Everybody firmly believes in it because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
About this quote
- What does it mean?
- Poincare notes that people believe in certain mathematical facts because mathematicians think they are observations and observers think they are theories.
- In plain terms
- People believe in math facts because mathematicians see them as observations and observers see them as theories.
- What can you take from it?
- Misunderstandings arise when experts and observers differ on the nature of knowledge.
Where it applies
Putting it to work
Questions to consider
- How do beliefs form around abstract ideas?
- Why do experts and others see things differently?
Another view
The quote assumes a specific dynamic between mathematicians and observers that may not always hold.
More from Henri Poincare
Toute definition implique un axiome, puisqu'elle affirme l'existence de l'objet defini. La definition ne sera donc justifiee, au point de vue purement logique,…
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Permalink to quote #18 C'est par la logique qu'on demontre, c'est par l'intuition qu'on invente.
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