--- title: "Meaning & Key Takeaway of: I then began to study arithmetical…" description: "\"I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my..." image: "https://sms4smile.com/quotes/i/c4e/henri-poincare-3339_certainty_i-then-began-to-study-arithmetical-quest_2533045.jpg" --- # I then began to study arithmetical questions without any… ![“I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things…” quote by Henri Poincare](https://sms4smile.com/quotes/i/c4e/henri-poincare-3339_certainty_i-then-began-to-study-arithmetical-quest_2533045.jpg) [Download](https://sms4smile.com/quotes/i/c4e/henri-poincare-3339_certainty_i-then-began-to-study-arithmetical-quest_2533045.jpg) [Open image](https://sms4smile.com/quotes/i/c4e/henri-poincare-3339_certainty_i-then-began-to-study-arithmetical-quest_2533045.jpg) > “I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.” [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. He discovered a deep link between algebraic forms and non‑Euclidean geometry while distracted by a seaside walk. **In simple terms:** A sudden insight connected two seemingly unrelated math fields. Key Takeaway Stay open to unexpected connections. Themes creativity mathematics insight Mood curious reflective Type philosophical inspirational When to use this quote - research brainstorming - problem solving - academic study Key Concepts non‑Euclidean geometry quadratic forms interdisciplinary thinking Questions to Reflect On - How can unrelated foster environments that allow sudden insights? - What role does distraction play in creativity? A Different Perspective Such insights often need rigorous proof before acceptance. ★ ★ ★ ★ ★ No ratings yet [Arithmetical Transformations](https://sms4smile.com/quotes/about/arithmetical-transformations-1361935/) [Certainty](https://sms4smile.com/quotes/about/certainty/) [Certainty Arithmetical](https://sms4smile.com/quotes/about/certainty-arithmetical-1361939/) [Characteristics](https://sms4smile.com/quotes/about/characteristics/) [Cliffs](https://sms4smile.com/quotes/about/cliffs/) [Conciseness Suddenness](https://sms4smile.com/quotes/about/conciseness-suddenness-1361937/) [Different](https://sms4smile.com/quotes/about/different/) [Disgusted](https://sms4smile.com/quotes/about/disgusted/) [Form](https://sms4smile.com/quotes/about/form/) [Geometry](https://sms4smile.com/quotes/about/geometry/) [Ideas](https://sms4smile.com/quotes/about/ideas/) [Identical](https://sms4smile.com/quotes/about/identical/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [One day](https://sms4smile.com/quotes/about/one-day/) [Quadratics](https://sms4smile.com/quotes/about/quadratics/) [Research](https://sms4smile.com/quotes/about/research/) [Results](https://sms4smile.com/quotes/about/results/) [Science](https://sms4smile.com/quotes/about/science/) [Study](https://sms4smile.com/quotes/about/study/) [Success](https://sms4smile.com/quotes/about/success/) [Ternary Quadratic](https://sms4smile.com/quotes/about/ternary-quadratic-1361936/) [Transformation](https://sms4smile.com/quotes/about/transformation/) [Transformations Indefinite](https://sms4smile.com/quotes/about/transformations-indefinite-1361938/) [Walking](https://sms4smile.com/quotes/about/walking/) [Want](https://sms4smile.com/quotes/about/want/) ## Related quotes > [...the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic…](https://sms4smile.com/quotes/thomas-jefferson/the-science-of-calculation-also-is-indispensable-as-far-as-the/) [Thomas Jefferson](https://sms4smile.com/quotes/author/thomas-jefferson/) > [Quadratic reciprocity is the song of love in the land of prime numbers.](https://sms4smile.com/quotes/kato/quadratic-reciprocity-is-the-song-of-love-in-the-land-of-prime-numbers/) [Kato](https://sms4smile.com/quotes/author/kato/) > [This specter of the female politician, who abandons her family to neglect for the sake of passing bills in parliament, is just as complete…](https://sms4smile.com/quotes/frances-power-cobbe/this-specter-of-the-female-politician-who-abandons-her-family-to/) [Frances Power Cobbe](https://sms4smile.com/quotes/author/frances-power-cobbe/) > [I've said it before: equations are the devil's sentences. The worst one is that quadratic equation, an infernal salad of numbers, letters, and symbols.](https://sms4smile.com/quotes/stephen-colbert/i-ve-said-it-before-equations-are-the-devil-s-sentences-the-worst-one/) [Stephen Colbert](https://sms4smile.com/quotes/author/stephen-colbert/) > [Life is not an orderly progression, self-contained like a musical scale or a quadratic equation... If one is to record one's life truthfully, one…](https://sms4smile.com/quotes/leonard-woolf/life-is-not-an-orderly-progression-self-contained-like-a-musical/) [Leonard Woolf](https://sms4smile.com/quotes/author/leonard-woolf/) > [ It can be argued that the mathematics behind these images \[of the orbit diagram for quadratic functions and the Mandelbrot set\] is even prettier… ](https://sms4smile.com/quotes/robert-l-devaney/it-can-be-argued-that-the-mathematics-behind-these-images-of-the/) [Robert L. Devaney](https://sms4smile.com/quotes/author/robert-l-devaney/) > [Not a lot of people know this, but I'm very good at mathematics. When I was an angry teenager, I used to sit in…](https://sms4smile.com/quotes/samantha-bond/not-a-lot-of-people-know-this-but-i-m-very-good-at-mathematics-when-i/) [Samantha Bond](https://sms4smile.com/quotes/author/samantha-bond/) > [I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs,…](https://sms4smile.com/quotes/michael-atiyah/i-think-it-is-said-that-gauss-had-ten-different-proofs-for-the-law-of/) [Michael Atiyah](https://sms4smile.com/quotes/author/michael-atiyah/) > [ There's a lot of science in it, and as Slartibartfast \[in The Hitchhiker's Guide to the Galaxy\] said: 'I am a great fan of… ](https://sms4smile.com/quotes/terry-pratchett/there-s-a-lot-of-science-in-it-and-as-slartibartfast-in-the/) [Terry Pratchett](https://sms4smile.com/quotes/author/terry-pratchett/) > [Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble…](https://sms4smile.com/quotes/james-joseph-sylvester/aspiring-to-these-wide-generalizations-the-analysis-of-quadratic/) [James Joseph Sylvester](https://sms4smile.com/quotes/author/james-joseph-sylvester/) > [How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you…](https://sms4smile.com/quotes/stephen-leacock/how-can-you-shorten-the-subject-that-stern-struggle-with-the/) [Stephen Leacock](https://sms4smile.com/quotes/author/stephen-leacock/) > [What grinds me the most is that we’re sending kids out into the world who don’t know how to balance a checkbook, don’t know…](https://sms4smile.com/quotes/chris-colfer/what-grinds-me-the-most-is-that-we-re-sending-kids-out-into-the-world/) [Chris Colfer](https://sms4smile.com/quotes/author/chris-colfer/) > [All over China, parents tell their children to stop complaining and to finish their quadratic equations and trigonometric functions because there are sixty-five million…](https://sms4smile.com/quotes/michael-cunningham/all-over-china-parents-tell-their-children-to-stop-complaining-and-to/) [Michael Cunningham](https://sms4smile.com/quotes/author/michael-cunningham/) ## 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 Certainty quotes > [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/) > [Sometimes we have the absolute certainty there's something inside us that's so hideous and monstrous that if we ever search it out we won't…](https://sms4smile.com/quotes/hubert-selby-jr/sometimes-we-have-the-absolute-certainty-there-s-something-inside-us/) [Hubert Selby, Jr](https://sms4smile.com/quotes/author/hubert-selby-jr/) > [The past and the future become unimportant. There is only that moment, and the incredible certainty that everything under the sun has been written…](https://sms4smile.com/quotes/paulo-coelho/the-past-and-the-future-become-unimportant-there-is-only-that-moment/) [Paulo Coelho](https://sms4smile.com/quotes/author/paulo-coelho/) > [In the mental disturbance and effort of writing, what sustains you is the certainty that on every page there is something left unsaid.](https://sms4smile.com/quotes/cesare-pavese/in-the-mental-disturbance-and-effort-of-writing-what-sustains-you-is/) [Cesare Pavese](https://sms4smile.com/quotes/author/cesare-pavese/) > [Of course I doubt. I do not practice a certainty. I practice a faith.](https://sms4smile.com/quotes/robert-breault/of-course-i-doubt-i-do-not-practice-a-certainty-i-practice-a-faith/) [Robert Breault](https://sms4smile.com/quotes/author/robert-breault/) > [The world is a wonderfully weird place, consensual reality is significantly flawed, no institution can be trusted, certainty is a mirage, security a delusion,…](https://sms4smile.com/quotes/tom-robbins/the-world-is-a-wonderfully-weird-place-consensual-reality-is/) [Tom Robbins](https://sms4smile.com/quotes/author/tom-robbins/) > [As a businessman, I know that businesses need certainty.](https://sms4smile.com/quotes/bill-foster/as-a-businessman-i-know-that-businesses-need-certainty/) [Bill Foster](https://sms4smile.com/quotes/author/bill-foster/) > [It is suggested that in domestic violence at least the presence or absence of a firearm, or of any other type of weapon, is…](https://sms4smile.com/quotes/colin-greenwood/it-is-suggested-that-in-domestic-violence-at-least-the-presence-or/) [Colin Greenwood](https://sms4smile.com/quotes/author/colin-greenwood/) > [Every single person who is a member of our party deserves to have certainty. They deserve to know that my attention and focus is…](https://sms4smile.com/quotes/annamie-paul/every-single-person-who-is-a-member-of-our-party-deserves-to-have/) [Annamie Paul](https://sms4smile.com/quotes/author/annamie-paul/) > [The significance and volume of repairs that are needed across the country demand that we give state and local governments the long-term certainty they…](https://sms4smile.com/quotes/sam-graves/the-significance-and-volume-of-repairs-that-are-needed-across-the/) [Sam Graves](https://sms4smile.com/quotes/author/sam-graves/) > [“Death is the one great certainty in life. That’s what my dad used to say. Nothing else is certain. Not love. Not happiness. Not…](https://sms4smile.com/quotes/mila-gray/death-is-the-one-great-certainty-in-life-that-s-what-my-dad-used-to/) [Mila Gray](https://sms4smile.com/quotes/author/mila-gray/) > [ \[I\]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge… ](https://sms4smile.com/quotes/roger-bacon/i-f-in-other-sciences-we-should-arrive-at-certainty-without-doubt-and/) [Roger Bacon](https://sms4smile.com/quotes/author/roger-bacon/) > [Do not lose hope; St. Joseph also experienced moments of difficulty, but he never lost faith and was able to overcome them, in the…](https://sms4smile.com/quotes/pope-francis/do-not-lose-hope-st-joseph-also-experienced-moments-of-difficulty-but/) [Pope Francis](https://sms4smile.com/quotes/author/pope-francis/) > [As the future is never known with certainty, the evaluation of the prospective benefits requires the formation of expectations. An acceptable house, partner or…](https://sms4smile.com/quotes/dale-t-mortensen/as-the-future-is-never-known-with-certainty-the-evaluation-of-the/) [Dale T. Mortensen](https://sms4smile.com/quotes/author/dale-t-mortensen/) > [Finding someone that trusted my vision helped me find certainty in who I was.](https://sms4smile.com/quotes/syd/finding-someone-that-trusted-my-vision-helped-me-find-certainty-in/) [Syd](https://sms4smile.com/quotes/author/syd/) [Browse all 1,776 Certainty quotes ](https://sms4smile.com/quotes/about/certainty/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. 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