Affair Quote by Edward Kasner
“When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.”
About This Quote
Source Book: Mathematics and the Imagination by Edward Kasner and James Newman, 1940
Extending a specific truth to all cases can be both illuminating and risky; mathematics advances by generalizing, but over‑generalization leads to paradoxes and setbacks.
In simple terms: Broad claims can be powerful but dangerous.
Key Takeaway
Generalize carefully, test limits.
Themes
mathematics
logic
progress
risk
Mood
thoughtful
cautious
Type
analytical
philosophical
When to use this quote
- theoretical research
- teaching
- model building
- policy analysis
- philosophical inquiry
Key Concepts
generalization
paradox
foundations
Questions to Reflect On
- How do you balance curiosity with rigor?
- When should a hypothesis be limited?
A Different Perspective
Broad generalizations may ignore exceptions, causing errors.
![“[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one…” quote by Anonymous](https://sms4smile.com/quotes/img-quotes/446/anonymous-1_algebra_mathematics-is-security-certainty-truth_1430754.jpg)
![“Puzzles are made of the things that the mathematician, no less than the child, plays with, and dreams and wonders about, for they are made of things and circumstances of the world he [or she] live in.” quote by Edward Kasner](https://sms4smile.com/quotes/img-quotes/014/edward-kasner-41808_children_puzzles-are-made-of-the-things-that-the_293115.jpg)
