--- title: "Meaning & Key Takeaway of: If others would but reflect on…" description: "\"If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries.\" — Carl Friedrich Gauss" image: "https://sms4smile.com/quotes/i/b6f/carl-friedrich-gauss-9412_discovery_if-others-would-but-reflect-on-mathemati_101536.png" --- # If others would but reflect on mathematical truths as… ![“If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries.” quote by Carl Friedrich Gauss](https://sms4smile.com/quotes/i/b6f/carl-friedrich-gauss-9412_discovery_if-others-would-but-reflect-on-mathemati_101536.png) [Download](https://sms4smile.com/quotes/i/b6f/carl-friedrich-gauss-9412_discovery_if-others-would-but-reflect-on-mathemati_101536.png) [Open image](https://sms4smile.com/quotes/i/b6f/carl-friedrich-gauss-9412_discovery_if-others-would-but-reflect-on-mathemati_101536.png) > “If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries.” [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Deep, sustained contemplation of mathematical truths reveals insights that others may overlook, leading to breakthroughs. **In simple terms:** Persistent reflection uncovers hidden mathematical discoveries. Key Takeaway Thorough contemplation drives innovation. Themes mathematics creativity reflection intellectual perseverance Mood inspirational thoughtful Type philosophical educational When to use this quote - research seminars encouraging deep study - individual mathematicians pursuing long‑term problems Key Concepts cognitive depth epistemic humility Practical Applications - schedule regular reflective sessions - maintain detailed notebooks of insights Questions to Reflect On - What balance should be struck between solitary reflection and collaborative work? - How can one cultivate sustained focus in a distracted world? A Different Perspective Not everyone has the time or resources for prolonged contemplation; collaboration can also yield discoveries. ★ ★ ★ ★ ★ No ratings yet [Discovery](https://sms4smile.com/quotes/about/discovery/) [Truth](https://sms4smile.com/quotes/about/truth/) [Truths](https://sms4smile.com/quotes/about/truths/) ## Related quotes > [“The whisper of the wind through the grass speaks to my soul, revealing life's truths more deeply than the clamour of my thoughts.”](https://sms4smile.com/quotes/bhuwan-thapaliya/the-whisper-of-the-wind-through-the-grass-speaks-to-my-soul-revealing/) [Bhuwan Thapaliya](https://sms4smile.com/quotes/author/bhuwan-thapaliya/) > [There are several kinds of truths, and it is customary to place in the first order mathematical truths, which are, however, only truths of…](https://sms4smile.com/quotes/georges-louis-leclerc-comte-de-buffon/there-are-several-kinds-of-truths-and-it-is-customary-to-place-in-the/) [Georges-Louis Leclerc, Comte de Buffon](https://sms4smile.com/quotes/author/georges-louis-leclerc-comte-de-buffon/) > [. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even…](https://sms4smile.com/quotes/anonymous/we-have-overcome-the-notion-that-mathematical-truths-have-an/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with…](https://sms4smile.com/quotes/charles-hermite/there-exists-if-i-am-not-mistaken-an-entire-world-which-is-the/) [Charles Hermite](https://sms4smile.com/quotes/author/charles-hermite/) > [It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves…](https://sms4smile.com/quotes/ada-lovelace/it-is-however-pretty-evident-on-general-principles-that-in-devising/) [Ada Lovelace](https://sms4smile.com/quotes/author/ada-lovelace/) > [The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of…](https://sms4smile.com/quotes/alfred-north-whitehead/the-point-of-mathematics-is-that-in-it-we-have-always-got-rid-of-the/) [Alfred North Whitehead](https://sms4smile.com/quotes/author/alfred-north-whitehead/) > [The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.](https://sms4smile.com/quotes/george-washington/the-investigation-of-mathematical-truths-accustoms-the-mind-to-method/) [George Washington](https://sms4smile.com/quotes/author/george-washington/) > [The peculiarity of the evidence of mathematical truths is that all the argument is on one side.](https://sms4smile.com/quotes/john-stuart-mill/the-peculiarity-of-the-evidence-of-mathematical-truths-is-that-all-2/) [John Stuart Mill](https://sms4smile.com/quotes/author/john-stuart-mill/) > [“She said there was comfort to be found in the permanence of mathematical truths, in the lack of arbitrariness and the absence of ambiguity.…](https://sms4smile.com/quotes/khaled-hosseini/she-said-there-was-comfort-to-be-found-in-the-permanence-of-2/) [Khaled Hosseini](https://sms4smile.com/quotes/author/khaled-hosseini/) > [“She said there was comfort to be found in the permanence of mathematical truths, in the lack of arbitrariness and the absence of ambiguity.…](https://sms4smile.com/quotes/khaled-hosseini/she-said-there-was-comfort-to-be-found-in-the-permanence-of/) [Khaled Hosseini](https://sms4smile.com/quotes/author/khaled-hosseini/) > [I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is…](https://sms4smile.com/quotes/roger-penrose/i-imagine-that-whenever-the-mind-perceives-a-mathematical-idea-it/) [Roger Penrose](https://sms4smile.com/quotes/author/roger-penrose/) > [“The peculiarity of the evidence of mathematical truths is, that all the argument is on one side. There are no objections, and no answers…](https://sms4smile.com/quotes/john-stuart-mill/the-peculiarity-of-the-evidence-of-mathematical-truths-is-that-all/) [John Stuart Mill](https://sms4smile.com/quotes/author/john-stuart-mill/) > [“Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt…](https://sms4smile.com/quotes/charles-proteus-steinmetz/mathematics-is-the-most-exact-science-and-its-conclusions-are-capable/) [Charles Proteus Steinmetz](https://sms4smile.com/quotes/author/charles-proteus-steinmetz/) > [However gemlike mathematical truths may be, research is but a human endeavor.](https://sms4smile.com/quotes/h-david-burton/however-gemlike-mathematical-truths-may-be-research-is-but-a-human/) [H. David Burton](https://sms4smile.com/quotes/author/h-david-burton/) > [Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt…](https://sms4smile.com/quotes/charles-proteus-steinmetz/mathematics-is-the-most-exact-science-and-its-conclusions-are-capable-2/) [Charles Proteus Steinmetz](https://sms4smile.com/quotes/author/charles-proteus-steinmetz/) ## More by Carl Friedrich Gauss > [To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much…](https://sms4smile.com/quotes/carl-friedrich-gauss/to-the-distracting-occupations-belong-especially-my-lecture-courses/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.](https://sms4smile.com/quotes/carl-friedrich-gauss/the-total-number-of-dirichlet-s-publications-is-not-large-jewels-are/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [“Thou, nature, art my goddess; to thy laws my services are bound... { His second motto, from King Lear by Shakespeare }”](https://sms4smile.com/quotes/carl-friedrich-gauss/thou-nature-art-my-goddess-to-thy-laws-my-services-are-bound-his/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending…](https://sms4smile.com/quotes/carl-friedrich-gauss/i-have-the-vagary-of-taking-a-lively-interest-in-mathematical/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.](https://sms4smile.com/quotes/carl-friedrich-gauss/arc-amplitude-and-curvature-sustain-a-similar-relation-to-each-other/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our…](https://sms4smile.com/quotes/carl-friedrich-gauss/there-are-problems-to-whose-solution-i-would-attach-an-infinitely/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other…](https://sms4smile.com/quotes/carl-friedrich-gauss/mathematics-is-the-queen-of-sciences-and-number-theory-is-the-queen/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [I protest against the use of infinite magnitude ..., which is never permissible in mathematics.](https://sms4smile.com/quotes/carl-friedrich-gauss/i-protest-against-the-use-of-infinite-magnitude-which-is-never/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [ It is always noteworthy that all those who seriously study this science \[the theory of numbers\] conceive a sort of passion for it. ](https://sms4smile.com/quotes/carl-friedrich-gauss/it-is-always-noteworthy-that-all-those-who-seriously-study-this/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [You have no idea, how much poetry there is in the calculation of a table of logarithms!](https://sms4smile.com/quotes/carl-friedrich-gauss/you-have-no-idea-how-much-poetry-there-is-in-the-calculation-of-a/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [The Infinite is only a manner of speaking.](https://sms4smile.com/quotes/carl-friedrich-gauss/the-infinite-is-only-a-manner-of-speaking/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that…](https://sms4smile.com/quotes/carl-friedrich-gauss/sophie-germain-proved-to-the-world-that-even-a-woman-can-accomplish/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [God does arithmetic.](https://sms4smile.com/quotes/carl-friedrich-gauss/god-does-arithmetic/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [ Mathematics is the queen of the sciences and arithmetic \[number theory\] is the queen of mathematics. She often condescends to render service to astronomy… ](https://sms4smile.com/quotes/carl-friedrich-gauss/mathematics-is-the-queen-of-the-sciences-and-arithmetic-number-theory/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) > [Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.](https://sms4smile.com/quotes/carl-friedrich-gauss/mathematical-discoveries-like-springtime-violets-in-the-woods-have/) [Carl Friedrich Gauss](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) [Explore all 73 Carl Friedrich Gauss quotes ](https://sms4smile.com/quotes/author/carl-friedrich-gauss/) ## More Discovery quotes > [ Next came the Patent laws. These began in England in 1624; and, in this country, with the adoption of our constitution. Before then \[these?\],… ](https://sms4smile.com/quotes/abraham-lincoln/next-came-the-patent-laws-these-began-in-england-in-1624-and-in-this/) [Abraham Lincoln](https://sms4smile.com/quotes/author/abraham-lincoln/) > [Throughout my work, I have assumed that the standard model is correct, and hence, the Higgs boson should be found. Although this is not…](https://sms4smile.com/quotes/ashoke-sen/throughout-my-work-i-have-assumed-that-the-standard-model-is-correct/) [Ashoke Sen](https://sms4smile.com/quotes/author/ashoke-sen/) > [There is usually no dreamer so unworldly as the anthologist. He wanders in a vast garden, lost in wonder, unable to decide often between…](https://sms4smile.com/quotes/mary-webb/there-is-usually-no-dreamer-so-unworldly-as-the-anthologist-he/) [Mary Webb](https://sms4smile.com/quotes/author/mary-webb/) > [New generations of humans inherit the acquired discoveries of generations past, allowing cosmic insight to accumulate without limit. Each discovery of science therefore adds…](https://sms4smile.com/quotes/neil-degrasse-tyson/new-generations-of-humans-inherit-the-acquired-discoveries-of/) [Neil deGrasse Tyson](https://sms4smile.com/quotes/author/neil-degrasse-tyson/) > [The discovery that heartbreak is indeed heartbreaking consoles us about our humanity.](https://sms4smile.com/quotes/lionel-shriver/the-discovery-that-heartbreak-is-indeed-heartbreaking-consoles-us/) [Lionel Shriver](https://sms4smile.com/quotes/author/lionel-shriver/) > [ “\[W\]e must learn to accommodate ourselves to the discovery that some of those cunningly-fashioned instruments called human souls have only a very limited range… ](https://sms4smile.com/quotes/george-eliot/w-e-must-learn-to-accommodate-ourselves-to-the-discovery-that-some-of/) [George Eliot](https://sms4smile.com/quotes/author/george-eliot/) > [We cannot predict the new forces, powers, and discoveries that will be disclosed to us when we reach the other planets and set up…](https://sms4smile.com/quotes/arthur-c-clarke/we-cannot-predict-the-new-forces-powers-and-discoveries-that-will-be/) [Arthur C. Clarke](https://sms4smile.com/quotes/author/arthur-c-clarke/) > [ That has been another interesting discovery: that basically a city \[Lagos\] could recover from a really deep, deep, deep pit. ](https://sms4smile.com/quotes/rem-koolhaas/that-has-been-another-interesting-discovery-that-basically-a-city/) [Rem Koolhaas](https://sms4smile.com/quotes/author/rem-koolhaas/) > [Every fact of science was once Damned. Every invention was considered impossible. Every discovery was a nervous shock to some orthodoxy. Every artistic innovation…](https://sms4smile.com/quotes/robert-anton-wilson/every-fact-of-science-was-once-damned-every-invention-was-considered/) [Robert Anton Wilson](https://sms4smile.com/quotes/author/robert-anton-wilson/) > [When we look at the love of Christ, we make a wonderful discovery. Love is more a decision than an emotion! Christ-like love applauds…](https://sms4smile.com/quotes/max-lucado/when-we-look-at-the-love-of-christ-we-make-a-wonderful-discovery-love/) [Max Lucado](https://sms4smile.com/quotes/author/max-lucado/) > [Discovery is the ability to be puzzled by simple things. Noam Chomsky](https://sms4smile.com/quotes/noam-chomsky/discovery-is-the-ability-to-be-puzzled-by-simple-things-noam-chomsky/) [Noam Chomsky](https://sms4smile.com/quotes/author/noam-chomsky/) > [“In December of 2007 human bones including skulls, which have been radiocarbon dated back to between 1304 and 1424, were found in a museum…](https://sms4smile.com/quotes/captain-hank-bracker-seawater-one/in-december-of-2007-human-bones-including-skulls-which-have-been/) Captain Hank Bracker, "Seawater One > [The European talks of progress because by the aid of a few scientific discoveries he has established a society which has mistaken comfort for…](https://sms4smile.com/quotes/benjamin-disraeli/the-european-talks-of-progress-because-by-the-aid-of-a-few-scientific/) [Benjamin Disraeli](https://sms4smile.com/quotes/author/benjamin-disraeli/) > [Education is a progressive discovery of our own ignorance.](https://sms4smile.com/quotes/will-durant/education-is-a-progressive-discovery-of-our-own-ignorance/) [Will Durant](https://sms4smile.com/quotes/author/will-durant/) > [The characters in my novels are my own unrealized possibilities. 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