But in the present century, thanks in good part to the…
“But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Hilbert's influence shows that axioms are chosen for consistency and potential richness, not arbitrary truth.
In simple terms: Axioms must be consistent and interesting.
Key Takeaway
Choose axioms that lead to fruitful theory.
Themes
mathematics
foundations
logic
Mood
analytical
inquisitive
critical
Type
philosophical
educational
When to use this quote
- research design
- theory building
- educational curricula
- philosophical debate
Key Concepts
axiom selection
consistency
creativity
Questions to Reflect On
- What criteria should guide axiom choice?
- How do we test 'interestingness'?
A Different Perspective
Axioms may still be limited by human intuition and existing frameworks.