Certainty Quote by Rene Descartes
“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.”
About This Quote
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.
![“[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable…” quote by Rene Descartes](https://sms4smile.com/quotes/img-quotes/588/ren-descartes-1376_able_about-pierre-de-fermat-it-cannot-be-deni_89929.jpg)
![“And what more am I? I look for aid to the imagination. [But how mistakenly!] I am not that assemblage of limbs we call the human body; I am not a subtle penetrating air distributed throughout all these members; I am not a wind, a fire, a vapor, a breath or anything at all that I can image. I am…” quote by René Descartes](https://sms4smile.com/quotes/img-quotes/207/ren-descartes-1376_human-body_and-what-more-am-i-i-look-for-aid-to-the_115493.jpg)
![“[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 in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.” quote by Roger Bacon](https://sms4smile.com/quotes/img-quotes/d13/roger-bacon-15067_able_i-f-in-other-sciences-we-should-arrive-a_24209.jpg)