--- title: "Meaning & Key Takeaway of: The object of mathematical rigor is to…" description: "\"The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.\" — Jacques Hada..." image: "https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png" --- # The object of mathematical rigor is to sanction and… ![“The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.” quote by Jacques Hadamard](https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png) [Download](https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png) [Open image](https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png) > “The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.” [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical rigor exists to formalize intuition, not to replace it; it validates intuitive insights. **In simple terms:** Rigor formalizes intuition. Key Takeaway Use rigor to test and strengthen ideas. Themes mathematics philosophy methodology Mood analytical inquisitive Type philosophical critical When to use this quote - research design - education - problem solving - theory development Key Concepts intuition formal proof validation Questions to Reflect On - When should intuition be trusted over proof? - How to balance rigor with imagination? A Different Perspective Rigor can stifle creativity if applied dogmatically. ★ ★ ★ ★ ★ No ratings yet [Conquest](https://sms4smile.com/quotes/about/conquest/) [Intuition](https://sms4smile.com/quotes/about/intuition/) [Intuition Object](https://sms4smile.com/quotes/about/intuition-object-3545586/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematical Rigor](https://sms4smile.com/quotes/about/mathematical-rigor-3224220/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Object Mathematical](https://sms4smile.com/quotes/about/object-mathematical-3545588/) [Objects](https://sms4smile.com/quotes/about/objects/) [Rigor](https://sms4smile.com/quotes/about/rigor/) [Rigor Sanction](https://sms4smile.com/quotes/about/rigor-sanction-3545587/) [Sanctions](https://sms4smile.com/quotes/about/sanctions/) [Statistics](https://sms4smile.com/quotes/about/statistics/) ## Related quotes > [If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous…](https://sms4smile.com/quotes/richard-p-feynman/if-there-is-something-very-slightly-wrong-in-our-definition-of-the/) [Richard P. Feynman](https://sms4smile.com/quotes/author/richard-p-feynman/) > [One of the central developments of 19th century mathematics involved a dramatic increase in the standards of mathematical rigor. This was for a variety…](https://sms4smile.com/quotes/richard-f-heck/one-of-the-central-developments-of-19th-century-mathematics-involved/) [Richard F. Heck](https://sms4smile.com/quotes/author/richard-f-heck/) > [Logic merely sanctions the conquests of the intuition.](https://sms4smile.com/quotes/jacques-hadamard/logic-merely-sanctions-the-conquests-of-the-intuition/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) > [Night is a time of rigor, but also of mercy. There are truths which one can see only when it’s dark](https://sms4smile.com/quotes/isaac-bashevis-singer/night-is-a-time-of-rigor-but-also-of-mercy-there-are-truths-which-one/) [Isaac Bashevis Singer](https://sms4smile.com/quotes/author/isaac-bashevis-singer/) > [Alchemy and Kabbalah are later developments in my thinking. I think the primary interest has been the relationship of magic and mystery to logic…](https://sms4smile.com/quotes/fred-alan-wolf/alchemy-and-kabbalah-are-later-developments-in-my-thinking-i-think/) [Fred Alan Wolf](https://sms4smile.com/quotes/author/fred-alan-wolf/) > [I have the loving support of my girlfriend who still attends Wake Forest and is nearing graduation. She helps me cope with the everyday…](https://sms4smile.com/quotes/tim-duncan/i-have-the-loving-support-of-my-girlfriend-who-still-attends-wake/) [Tim Duncan](https://sms4smile.com/quotes/author/tim-duncan/) > [Jesuits encourage an intellectual rigor in a way that I like.](https://sms4smile.com/quotes/alexander-payne/jesuits-encourage-an-intellectual-rigor-in-a-way-that-i-like/) [Alexander Payne](https://sms4smile.com/quotes/author/alexander-payne/) > [Extremes, though contrary, have the like effects. Extreme heat kills, and so extreme cold: extreme love breeds satiety, and so extreme hatred; and too…](https://sms4smile.com/quotes/george-chapman/extremes-though-contrary-have-the-like-effects-extreme-heat-kills-and/) [George Chapman](https://sms4smile.com/quotes/author/george-chapman/) > [What gets projects done for me is not inspiration. It's curiosity and rigor.](https://sms4smile.com/quotes/andrew-zuckerman/what-gets-projects-done-for-me-is-not-inspiration-it-s-curiosity-and/) [Andrew Zuckerman](https://sms4smile.com/quotes/author/andrew-zuckerman/) > [The conventional explanation for Jewish success, of course, is that Jews come from a literate, intellectual culture. They are famously "the people of the…](https://sms4smile.com/quotes/malcolm-gladwell/the-conventional-explanation-for-jewish-success-of-course-is-that/) [Malcolm Gladwell](https://sms4smile.com/quotes/author/malcolm-gladwell/) > [The writer’s job is to write with rigor, with commitment, to defend what they believe with all the talent they have. I think that’s…](https://sms4smile.com/quotes/mario-vargas-llosa/the-writer-s-job-is-to-write-with-rigor-with-commitment-to-defend/) [Mario Vargas Llosa](https://sms4smile.com/quotes/author/mario-vargas-llosa/) > [Lenity will operate with greater force, in some instances, than rigor. It is, therefore, my first wish, to have my whole conduct distinguished by…](https://sms4smile.com/quotes/george-washington/lenity-will-operate-with-greater-force-in-some-instances-than-rigor/) [George Washington](https://sms4smile.com/quotes/author/george-washington/) > [The idea of freedom can never be disassociated from real Prussia. The real Prussian spirit means a synthesis between restraint and freedom, between voluntary…](https://sms4smile.com/quotes/henning-von-tresckow/the-idea-of-freedom-can-never-be-disassociated-from-real-prussia-the/) [Henning von Tresckow](https://sms4smile.com/quotes/author/henning-von-tresckow/) > [ Again, I hear almost everyday from atheists who write off religion as primitive, premodern nonsense. I summon Aquinas, Augustine, Paul \[of Tarsus\], Teresa of… ](https://sms4smile.com/quotes/robert-barron/again-i-hear-almost-everyday-from-atheists-who-write-off-religion-as/) [Robert Barron](https://sms4smile.com/quotes/author/robert-barron/) > [Like many others, I have deep misgivings about the state of education in the United States. Too many of our students fail to graduate…](https://sms4smile.com/quotes/bill-gates/like-many-others-i-have-deep-misgivings-about-the-state-of-education/) [Bill Gates](https://sms4smile.com/quotes/author/bill-gates/) ## More by Jacques Hadamard > [To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic,…](https://sms4smile.com/quotes/jacques-hadamard/to-parents-who-despair-because-their-children-are-unable-to-master/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) > [Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle.](https://sms4smile.com/quotes/jacques-hadamard/practical-application-is-found-by-not-looking-for-it-and-one-can-say/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) > [Logic merely sanctions the conquests of the intuition.](https://sms4smile.com/quotes/jacques-hadamard/logic-merely-sanctions-the-conquests-of-the-intuition/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) > [The shortest path between two truths in the real domain passes through the complex domain.](https://sms4smile.com/quotes/jacques-hadamard/the-shortest-path-between-two-truths-in-the-real-domain-passes/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) > [Can the existence of a mathematical entity be proved without defining it ?](https://sms4smile.com/quotes/jacques-hadamard/can-the-existence-of-a-mathematical-entity-be-proved-without-defining/) [Jacques Hadamard](https://sms4smile.com/quotes/author/jacques-hadamard/) [Explore all 6 Jacques Hadamard quotes ](https://sms4smile.com/quotes/author/jacques-hadamard/) ## More Conquest quotes > [Here's the reality. The image of a white Jesus has been used to justify enslavement, conquest, colonialism, the genocide of indigenous peoples. There are…](https://sms4smile.com/quotes/tim-wise/here-s-the-reality-the-image-of-a-white-jesus-has-been-used-to/) [Tim Wise](https://sms4smile.com/quotes/author/tim-wise/) > [Politics...You see, it depends on what kind of politics. What we did during my father's generation was a duty. And it was beautiful because…](https://sms4smile.com/quotes/indira-gandhi/politics-you-see-it-depends-on-what-kind-of-politics-what-we-did/) [Indira Gandhi](https://sms4smile.com/quotes/author/indira-gandhi/) > [If love is the quest, then marriage is the conquest](https://sms4smile.com/quotes/anonymous/if-love-is-the-quest-then-marriage-is-the-conquest/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [We must not forget that what I mean by the conquest of the world by spiritual thought is the sending out of the life-giving…](https://sms4smile.com/quotes/swami-vivekananda/we-must-not-forget-that-what-i-mean-by-the-conquest-of-the-world-by/) [Swami Vivekananda](https://sms4smile.com/quotes/author/swami-vivekananda/) > [Any piece of knowledge which the pupil has himself acquired- any problem which he has himself solved, becomes, by virtue of the conquest, much…](https://sms4smile.com/quotes/herbert-spencer/any-piece-of-knowledge-which-the-pupil-has-himself-acquired-any/) [Herbert Spencer](https://sms4smile.com/quotes/author/herbert-spencer/) > [I have visited sweatshops, factories, and crowded slums. If I could not see it, I could smell it. The foundation of society is laid…](https://sms4smile.com/quotes/helen-keller/i-have-visited-sweatshops-factories-and-crowded-slums-if-i-could-not/) [Helen Keller](https://sms4smile.com/quotes/author/helen-keller/) > [It is in meeting the great tests that mankind can most successfully rise to great heights. Out of danger and restless insecurity comes the…](https://sms4smile.com/quotes/isaac-asimov/it-is-in-meeting-the-great-tests-that-mankind-can-most-successfully/) [Isaac Asimov](https://sms4smile.com/quotes/author/isaac-asimov/) > [By the age of three, the child has already laid down the foundations of his personality as a human being, and only then does…](https://sms4smile.com/quotes/maria-montessori/by-the-age-of-three-the-child-has-already-laid-down-the-foundations/) [Maria Montessori](https://sms4smile.com/quotes/author/maria-montessori/) > [I refer to the misunderstanding of Soviet Russia as an aggressive power, militaristically and ideologically bent upon world domination 'seeing', to quote a recent…](https://sms4smile.com/quotes/enoch-powell/i-refer-to-the-misunderstanding-of-soviet-russia-as-an-aggressive/) [Enoch Powell](https://sms4smile.com/quotes/author/enoch-powell/) > [At length weariness succeeds to labor, and the mind lies at ease in the contemplation of her own attainments without any desire of new…](https://sms4smile.com/quotes/samuel-johnson/at-length-weariness-succeeds-to-labor-and-the-mind-lies-at-ease-in/) [Samuel Johnson](https://sms4smile.com/quotes/author/samuel-johnson/) > [The film The Conquest will be seen on many different levels and the American point of view is always more technical. The French are…](https://sms4smile.com/quotes/xavier-durringer/the-film-the-conquest-will-be-seen-on-many-different-levels-and-the/) [Xavier Durringer](https://sms4smile.com/quotes/author/xavier-durringer/) > [Misgovernment is of four kinds, often in combination. They are: 1) tyranny or oppression, of which history provides so many well-known examples that they…](https://sms4smile.com/quotes/barbara-tuchman/misgovernment-is-of-four-kinds-often-in-combination-they-are-1/) [Barbara Tuchman](https://sms4smile.com/quotes/author/barbara-tuchman/) > [In scientific thought, the concept functions all the better for being cut off from all background images. In its full exercise, the scientific concept…](https://sms4smile.com/quotes/gaston-bachelard/in-scientific-thought-the-concept-functions-all-the-better-for-being/) [Gaston Bachelard](https://sms4smile.com/quotes/author/gaston-bachelard/) > [There must be a law if there is to be liberty. Try to play a piano and you will run into laws as fixed…](https://sms4smile.com/quotes/adrian-rogers/there-must-be-a-law-if-there-is-to-be-liberty-try-to-play-a-piano-and/) [Adrian Rogers](https://sms4smile.com/quotes/author/adrian-rogers/) > [The Islamic conquest of India is probably the bloodiest story in history. It is a discouraging tale, for its evident moral is that civilization…](https://sms4smile.com/quotes/will-durant/the-islamic-conquest-of-india-is-probably-the-bloodiest-story-in/) [Will Durant](https://sms4smile.com/quotes/author/will-durant/) [Browse all 567 Conquest quotes ](https://sms4smile.com/quotes/about/conquest/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.", "creator": { "@type": "Person", "name": "Jacques Hadamard" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/jacques-hadamard/the-object-of-mathematical-rigor-is-to-sanction-and-legitimize-the/", "about": { "@type": "Thing", "name": "Conquest" }, "@id": "https://sms4smile.com/quotes/jacques-hadamard/the-object-of-mathematical-rigor-is-to-sanction-and-legitimize-the/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png", "contentUrl": "https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png", "url": "https://sms4smile.com/quotes/i/ce3/jacques-hadamard-51080_conquest_the-object-of-mathematical-rigor-is-to-s_1192638.png", "width": 1080, "height": 1080, "caption": "“The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was…” — Jacques Hadamard", "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": "Jacques Hadamard", "item": "https://sms4smile.com/quotes/author/jacques-hadamard/" }, { "@type": "ListItem", "position": 4, "name": "The object of mathematical rigor is...", "item": "https://sms4smile.com/quotes/jacques-hadamard/the-object-of-mathematical-rigor-is-to-sanction-and-legitimize-the/" } ], "@id": "https://sms4smile.com/quotes/jacques-hadamard/the-object-of-mathematical-rigor-is-to-sanction-and-legitimize-the/#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 } } ] } ```