology-is-precisely-the-mathematical-discipline-that-allows-the/) [Rene Thom](https://sms4smile.com/quotes/author/rene-thom/) ## More by Raymond Louis Wilder > [Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and…](https://sms4smile.com/quotes/raymond-louis-wilder/mathematics-was-born-and-nurtured-in-a-cultural-environment-without/) [Raymond Louis Wilder](https://sms4smile.com/quotes/author/raymond-louis-wilder/) > [There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be…](https://sms4smile.com/quotes/raymond-louis-wilder/there-is-nothing-mysterious-as-some-have-tried-to-maintain-about-the/) [Raymond Louis Wilder](https://sms4smile.com/quotes/author/raymond-louis-wilder/) [Explore all 3 Raymond Louis Wilder quotes ](https://sms4smile.com/quotes/author/raymond-louis-wilder/) ## More Abstract quotes > [Love is like that, fragile and light. No wonder it rests upon our hearts in intangible moments, bids us follow fleeting thoughts and ideas…](https://sms4smile.com/quotes/anonymous/love-is-like-that-fragile-and-light-no-wonder-it-rests-upon-our/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Wisdom is the abstract of the past, but beauty is the promise of the future.](https://sms4smile.com/quotes/anonymous/wisdom-is-the-abstract-of-the-past-but-beauty-is-the-promise-of-the/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Where human eyes have never seen, where human beings have never been, I build a world of abstract dreams, and I wait for you.](https://sms4smile.com/quotes/sun-ra/where-human-eyes-have-never-seen-where-human-beings-have-never-been-i/) [Sun Ra](https://sms4smile.com/quotes/author/sun-ra/) > [A little too abstract, a little too wise, It is time for us to kiss the earth again, It is time to let the…](https://sms4smile.com/quotes/robinson-jeffers/a-little-too-abstract-a-little-too-wise-it-is-time-for-us-to-kiss-the/) [Robinson Jeffers](https://sms4smile.com/quotes/author/robinson-jeffers/) > [“Happy is very abstract, you can't touch it.”](https://sms4smile.com/quotes/julius-veal/happy-is-very-abstract-you-can-t-touch-it/) [Julius Veal](https://sms4smile.com/quotes/author/julius-veal/) > [Abstract Expressionism was invented by New York drunks.](https://sms4smile.com/quotes/joni-mitchell/abstract-expressionism-was-invented-by-new-york-drunks/) [Joni Mitchell](https://sms4smile.com/quotes/author/joni-mitchell/) > [The more horrible this world (as today, for instance), the more abstract our art, whereas a happy world brings forth an art of the…](https://sms4smile.com/quotes/paul-klee/the-more-horrible-this-world-as-today-for-instance-the-more-abstract/) [Paul Klee](https://sms4smile.com/quotes/author/paul-klee/) > [Describing comic sensibility is near impossible. 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. Stuck in a prison of abstract ideas and overpowering emotions, I have this personality that makes it really…](https://sms4smile.com/quotes/natsuo-kirino/i-m-this-superphilosophical-kind-of-person-stuck-in-a-prison-of/) [Natsuo Kirino](https://sms4smile.com/quotes/author/natsuo-kirino/) > [Future lawyers should be more aware that law is not a system of abstract logic, but the web of arrangements, rooted in history but…](https://sms4smile.com/quotes/felix-frankfurter/future-lawyers-should-be-more-aware-that-law-is-not-a-system-of/) [Felix Frankfurter](https://sms4smile.com/quotes/author/felix-frankfurter/) > [The trouble is that when you read criticisms about the other films that I've made you get the impression that they're all about themes,…](https://sms4smile.com/quotes/michael-haneke/the-trouble-is-that-when-you-read-criticisms-about-the-other-films/) [Michael Haneke](https://sms4smile.com/quotes/author/michael-haneke/) > [Painting is... a richer language than words... Painting operates through signs which are not abstract and incorporeal like words. The signs of painting are…](https://sms4smile.com/quotes/jean-dubuffet/painting-is-a-richer-language-than-words-painting-operates-through/) [Jean Dubuffet](https://sms4smile.com/quotes/author/jean-dubuffet/) [Browse all 1,403 Abstract quotes ](https://sms4smile.com/quotes/about/abstract/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.", "creator": { "@type": "Person", "name": "Raymond Louis Wilder" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/raymond-louis-wilder/probably-no-branch-of-mathematics-has-experienced-a-more-surprising/", "about": { "@type": "Thing", "name": "Abstract" }, "@id": "https://sms4smile.com/quotes/raymond-louis-wilder/probably-no-branch-of-mathematics-has-experienced-a-more-surprising/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png", "contentUrl": "https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png", "url": "https://sms4smile.com/quotes/i/f41/raymond-louis-wilder-82780_abstract_probably-no-branch-of-mathematics-has-ex_919488.png", "width": 1080, "height": 1080, "caption": "“Probably no branch of mathematics has experienced a more surprising growth than has... topology…” — Raymond Louis Wilder", "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": "Raymond Louis Wilder", "item": "https://sms4smile.com/quotes/author/raymond-louis-wilder/" }, { "@type": "ListItem", "position": 4, "name": "Probably no branch of mathematics has...", "item": "https://sms4smile.com/quotes/raymond-louis-wilder/probably-no-branch-of-mathematics-has-experienced-a-more-surprising/" } ], "@id": "https://sms4smile.com/quotes/raymond-louis-wilder/probably-no-branch-of-mathematics-has-experienced-a-more-surprising/#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 } } ] } ```