On foundations we believe in the reality of mathematics…
“On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Mathematicians view their work as real despite acknowledging its abstract nature, using formalism as a protective shield.
In simple terms: Math feels real but is abstract; formalism hides paradoxes.
Key Takeaway
Accept abstraction while valuing concrete intuition.
Themes
mathematics
philosophy
reality
Mood
thoughtful
inquisitive
Type
philosophical
reflective
When to use this quote
- research
- teaching
- theoretical work
- philosophical debate
Key Concepts
formalism
illusion
convenience
Questions to Reflect On
- What does “real” mean in abstract fields?
- How can paradoxes inspire deeper understanding?
A Different Perspective
Overreliance on formalism can stifle creative insight.