--- title: "Meaning & Key Takeaway of: Yet there have been and still are…" description: "\"“Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, w..." image: "https://sms4smile.com/quotes/i/95a/fyodor-dostoyevsky-94_dare-to-dream_yet-there-have-been-and-still-are-mathem_1780809.jpg" --- # Yet there have been and still are mathematicians and… ![“Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry. They even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet…” quote by Fyodor Dostoyevsky](https://sms4smile.com/quotes/i/95a/fyodor-dostoyevsky-94_dare-to-dream_yet-there-have-been-and-still-are-mathem_1780809.jpg) [Download](https://sms4smile.com/quotes/i/95a/fyodor-dostoyevsky-94_dare-to-dream_yet-there-have-been-and-still-are-mathem_1780809.jpg) [Open image](https://sms4smile.com/quotes/i/95a/fyodor-dostoyevsky-94_dare-to-dream_yet-there-have-been-and-still-are-mathem_1780809.jpg) > ““Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry. They even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity.”” [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Some thinkers question whether Euclidean geometry fully describes reality, imagining that parallel lines might intersect in an infinite realm. **In simple terms:** Questioning basic assumptions can reveal deeper possibilities. Key Takeaway Explore beyond conventional frameworks. Themes philosophy mathematics infinity Mood curious speculative Type philosophical inspirational When to use this quote - academic research - theoretical physics - creative problem solving Key Concepts metaphysics critical thinking Questions to Reflect On - What would a non‑Euclidean universe look like? - How does questioning fundamentals spark innovation? A Different Perspective Euclidean limits may be too restrictive. ★ ★ ★ ★ ★ No ratings yet [Dare to dream](https://sms4smile.com/quotes/about/dare-to-dream/) [Parallel lines](https://sms4smile.com/quotes/about/parallel-lines/) [Philosophy](https://sms4smile.com/quotes/about/philosophy/) ## Related quotes > [“And so will I here state just plainly and briefly that I accept God. 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We are in danger…](https://sms4smile.com/quotes/g-k-chesterton/we-are-on-the-road-to-producing-a-race-of-men-too-mentally-modest-to/) [G.K. Chesterton](https://sms4smile.com/quotes/author/g-k-chesterton/) > [“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as…](https://sms4smile.com/quotes/bernhard-riemann/it-is-well-known-that-geometry-presupposes-not-only-the-concept-of/) Bernhard Riemann > [ For other great mathematicians or philosophers, he \[Gauss\] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus. ](https://sms4smile.com/quotes/anonymous/for-other-great-mathematicians-or-philosophers-he-gauss-used-the/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [“The truth, he thought, has never been of any real value to any human being - it is a symbol for mathematicians and philosophers…](https://sms4smile.com/quotes/graham-greene/the-truth-he-thought-has-never-been-of-any-real-value-to-any-human/) [Graham Greene](https://sms4smile.com/quotes/author/graham-greene/) > [“For what is it you and I are trying to do now? What I'm trying to do is to attempt to explain to you…](https://sms4smile.com/quotes/fyodor-dostoyevsky/for-what-is-it-you-and-i-are-trying-to-do-now-what-i-m-trying-to-do/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [ I was there when Abbe Georges Lemaître first proposed this \[Big Bang\] theory. ... There is no rational reason to doubt that the universe… ](https://sms4smile.com/quotes/hannes-alfven/i-was-there-when-abbe-georges-lema-tre-first-proposed-this-big-bang/) [Hannes Alfven](https://sms4smile.com/quotes/author/hannes-alfven/) > [“When we doubt, we learn to accept that we may not ever know. When we question, we learn to accept that there may be…](https://sms4smile.com/quotes/marya-hornbacher/when-we-doubt-we-learn-to-accept-that-we-may-not-ever-know-when-we/) [Marya Hornbacher](https://sms4smile.com/quotes/author/marya-hornbacher/) > [There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only myth that attempts to…](https://sms4smile.com/quotes/hannes-alfven/there-is-no-rational-reason-to-doubt-that-the-universe-has-existed/) [Hannes Alfven](https://sms4smile.com/quotes/author/hannes-alfven/) > [“Whether or not it is clear to you, no doubt the universe is unfolding as it should.”](https://sms4smile.com/quotes/max-ehrmann/whether-or-not-it-is-clear-to-you-no-doubt-the-universe-is-unfolding/) [Max Ehrmann](https://sms4smile.com/quotes/author/max-ehrmann/) > [Whether of not it is clear to you, no doubt the universe is unfolding as it should...](https://sms4smile.com/quotes/max-ehrmann/whether-of-not-it-is-clear-to-you-no-doubt-the-universe-is-unfolding/) [Max Ehrmann](https://sms4smile.com/quotes/author/max-ehrmann/) > [“The best description of this book is found within the title. The full title of this book is: "This is the story my great-grandfather…](https://sms4smile.com/quotes/jarod-kintz/the-best-description-of-this-book-is-found-within-the-title-the-full/) [Jarod Kintz](https://sms4smile.com/quotes/author/jarod-kintz/) > [“Our lives may be separate, but they run in the same direction, like parallel lines.”](https://sms4smile.com/quotes/milan-kundera/our-lives-may-be-separate-but-they-run-in-the-same-direction-like/) [Milan Kundera](https://sms4smile.com/quotes/author/milan-kundera/) ## More by Fyodor Dostoyevsky > [“Beauty is not only a terrible thing, it is also a mysterious thing. There God and the Devil strive for mastery, and the battleground…](https://sms4smile.com/quotes/fyodor-dostoyevsky/beauty-is-not-only-a-terrible-thing-it-is-also-a-mysterious-thing/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“Listen! I know it's not right to talk. Better to set an example, better to just start - I have already started - and…](https://sms4smile.com/quotes/fyodor-dostoyevsky/listen-i-know-it-s-not-right-to-talk-better-to-set-an-example-better/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“When all are undressed, one is somehow not ashamed, but when one's the only one undressed and everybody is looking, it's degrading,' he kept…](https://sms4smile.com/quotes/fyodor-dostoyevsky/when-all-are-undressed-one-is-somehow-not-ashamed-but-when-one-s-the/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“And what if there are only spiders there, or something of that sort”](https://sms4smile.com/quotes/fyodor-dostoyevsky/and-what-if-there-are-only-spiders-there-or-something-of-that-sort/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“The morning was so damp and misty”](https://sms4smile.com/quotes/fyodor-dostoyevsky/the-morning-was-so-damp-and-misty/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“I repeat, I repeat with emphasis: all "direct" persons and men of action are active just because they are stupid and limited. How explain…](https://sms4smile.com/quotes/fyodor-dostoyevsky/i-repeat-i-repeat-with-emphasis-all-direct-persons-and-men-of-action/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“He is a man of intelligence, but to act sensibly, intelligence is not enough.”](https://sms4smile.com/quotes/fyodor-dostoyevsky/he-is-a-man-of-intelligence-but-to-act-sensibly-intelligence-is-not/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [ “if \[God\] doesn't exist, man is the chief of the earth, of the universe. Magnificent! Only how is he going to be good without… ](https://sms4smile.com/quotes/fyodor-dostoyevsky/if-god-doesn-t-exist-man-is-the-chief-of-the-earth-of-the-universe/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“From an encounter in 1862... “Dickens told me,” Dostoyevsky recalled in a letter written years later, “that all the good, simple people in his…](https://sms4smile.com/quotes/fyodor-dostoyevsky/from-an-encounter-in-1862-dickens-told-me-dostoyevsky-recalled-in-a/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“It must be the top drawer," he reflected. "So she carries the keys in a pocket on the right. All in one bunch on…](https://sms4smile.com/quotes/fyodor-dostoyevsky/it-must-be-the-top-drawer-he-reflected-so-she-carries-the-keys-in-a/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“- You take evil for good. It's a passing crisis. It's the result of your illness, perhaps. - You do despise me! It's simply…](https://sms4smile.com/quotes/fyodor-dostoyevsky/you-take-evil-for-good-it-s-a-passing-crisis-it-s-the-result-of-your/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“Clouds overlaid the sky as with a shroud of mist, and everything looked sad, rainy, and threatening under a fine drizzle which was beating…](https://sms4smile.com/quotes/fyodor-dostoyevsky/clouds-overlaid-the-sky-as-with-a-shroud-of-mist-and-everything/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“People who can speak well, speak briefly.”](https://sms4smile.com/quotes/fyodor-dostoyevsky/people-who-can-speak-well-speak-briefly/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“I think I could stand anything, any suffering, only to be able to say and to repeat to myself every moment, 'I exist.' In…](https://sms4smile.com/quotes/fyodor-dostoyevsky/i-think-i-could-stand-anything-any-suffering-only-to-be-able-to-say/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) > [“There is no more ceaseless or tormenting care for man, as long as he remains free, than to find someone to bow down to…](https://sms4smile.com/quotes/fyodor-dostoyevsky/there-is-no-more-ceaseless-or-tormenting-care-for-man-as-long-as-he/) [Fyodor Dostoyevsky](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) [Explore all 1,078 Fyodor Dostoyevsky quotes ](https://sms4smile.com/quotes/author/fyodor-dostoyevsky/) ## More Dare to dream quotes > [Dare to dream! Never underestimate the Power of Our Dream!](https://sms4smile.com/quotes/anonymous/dare-to-dream-never-underestimate-the-power-of-our-dream/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [I do not believe we are all created equal. Physical and emotional differences, parental guidance, varying environments, being in the right place at the…](https://sms4smile.com/quotes/anonymous/i-do-not-believe-we-are-all-created-equal-physical-and-emotional/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Dare to dream... and when you dream, dream big.](https://sms4smile.com/quotes/henrietta-szold/dare-to-dream-and-when-you-dream-dream-big/) [Henrietta Szold](https://sms4smile.com/quotes/author/henrietta-szold/) > [Dare to dream, believe & never say never!](https://sms4smile.com/quotes/anonymous/dare-to-dream-believe-never-say-never/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [“It's better to dare to dream big and achieve half of your dreams than to dream small dreams and achieve all”](https://sms4smile.com/quotes/bernard-kelvin-clive/it-s-better-to-dare-to-dream-big-and-achieve-half-of-your-dreams-than/) [Bernard Kelvin Clive](https://sms4smile.com/quotes/author/bernard-kelvin-clive/) > [Somewhere over the rainbow, way up high In the land that I heard of once, once in a lullaby. Somewhere over the rainbow, skies…](https://sms4smile.com/quotes/eva-cassidy/somewhere-over-the-rainbow-way-up-high-in-the-land-that-i-heard-of/) [Eva Cassidy](https://sms4smile.com/quotes/author/eva-cassidy/) > [“Dare to dream, for in the daring there is defiance to live beyond your circumstances”](https://sms4smile.com/quotes/anonymous/dare-to-dream-for-in-the-daring-there-is-defiance-to-live-beyond-your/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [“Dare to realize your dreams. Dare to dream your reality. - Master Wei Priest of the K’un Lun”](https://sms4smile.com/quotes/joseph-j-bailey/dare-to-realize-your-dreams-dare-to-dream-your-reality-master-wei/) [Joseph J. Bailey](https://sms4smile.com/quotes/author/joseph-j-bailey/) > [In a world filled with hate, we must still dare to hope. In a world filled with anger, we must still dare to comfort.…](https://sms4smile.com/quotes/michael-jackson/in-a-world-filled-with-hate-we-must-still-dare-to-hope-in-a-world/) [Michael Jackson](https://sms4smile.com/quotes/author/michael-jackson/) > [I didn't dare to dream of making money. But now of course, I've made many thousands of dollars sharpening pencils.](https://sms4smile.com/quotes/david-rees/i-didn-t-dare-to-dream-of-making-money-but-now-of-course-i-ve-made/) [David Rees](https://sms4smile.com/quotes/author/david-rees/) > [“Perhaps the LORD will act in our behalf.” Don't play defense with your life. Play offense with your kids, your wife, your life. Don't…](https://sms4smile.com/quotes/mark-batterson/perhaps-the-lord-will-act-in-our-behalf-don-t-play-defense-with-your/) [Mark Batterson](https://sms4smile.com/quotes/author/mark-batterson/) > [Dare to dream and work to achieve...](https://sms4smile.com/quotes/anonymous/dare-to-dream-and-work-to-achieve/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Your victory has demonstrated that no person anywhere in the world should not dare to dream of wanting to change the world for a…](https://sms4smile.com/quotes/nelson-mandela/your-victory-has-demonstrated-that-no-person-anywhere-in-the-world/) [Nelson Mandela](https://sms4smile.com/quotes/author/nelson-mandela/) > [“It’s no coincidence that geniuses not only dare to dream of the impossible for their work, but do the same for their lives. They’re…](https://sms4smile.com/quotes/sean-patrick/it-s-no-coincidence-that-geniuses-not-only-dare-to-dream-of-the/) [Sean Patrick](https://sms4smile.com/quotes/author/sean-patrick/) > [“Dreams can come true. Dare to dream.”](https://sms4smile.com/quotes/lailah-gifty-akita/dreams-can-come-true-dare-to-dream/) [Lailah Gifty Akita](https://sms4smile.com/quotes/author/lailah-gifty-akita/) [Browse all 157 Dare to dream quotes ](https://sms4smile.com/quotes/about/dare-to-dream/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "“Yet there have been and still are mathematicians and philosophers who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry. 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