--- title: "Meaning & Key Takeaway of: Mathematics has the completely false…" description: "\"Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not fou..." image: "https://sms4smile.com/quotes/i/f69/johann-wolfgang-von-goethe-36_conclusion_mathematics-has-the-completely-false-rep_2850814.jpg" --- # Mathematics has the completely false reputation of… ![“Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its…” quote by Johann Wolfgang von Goethe](https://sms4smile.com/quotes/i/f69/johann-wolfgang-von-goethe-36_conclusion_mathematics-has-the-completely-false-rep_2850814.jpg) [Download](https://sms4smile.com/quotes/i/f69/johann-wolfgang-von-goethe-36_conclusion_mathematics-has-the-completely-false-rep_2850814.jpg) [Open image](https://sms4smile.com/quotes/i/f69/johann-wolfgang-von-goethe-36_conclusion_mathematics-has-the-completely-false-rep_2850814.jpg) > “Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.” [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematics appears infallible but is based on identity; its conclusions are constructs, not absolute truths. **In simple terms:** Math is built on identity, not absolute truth. Key Takeaway Question mathematical certainty. Themes philosophy mathematics identity truth Mood inquisitive critical Type philosophical academic When to use this quote - education - research - critical thinking Key Concepts epistemology logic abstract reasoning Questions to Reflect On - What assumptions underlie mathematical truths? - How does identity shape conclusions? A Different Perspective May misinterpret mathematical rigor. ★ ★ ★ ★ ★ No ratings yet [Conclusion](https://sms4smile.com/quotes/about/conclusion/) [Identity](https://sms4smile.com/quotes/about/identity/) [Infallibility](https://sms4smile.com/quotes/about/infallibility/) [Justice](https://sms4smile.com/quotes/about/justice/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Nothing new](https://sms4smile.com/quotes/about/nothing-new/) [Reputation](https://sms4smile.com/quotes/about/reputation/) ## Related quotes > [There is nothing new on earth / For a person who lives long and experiences much. / In my years of youthful wandering /…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/there-is-nothing-new-on-earth-for-a-person-who-lives-long-and/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/when-the-boy-begins-to-understand-that-the-visible-point-is-preceded/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [New inventions can and will be made; however, nothing new can be thought of that concerns moral man. Everything has already been thought and…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/new-inventions-can-and-will-be-made-however-nothing-new-can-be/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [“Those who would argue for the infallibility or the inerrancy of scripture logically should also claim the same infallibility for the churches in the…](https://sms4smile.com/quotes/lee-m-mcdonald/those-who-would-argue-for-the-infallibility-or-the-inerrancy-of/) Lee M. McDonald > [Errors of knowledge are not breaches of morality; no proper moral code can demand infallibility or omniscience.](https://sms4smile.com/quotes/ayn-rand/errors-of-knowledge-are-not-breaches-of-morality-no-proper-moral-code/) [Ayn Rand](https://sms4smile.com/quotes/author/ayn-rand/) > [The failure of the Reformation to capture France had left for Frenchmen no half-way house between infallibility and infidelity; and while the intellect of…](https://sms4smile.com/quotes/will-durant/the-failure-of-the-reformation-to-capture-france-had-left-for/) [Will Durant](https://sms4smile.com/quotes/author/will-durant/) > [You're only infallible about your own nervous system. 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Some of them are clever men and some of…](https://sms4smile.com/quotes/agatha-christie/i-have-had-too-much-experience-of-life-to-believe-in-the/) [Agatha Christie](https://sms4smile.com/quotes/author/agatha-christie/) > [ “\[For people\] to refuse a hearing to an opinion, because they are sure that it is false, is to assume that their certainty is… ](https://sms4smile.com/quotes/john-stuart-mill/for-people-to-refuse-a-hearing-to-an-opinion-because-they-are-sure/) [John Stuart Mill](https://sms4smile.com/quotes/author/john-stuart-mill/) > [knowledge, absolutely sure of its infallibility, is faith](https://sms4smile.com/quotes/yevgeny-zamyatin/knowledge-absolutely-sure-of-its-infallibility-is-faith/) [Yevgeny Zamyatin](https://sms4smile.com/quotes/author/yevgeny-zamyatin/) > [A common fallacy in much of the adverse criticism to which science is subjected today is that it claims certainty, infallibility and complete emotional…](https://sms4smile.com/quotes/cyril-norman-hinshelwood/a-common-fallacy-in-much-of-the-adverse-criticism-to-which-science-is/) [Cyril Norman Hinshelwood](https://sms4smile.com/quotes/author/cyril-norman-hinshelwood/) ## More by Johann Wolfgang von Goethe > [True works of art contain their own theory and give us the measurement according to which we should judge them.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/true-works-of-art-contain-their-own-theory-and-give-us-the/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [I never believed in trying to do anything. Whatever I set out to do I found I had already accomplished.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/i-never-believed-in-trying-to-do-anything-whatever-i-set-out-to-do-i/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [All lyrical work must, as a whole, be perfectly intelligible, but in some particulars a little unintelligible.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/all-lyrical-work-must-as-a-whole-be-perfectly-intelligible-but-in/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [We know accurately only when we know little, with knowledge doubt increases.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/we-know-accurately-only-when-we-know-little-with-knowledge-doubt/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [It is easier to perceive error than to find truth, for the former lies on the surface and is easily seen, while the latter…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/it-is-easier-to-perceive-error-than-to-find-truth-for-the-former-lies/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [There is no patriotic art and no patriotic science.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/there-is-no-patriotic-art-and-no-patriotic-science/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [The connoisseur of art must be able to appreciate what is simply beautiful, but the common run of people is satisfied with ornament](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/the-connoisseur-of-art-must-be-able-to-appreciate-what-is-simply/) [Johann Wolfgang Von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Nothing is worse than active ignorance.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/nothing-is-worse-than-active-ignorance/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Let us not dream that reason can ever be popular. Passions, emotions, may be made popular; but reason remains ever the property of an…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/let-us-not-dream-that-reason-can-ever-be-popular-passions-emotions/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Our foibles are really what make us lovable.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/our-foibles-are-really-what-make-us-lovable/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Instruction does much, but encouragement everything.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/instruction-does-much-but-encouragement-everything/) [Johann Wolfgang Von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Giving is the business of the rich.](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/giving-is-the-business-of-the-rich/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [Just begin and the mind grows heated; continue, and the task will be completed!](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/just-begin-and-the-mind-grows-heated-continue-and-the-task-will-be/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [I look upon all four Gospels as thoroughly genuine, for there shines forth from them the reflected splendor of a sublimity proceeding from Jesus…](https://sms4smile.com/quotes/johann-wolfgang-von-goethe/i-look-upon-all-four-gospels-as-thoroughly-genuine-for-there-shines/) [Johann Wolfgang von Goethe](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) > [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/) [Explore all 2,052 Johann Wolfgang von Goethe quotes ](https://sms4smile.com/quotes/author/johann-wolfgang-von-goethe/) ## More Conclusion quotes > [I'm not going to be part of looking at information only partially. I'm not going to be part of just coming to quick conclusions.…](https://sms4smile.com/quotes/max-cleland/i-m-not-going-to-be-part-of-looking-at-information-only-partially-i-m/) [Max Cleland](https://sms4smile.com/quotes/author/max-cleland/) > [From what I have seen, I am driven to the conclusion that religion is only good for good people.](https://sms4smile.com/quotes/mary-mccarthy/from-what-i-have-seen-i-am-driven-to-the-conclusion-that-religion-is/) [Mary McCarthy](https://sms4smile.com/quotes/author/mary-mccarthy/) > [The thing about living alone is that it gives you a lot of time to think. 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