Archimedes — "There are things which seem incredible to most men who have not studied mathemat…"
There are things which seem incredible to most men who have not studied mathematics.
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More from Archimedes
"I have discovered a way to measure the circumference of the Earth."
"The diameter of the Earth is greater than the diameter of the Moon and the diameter of the Sun is greater than the diameter of the Earth."
"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty."
"By a method of mechanical reasoning, I first discovered that the area of a segment of a parabola is four-thirds of the triangle with the same base and equal height."
"The cone is one third of the cylinder on the same base and of the same height."
Details
General reflection on the power of mathematics.
Date: Undated, but from accounts of his life and work.
GeneralVerification
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Understanding this quote
What it means
Mathematics reveals truths that defy ordinary intuition. Without training, people dismiss mathematical conclusions as impossible—that a lever could move the Earth, that pi could be precisely bounded, that a sphere's volume relates exactly to a cylinder. The quote defends mathematical reasoning against skepticism: counterintuitive results are not errors or boasts but proven facts. Mathematical literacy is the dividing line between what seems miraculous and what is demonstrably, rigorously true.
Relevance to Archimedes
Archimedes spent his life proving results that stunned contemporaries. He calculated pi's bounds, found the sphere-to-cylinder volume ratio, and claimed levers could move the Earth—bold assertions requiring mathematical proof to believe. His Sand Reckoner computed grains in the universe, which sounded absurd yet was rigorous. He likely wrote this reflecting on audiences who refused to accept his proofs without first grasping the underlying geometry that made each conclusion inevitable.
The era
In third-century BC Syracuse, mathematics was a rarefied discipline practiced by a small educated elite. Most people—farmers, soldiers, merchants—had no exposure to geometric proof or formal reasoning. Greek society exalted philosophy and mathematical order, yet most citizens encountered math only in basic commerce. The Hellenistic world was expanding scientific knowledge rapidly after Alexander, but widespread mathematical literacy remained impossible. What trained geometers proved as certain, ordinary observers could only experience as astonishing.
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