They [the mathematicians of the Enlightenment] defined…
![“They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the…” quote by Tobias Dantzig](https://sms4smile.com/q/img-quotes/34e/tobias-dantzig-42181_argument_they-the-mathematicians-of-the-enlighten_1505184.jpg)
“They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the introduction of the infinitesimals... was but a natural reaction. Intuition had too long been held imprisoned by the severe rigor of the Greeks. Now it broke loose, and there were no Euclids to keep its romantic flight in check.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Enlightenment mathematicians relaxed strict rigor, allowing intuition to guide new concepts like infinitesimals, sparking creative breakthroughs.
In simple terms: Relaxed rules let intuition thrive.
Key Takeaway
Balance rigor with intuition.
Themes
science
philosophy
creativity
Mood
analytical
thoughtful
Type
theoretical
historical
When to use this quote
- research methodology
- educational reform
- theoretical exploration
- philosophical debate
Key Concepts
mathematical rigor
intuition
infinitesimals
Questions to Reflect On
- How to guard against intuition without rigor?
- What is the role of intuition in modern science?
A Different Perspective
Overreliance on intuition can lead to errors.