Artifice Quote by Augustus De Morgan
“Common integration is only the memory of differentiation... The different artifices by which integration is effected, are changes, not from the known to the unknown, but from forms in which memory does not serve us to those in which it does.”
About This Quote
Source Treatise: Formal Logic, 1847
Differentiation and integration are inverse processes; integration reconstructs what differentiation removed, moving from known to unknown forms.
In simple terms: Integration undoes differentiation, turning known into unknown forms.
Key Takeaway
Use integration to explore beyond familiar patterns.
Themes
mathematics
logic
inverse processes
Mood
analytical
reflective
Type
educational
philosophical
When to use this quote
- solving equations
- learning new concepts
- research
- teaching
Key Concepts
calculus
memory
transformation
Questions to Reflect On
- How does integration expand understanding beyond differentiation?
- When does memory hinder new insights?
A Different Perspective
Integration may still rely on prior knowledge, limiting true novelty.
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![“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)
