Academy Quote by George Polya
“In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.”
About This Quote
Source Paper: Commentatio to the Russian Academy, 1752
Euler presented his polyhedron formula without a formal proof, using many examples instead.
In simple terms: Euler used examples, not proof.
Key Takeaway
Consider examples when proof is hard.
Themes
mathematics
logic
induction
Mood
analytical
curious
Type
educational
philosophical
When to use this quote
- teaching
- research
- problem solving
Key Concepts
Eulerian formula
polyhedra
proof methods
Questions to Reflect On
- When is an inductive approach insufficient?
- How to verify a theorem rigorously?
A Different Perspective
Reliance on examples can miss hidden exceptions.
![“Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever…” quote by George Polya](https://sms4smile.com/quotes/img-quotes/927/george-polya-10766_action_pedantry-and-mastery-are-opposite-attitu_112396.jpg)
