--- title: "Meaning & Key Takeaway of: Neither the true nor the false roots are…" description: "\"Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equatio..." image: "https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png" --- # Neither the true nor the false roots are always real… ![“Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equation as I have assigned, yet there is not always a definite quantity corresponding to each root we have imagined.” quote by Rene Descartes](https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png) [Download](https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png) [Open image](https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png) > “Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equation as I have assigned, yet there is not always a definite quantity corresponding to each root we have imagined.” [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Mathematical expressions can have solutions that are not physically observable, existing only as abstract concepts. **In simple terms:** Some equation solutions are abstract, not real. Key Takeaway Recognize abstract solutions as useful tools. Themes mathematics abstraction logic Mood thoughtful analytical Type educational philosophical When to use this quote - solving equations - modeling phenomena - teaching algebra Key Concepts complex numbers imaginary roots theory Questions to Reflect On - How do imaginary numbers aid problem solving? - When should we treat a solution as purely theoretical? A Different Perspective Abstract solutions may not correspond to tangible reality. ★ ★ ★ ★ ★ No ratings yet [Certainty](https://sms4smile.com/quotes/about/certainty/) [Logic](https://sms4smile.com/quotes/about/logic/) [Ontology](https://sms4smile.com/quotes/about/ontology/) [Reasoning](https://sms4smile.com/quotes/about/reasoning/) [Roots](https://sms4smile.com/quotes/about/roots/) [Uncertainty](https://sms4smile.com/quotes/about/uncertainty/) ## Related quotes > [“The way to be invisible - is to truly be imaginary. But since you cannot imagine yourself, you have to clone your imagination into…](https://sms4smile.com/quotes/will-advise/the-way-to-be-invisible-is-to-truly-be-imaginary-but-since-you-cannot/) Will Advise > [Much of what we see in the universe ... starts out as imaginary. Often you must imagine something before you can come to terms…](https://sms4smile.com/quotes/clifford-d-simak/much-of-what-we-see-in-the-universe-starts-out-as-imaginary-often-you/) [Clifford D. Simak](https://sms4smile.com/quotes/author/clifford-d-simak/) > [Although my knowledge grows more and more, nevertheless I do not for that reason believe that it can ever be actually infinite, since it…](https://sms4smile.com/quotes/ren-descartes/although-my-knowledge-grows-more-and-more-nevertheless-i-do-not-for/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [We call infinite that thing whose limits we have not perceived, and so by that word we do not signify what we understand about…](https://sms4smile.com/quotes/ren-descartes/we-call-infinite-that-thing-whose-limits-we-have-not-perceived-and-so/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [“Life is a complex with real and imaginary parts”](https://sms4smile.com/quotes/angela-suba-natarajan/life-is-a-complex-with-real-and-imaginary-parts/) [Angela Suba Natarajan](https://sms4smile.com/quotes/author/angela-suba-natarajan/) > [It’s strange how dreams get under your skin and give your heart a test for what’s real and what’s imaginary.](https://sms4smile.com/quotes/jason-mraz/it-s-strange-how-dreams-get-under-your-skin-and-give-your-heart-a/) [Jason Mraz](https://sms4smile.com/quotes/author/jason-mraz/) > [Art is real and imaginary, two worlds rolled into one - the fulfillment of the artist's insatiable soul.](https://sms4smile.com/quotes/edward-j-fraughton/art-is-real-and-imaginary-two-worlds-rolled-into-one-the-fulfillment/) [Edward J. Fraughton](https://sms4smile.com/quotes/author/edward-j-fraughton/) > [“The distinction between what is real and what is imaginary is not one that can be finally maintained...all existing things are, in an intelligible…](https://sms4smile.com/quotes/anonymous/the-distinction-between-what-is-real-and-what-is-imaginary-is-not-one-2/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [From the first time I saw you I knew I was going to have real and/or imaginary sex with you.](https://sms4smile.com/quotes/anonymous/from-the-first-time-i-saw-you-i-knew-i-was-going-to-have-real-and-or/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [There are two kinds of Arctic problems, the imaginary and the real. Of the two, the imaginary are the most real.](https://sms4smile.com/quotes/vilhjalmur-stefansson/there-are-two-kinds-of-arctic-problems-the-imaginary-and-the-real-of/) [Vilhjalmur Stefansson](https://sms4smile.com/quotes/author/vilhjalmur-stefansson/) > [“Up till a minute ago it felt so real, but now it seems imaginary. Just a few steps is all it takes for everything…](https://sms4smile.com/quotes/haruki-murakami/up-till-a-minute-ago-it-felt-so-real-but-now-it-seems-imaginary-just/) [Haruki Murakami](https://sms4smile.com/quotes/author/haruki-murakami/) > [“Books are like magic carpets, taking us to places real and imaginary that we never thought possible.”](https://sms4smile.com/quotes/anonymous/books-are-like-magic-carpets-taking-us-to-places-real-and-imaginary/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [I like to mix the real and the imaginary. Sometimes it is characters inspired by real people I know or know of. Sometimes it…](https://sms4smile.com/quotes/dana-spiotta/i-like-to-mix-the-real-and-the-imaginary-sometimes-it-is-characters/) [Dana Spiotta](https://sms4smile.com/quotes/author/dana-spiotta/) > [The distinction between what is real and what is imaginary is not one that can be finely maintained ... all existing thing are ... imaginary.](https://sms4smile.com/quotes/gregg-braden/the-distinction-between-what-is-real-and-what-is-imaginary-is-not-one/) [Gregg Braden](https://sms4smile.com/quotes/author/gregg-braden/) > [Some things can be both real and imaginary at the same time, . . . some lies can be true, . . . broken faith may be restored.](https://sms4smile.com/quotes/joanne-harris/some-things-can-be-both-real-and-imaginary-at-the-same-time-some-lies/) [Joanne Harris](https://sms4smile.com/quotes/author/joanne-harris/) ## More by Rene Descartes > [“My third maxim was to endeavour always to conquer myself rather than fortune, and change my desires rather than the order of the world,…](https://sms4smile.com/quotes/ren-descartes/my-third-maxim-was-to-endeavour-always-to-conquer-myself-rather-than/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [Your joy is your sorrow unmasked. And the self-same well from which your laughter rises was often-times filled with your tears.](https://sms4smile.com/quotes/ren-descartes/your-joy-is-your-sorrow-unmasked-and-the-self-same-well-from-which/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope…](https://sms4smile.com/quotes/ren-descartes/so-blind-is-the-curiosity-by-which-mortals-are-possessed-that-they/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [“For to be possessed of a vigorous mind is not enough; the prime requisite is rightly to apply it. The greatest minds, as they…](https://sms4smile.com/quotes/ren-descartes/for-to-be-possessed-of-a-vigorous-mind-is-not-enough-the-prime/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [“It is useful to know something of the manners of different nations, that we may be enabled to form a more correct judgment regarding…](https://sms4smile.com/quotes/ren-descartes/it-is-useful-to-know-something-of-the-manners-of-different-nations/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [A state is better governed which has few laws, and those laws strictly observed.](https://sms4smile.com/quotes/ren-descartes/a-state-is-better-governed-which-has-few-laws-and-those-laws-strictly/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [ \[About Pierre de Fermat\] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For… ](https://sms4smile.com/quotes/ren-descartes/about-pierre-de-fermat-it-cannot-be-denied-that-he-has-had-many/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [Science is practical philosophy.](https://sms4smile.com/quotes/ren-descartes/science-is-practical-philosophy/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [ “And what more am I? I look for aid to the imagination. \[But how mistakenly!\] I am not that assemblage of limbs we call… ](https://sms4smile.com/quotes/ren-descartes/and-what-more-am-i-i-look-for-aid-to-the-imagination-but-how/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [“And, in fine, of false sciences I thought I knew the worth sufficiently to escape being deceived by the professions of an alchemist, the…](https://sms4smile.com/quotes/ren-descartes/and-in-fine-of-false-sciences-i-thought-i-knew-the-worth-sufficiently/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [Nothing is more fairly distributed than common sense: no one thinks he needs more of it than he already has.](https://sms4smile.com/quotes/ren-descartes/nothing-is-more-fairly-distributed-than-common-sense-no-one-thinks-he/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [If I go for the alternative which is false, then obviously I shall be in error; if I take the other side, then it…](https://sms4smile.com/quotes/ren-descartes/if-i-go-for-the-alternative-which-is-false-then-obviously-i-shall-be/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [Everything is self-evident.](https://sms4smile.com/quotes/ren-descartes/everything-is-self-evident/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [It is only intelligence that is divided equally between people because everybody thinks he/she is enough wise](https://sms4smile.com/quotes/ren-descartes/it-is-only-intelligence-that-is-divided-equally-between-people/) [René Descartes](https://sms4smile.com/quotes/author/ren-descartes/) > [Even the mind depends so much on temperament and the disposition of one's bodily organs that, if it is possible to find a way…](https://sms4smile.com/quotes/ren-descartes/even-the-mind-depends-so-much-on-temperament-and-the-disposition-of/) [Rene Descartes](https://sms4smile.com/quotes/author/ren-descartes/) [Explore all 232 Rene Descartes quotes ](https://sms4smile.com/quotes/author/ren-descartes/) ## 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": "Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can always imagine as many roots for each equation as I have assigned, yet there is not always a definite quantity corresponding to each root we have imagined.", "creator": { "@type": "Person", "name": "Rene Descartes" }, "isPartOf": { "@id": "https://sms4smile.com/quotes/#website" }, "url": "https://sms4smile.com/quotes/ren-descartes/neither-the-true-nor-the-false-roots-are-always-real-sometimes-they/", "about": { "@type": "Thing", "name": "Certainty" }, "@id": "https://sms4smile.com/quotes/ren-descartes/neither-the-true-nor-the-false-roots-are-always-real-sometimes-they/#quotation", "image": { "@type": "ImageObject", "@id": "https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png", "contentUrl": "https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png", "url": "https://sms4smile.com/quotes/i/835/ren-descartes-1376_certainty_neither-the-true-nor-the-false-roots-are_156985.png", "width": 1080, "height": 1080, "caption": "“Neither the true nor the false roots are always real; sometimes they are imaginary; that is, while we can…” — Rene Descartes", "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": "Rene Descartes", "item": "https://sms4smile.com/quotes/author/ren-descartes/" }, { "@type": "ListItem", "position": 4, "name": "Neither the true nor the false...", "item": "https://sms4smile.com/quotes/ren-descartes/neither-the-true-nor-the-false-roots-are-always-real-sometimes-they/" } ], "@id": "https://sms4smile.com/quotes/ren-descartes/neither-the-true-nor-the-false-roots-are-always-real-sometimes-they/#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 } } ] } ```