Archimedes Quote by Archimedes
“Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.”
About This Quote
Source Letter: Archimedes to Eratosthenes, c. 3rd century BC
Mechanical methods can reveal insights that later need geometric proof, easing the search for rigorous demonstration.
In simple terms: Mechanical insight precedes formal proof.
Key Takeaway
Use intuition to guide formal proof.
Themes
science
methodology
intuition
Mood
curious
analytical
Type
philosophical
inspirational
When to use this quote
- engineering design
- mathematical research
- problem solving
Key Concepts
heuristics
deduction
Questions to Reflect On
- How can you test intuitive results?
- When should you seek formal proof?
A Different Perspective
Intuition may mislead without verification.
![“Spoken of the young Archimedes: . . . [he] was as much enchanted by the rudiments of algebra as he would have been if I had given him an engine worked by steam, with a methylated spirit lamp to heat the boiler; more enchanted, perhaps for the engine would have got broken, and, remaining always…” quote by Archimedes](https://sms4smile.com/quotes/img-quotes/514/archimedes-18068_algebra_spoken-of-the-young-archimedes-he-was-as_2465351.jpg)
![“[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in…” quote by Thomas Little Heath](https://sms4smile.com/quotes/img-quotes/ecd/thomas-little-heath-79814_awe_the-works-of-archimedes-are-without-exce_1614140.jpg)
