--- title: "Meaning & Key Takeaway of: Thus, be it understood, to demonstrate a…" description: "\"Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced b..." image: "https://sms4smile.com/quotes/i/041/henri-poincare-3339_alive_thus-be-it-understood-to-demonstrate-a-t_3144034.jpg" --- # Thus, be it understood, to demonstrate a theorem, it is… ![“Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while…” quote by Henri Poincare](https://sms4smile.com/quotes/i/041/henri-poincare-3339_alive_thus-be-it-understood-to-demonstrate-a-t_3144034.jpg) [Download](https://sms4smile.com/quotes/i/041/henri-poincare-3339_alive_thus-be-it-understood-to-demonstrate-a-t_3144034.jpg) [Open image](https://sms4smile.com/quotes/i/041/henri-poincare-3339_alive_thus-be-it-understood-to-demonstrate-a-t_3144034.jpg) > “Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.” [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical proof can be automated; understanding the meaning isn’t required for verification. **In simple terms:** Proofs can be done by machines without grasping meaning. Key Takeaway Focus on logical structure, not intuition. Themes mathematics automation philosophy Mood analytical skeptical Type philosophical technical When to use this quote - academic research - software verification - automated theorem proving Key Concepts logic formal systems computational proof Questions to Reflect On - Can machines replace human intuition in mathematics? - What are the risks of over‑reliance on automation? A Different Perspective Machines lack creativity and insight, limiting deep discovery. ★ ★ ★ ★ ★ No ratings yet [Alive](https://sms4smile.com/quotes/about/alive/) [Assumption](https://sms4smile.com/quotes/about/assumption/) [Chicago](https://sms4smile.com/quotes/about/chicago/) [Demonstrate Theorem](https://sms4smile.com/quotes/about/demonstrate-theorem-4557645/) [Doe](https://sms4smile.com/quotes/about/doe/) [Ends](https://sms4smile.com/quotes/about/ends/) [Ham](https://sms4smile.com/quotes/about/ham/) [Ifs](https://sms4smile.com/quotes/about/ifs/) [Imagination](https://sms4smile.com/quotes/about/imagination/) [Knows](https://sms4smile.com/quotes/about/knows/) [Legendary](https://sms4smile.com/quotes/about/legendary/) [Logic](https://sms4smile.com/quotes/about/logic/) [Machines](https://sms4smile.com/quotes/about/machines/) [Math](https://sms4smile.com/quotes/about/math/) [Mathematical](https://sms4smile.com/quotes/about/mathematical/) [Mathematician](https://sms4smile.com/quotes/about/mathematician/) [Mathematician Know](https://sms4smile.com/quotes/about/mathematician-know-3906583/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Mean](https://sms4smile.com/quotes/about/mean/) [Means Geometer](https://sms4smile.com/quotes/about/means-geometer-5614952/) [Might](https://sms4smile.com/quotes/about/might/) [Needs](https://sms4smile.com/quotes/about/needs/) [Piano](https://sms4smile.com/quotes/about/piano/) [Pigs](https://sms4smile.com/quotes/about/pigs/) [Replaced](https://sms4smile.com/quotes/about/replaced/) [Sausage](https://sms4smile.com/quotes/about/sausage/) [Stanley](https://sms4smile.com/quotes/about/stanley/) [Theorem Necessary](https://sms4smile.com/quotes/about/theorem-necessary-4557644/) [Theorems](https://sms4smile.com/quotes/about/theorems/) [Theorems Came](https://sms4smile.com/quotes/about/theorems-came-5614951/) [Transformed](https://sms4smile.com/quotes/about/transformed/) [Understood](https://sms4smile.com/quotes/about/understood/) [You choose](https://sms4smile.com/quotes/about/you-choose/) ## Related quotes > [Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means ...](https://sms4smile.com/quotes/henri-poincare/thus-be-it-understood-to-demonstrate-a-theorem-it-is-neither/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [No more than these machines need the mathematician know what he does.](https://sms4smile.com/quotes/henri-poincare/no-more-than-these-machines-need-the-mathematician-know-what-he-does/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [The best mobile phone had the best mathematician. They know how to fit a huge amount of data into a small amount of space.…](https://sms4smile.com/quotes/marcus-du-sautoy/the-best-mobile-phone-had-the-best-mathematician-they-know-how-to-fit/) [Marcus du Sautoy](https://sms4smile.com/quotes/author/marcus-du-sautoy/) > [One geometry cannot be more true than another; it can only be more convenient.](https://sms4smile.com/quotes/henri-poincare/one-geometry-cannot-be-more-true-than-another-it-can-only-be-more-2/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of…](https://sms4smile.com/quotes/niels-henrik-abel/there-are-very-few-theorems-in-advanced-analysis-which-have-been/) [Niels Henrik Abel](https://sms4smile.com/quotes/author/niels-henrik-abel/) > [For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that…](https://sms4smile.com/quotes/seymour-papert/for-what-is-important-when-we-give-children-a-theorem-to-use-is-not/) [Seymour Papert](https://sms4smile.com/quotes/author/seymour-papert/) > [Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation…](https://sms4smile.com/quotes/imre-lakatos/mathematics-does-not-grow-through-a-monotonous-increase-of-the-number/) [Imre Lakatos](https://sms4smile.com/quotes/author/imre-lakatos/) > [It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something,…](https://sms4smile.com/quotes/g-h-hardy/it-is-a-melancholy-experience-for-a-professional-mathematician-to/) [G. H. Hardy](https://sms4smile.com/quotes/author/g-h-hardy/) > [ In 1975, ... \[speaking with Shiing Shen Chern\], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound… ](https://sms4smile.com/quotes/chen-ning-yang/in-1975-speaking-with-shiing-shen-chern-i-told-him-i-had-finally/) [Chen-Ning Yang](https://sms4smile.com/quotes/author/chen-ning-yang/) > [The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments,…](https://sms4smile.com/quotes/christopher-zeeman/the-scientist-has-to-take-95-per-cent-of-his-subject-on-trust-he-has/) [Christopher Zeeman](https://sms4smile.com/quotes/author/christopher-zeeman/) > [Without computers we will be stuck only proving theorems that have short proofs.](https://sms4smile.com/quotes/kenneth-appel/without-computers-we-will-be-stuck-only-proving-theorems-that-have/) [Kenneth Appel](https://sms4smile.com/quotes/author/kenneth-appel/) > [A mathematician is a device for turning coffee into theorems.](https://sms4smile.com/quotes/paul-erdos/a-mathematician-is-a-device-for-turning-coffee-into-theorems/) [Paul Erdos](https://sms4smile.com/quotes/author/paul-erdos/) > [The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas…](https://sms4smile.com/quotes/g-h-hardy/the-seriousness-of-a-mathematical-theorem-lies-not-in-its-practical/) [G. H. Hardy](https://sms4smile.com/quotes/author/g-h-hardy/) > [The great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself recreates them.](https://sms4smile.com/quotes/jacob-bronowski/the-great-poem-and-the-deep-theorem-are-new-to-every-reader-and-yet/) [Jacob Bronowski](https://sms4smile.com/quotes/author/jacob-bronowski/) > [Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To believe otherwise…](https://sms4smile.com/quotes/marvin-minsky/theorems-often-tell-us-complex-truths-about-the-simple-things-but/) [Marvin Minsky](https://sms4smile.com/quotes/author/marvin-minsky/) ## More by Henri Poincare > [The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge…](https://sms4smile.com/quotes/henri-poincare/the-mathematical-facts-worthy-of-being-studied-are-those-which-by/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most…](https://sms4smile.com/quotes/henri-poincare/by-natural-selection-our-mind-has-adapted-itself-to-the-conditions-of/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation…](https://sms4smile.com/quotes/henri-poincare/if-we-knew-exactly-the-laws-of-nature-and-the-situation-of-the/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves,…](https://sms4smile.com/quotes/henri-poincare/absolute-space-that-is-to-say-the-mark-to-which-it-would-be-necessary/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Science is facts.](https://sms4smile.com/quotes/henri-poincare/science-is-facts/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves,…](https://sms4smile.com/quotes/henri-poincare/absolute-space-that-is-to-say-the-mark-to-which-it-would-be-necessary-2/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [All of mathematics is a tale about groups.](https://sms4smile.com/quotes/henri-poincare/all-of-mathematics-is-a-tale-about-groups/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.](https://sms4smile.com/quotes/henri-poincare/a-cat-is-witty-he-has-nerve-he-knows-how-to-do-precisely-the-right/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [In the old days when people invented a new function they had something useful in mind.](https://sms4smile.com/quotes/henri-poincare/in-the-old-days-when-people-invented-a-new-function-they-had/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Intuition is more important to discovery than logic.](https://sms4smile.com/quotes/henri-poincare/intuition-is-more-important-to-discovery-than-logic/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical…](https://sms4smile.com/quotes/henri-poincare/mathematics-has-a-threefold-purpose-it-must-provide-an-instrument-for/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [Experiment is the sole source of truth.](https://sms4smile.com/quotes/henri-poincare/experiment-is-the-sole-source-of-truth/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [“ Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se…](https://sms4smile.com/quotes/henri-poincare/qu-une-goutee-de-vin-tombe-dans-un-verre-d-eau-quelle-que-soit-la-loi/) [Henri Poincaré](https://sms4smile.com/quotes/author/henri-poincare/) > [If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the…](https://sms4smile.com/quotes/henri-poincare/if-that-enabled-us-to-predict-the-succeeding-situation-with-the-same/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) > [“ Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de…](https://sms4smile.com/quotes/henri-poincare/le-savant-doit-ordonner-on-fait-la-science-avec-des-faits-comme-une/) [Henri Poincare](https://sms4smile.com/quotes/author/henri-poincare/) [Explore all 130 Henri Poincare quotes ](https://sms4smile.com/quotes/author/henri-poincare/) ## More Alive quotes > [I understand that it's the music that keeps me alive... That's my lifeblood. And to give that up for, like, the TV, the cars,…](https://sms4smile.com/quotes/bruce-springsteen/i-understand-that-it-s-the-music-that-keeps-me-alive-that-s-my/) [Bruce Springsteen](https://sms4smile.com/quotes/author/bruce-springsteen/) > [I feel very grateful to be alive and well enough to make music.](https://sms4smile.com/quotes/adam-ant/i-feel-very-grateful-to-be-alive-and-well-enough-to-make-music/) [Adam Ant](https://sms4smile.com/quotes/author/adam-ant/) > [I don't crave applause. I'm not one of those guys who comes alive on stage. I'm much more alive at home, I think.](https://sms4smile.com/quotes/david-bowie/i-don-t-crave-applause-i-m-not-one-of-those-guys-who-comes-alive-on/) [David Bowie](https://sms4smile.com/quotes/author/david-bowie/) > [We must master our egoism, and through this mastery, step outside ourselves and educate ourselves in giving. Fasting requires that we rediscover all that…](https://sms4smile.com/quotes/tariq-ramadan/we-must-master-our-egoism-and-through-this-mastery-step-outside/) [Tariq Ramadan](https://sms4smile.com/quotes/author/tariq-ramadan/) > [I can't say that there are 'things' that make me come alive. There are thoughts that make me come alive.](https://sms4smile.com/quotes/marianne-williamson/i-can-t-say-that-there-are-things-that-make-me-come-alive-there-are/) [Marianne Williamson](https://sms4smile.com/quotes/author/marianne-williamson/) > [We're like the wicked witch. We promise gingerbread, then eat the little brats alive.](https://sms4smile.com/quotes/orson-scott-card/we-re-like-the-wicked-witch-we-promise-gingerbread-then-eat-the/) [Orson Scott Card](https://sms4smile.com/quotes/author/orson-scott-card/) > [If Jovan Belcher didn't possess a gun, he and Kasandra Perkins would both be alive today.](https://sms4smile.com/quotes/bob-costas/if-jovan-belcher-didn-t-possess-a-gun-he-and-kasandra-perkins-would/) [Bob Costas](https://sms4smile.com/quotes/author/bob-costas/) > [Peace is an ongoing process. It begins with the first step and it does not end. We, all of us alive today, are the…](https://sms4smile.com/quotes/david-krieger/peace-is-an-ongoing-process-it-begins-with-the-first-step-and-it-does/) [David Krieger](https://sms4smile.com/quotes/author/david-krieger/) > [I think adoption becomes complicated whenever the biological parents are alive.](https://sms4smile.com/quotes/james-haven/i-think-adoption-becomes-complicated-whenever-the-biological-parents/) [James Haven](https://sms4smile.com/quotes/author/james-haven/) > [The pain of love is the pain of being alive. It is a perpetual wound.](https://sms4smile.com/quotes/maureen-duffy/the-pain-of-love-is-the-pain-of-being-alive-it-is-a-perpetual-wound/) [Maureen Duffy](https://sms4smile.com/quotes/author/maureen-duffy/) > [I have tried to resign myself, and to console myself; and that, I hope, I may have done imperfectly; but what I cannot firmly…](https://sms4smile.com/quotes/charles-dickens/i-have-tried-to-resign-myself-and-to-console-myself-and-that-i-hope-i/) [Charles Dickens](https://sms4smile.com/quotes/author/charles-dickens/) > [If Melanchthon were alive today, he might not weep because of controversies that surround the Lord's Supper, but he might well sorrow because of…](https://sms4smile.com/quotes/erwin-w-lutzer/if-melanchthon-were-alive-today-he-might-not-weep-because-of/) [Erwin W. Lutzer](https://sms4smile.com/quotes/author/erwin-w-lutzer/) > [If you’re alive, don’t move, if you’re dead, don’t worry about it.](https://sms4smile.com/quotes/laurell-k-hamilton/if-you-re-alive-don-t-move-if-you-re-dead-don-t-worry-about-it/) [Laurell K. Hamilton](https://sms4smile.com/quotes/author/laurell-k-hamilton/) > [Here Greek and Roman find themselves alive along these crowded shelves; and Shakespeare treads again his stage, and Chaucer paints anew his age.](https://sms4smile.com/quotes/john-greenleaf-whittier/here-greek-and-roman-find-themselves-alive-along-these-crowded/) [John Greenleaf Whittier](https://sms4smile.com/quotes/author/john-greenleaf-whittier/) > [You're alive!" Fezzik cried. The man in black sat immobile, like a ventriloquist's dummy, just his mouth moving. "That is perhaps the most childishly…](https://sms4smile.com/quotes/william-goldman/you-re-alive-fezzik-cried-the-man-in-black-sat-immobile-like-a/) [William Goldman](https://sms4smile.com/quotes/author/william-goldman/) [Browse all 7,282 Alive quotes ](https://sms4smile.com/quotes/about/alive/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the \"logic piano\" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. 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