Argument Quote by George Polya
“Euclid 's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.”
About This Quote
Source Book: How to Solve It by George Polya, 1945
The exposition style moves step‑by‑step from known facts to conclusions, which is rigorous but can obscure the overall argument.
In simple terms: Detailed steps are rigorous but may hide the big picture.
Key Takeaway
Balance detail with clear overview.
Themes
methodology
clarity
logic
Mood
analytical
reflective
Type
educational
explanatory
When to use this quote
- Teaching mathematics
- writing proofs
- presenting research
- learning complex topics
Key Concepts
Pedagogy
expository technique
Questions to Reflect On
- How can you summarize the main point without losing rigor?
- When is a high‑level overview more helpful than stepwise detail?
A Different Perspective
Over‑emphasis on detail can overwhelm readers.
![“Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.” quote by Lucio Russo](https://sms4smile.com/quotes/img-quotes/66c/lucio-russo-43521_analysis_euclid-manages-to-obtain-a-rigorous-proo_2943863.jpg)
![“Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.” quote by Arthur Cayley](https://sms4smile.com/quotes/img-quotes/5dc/arthur-cayley-48537_euclid_euclid-avoids-it-the-treatment-of-the-in_1635536.jpg)
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