Absurdity Quote by Augustus De Morgan
“The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).”
About This Quote
Source Book: Foundations of Algebra, 1850
Imaginary and negative numbers both signal contradictions when used as solutions, highlighting limits of real-number reasoning.
In simple terms: Imaginary/negative numbers show inconsistency.
Key Takeaway
Understand when standard math fails.
Themes
mathematics
logic
abstraction
paradoxes
Mood
intellectual
thought‑provoking
Type
philosophical
educational
When to use this quote
- engineering calculations
- financial modeling
- theoretical research
Key Concepts
complex numbers
proof by contradiction
conceptual limits
Questions to Reflect On
- When do we accept non‑real solutions?
- How can contradictions guide deeper insight?
A Different Perspective
Complex numbers are essential, not merely absurd.
![“That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral…” quote by Carl Friedrich Gauss](https://sms4smile.com/quotes/img-quotes/acb/carl-friedrich-gauss-9412_adapted_that-this-subject-of-imaginary-magnitude_3134596.jpg)
![“Imagine a person with a gift of ridicule [He might say] First that a negative quantity has no logarithm; secondly that a negative quantity has no square root; thirdly that the first non-existent is to the second as the circumference of a circle is to the diameter.” quote by Augustus De Morgan](https://sms4smile.com/quotes/img-quotes/17f/augustus-de-morgan-18916_circles_imagine-a-person-with-a-gift-of-ridicule_136734.jpg)
![“As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.” quote by Augustus De Morgan](https://sms4smile.com/quotes/img-quotes/ed4/augustus-de-morgan-18916_age_as-to-writing-another-book-on-geometry-t_584350.jpg)
