... a result once generally accepted by mathematicians is…
“... a result once generally accepted by mathematicians is seldom retracted, and then only with great pangs. The Nature of Mathematics”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Mathematical truths are rarely overturned; when they are, it is a painful process for the community.
In simple terms: Math ideas rarely change; when they do, it hurts.
Key Takeaway
Accept change, but question assumptions.
Themes
science
mathematics
philosophy
progress
Mood
reflective
analytical
Type
philosophical
critical
When to use this quote
- academic research
- theoretical work
- educational curricula
Key Concepts
Paradigm shift
epistemic humility
Questions to Reflect On
- How do we balance respect for consensus with openness to revision?
- What mechanisms protect against entrenched errors?
A Different Perspective
Even accepted ideas can be wrong; overreliance on consensus may stall innovation.