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
"The center of gravity of any triangle is the point of intersection of its medians."
"The spiral, by a continuous motion, generates an infinite number of lines."
"The surface of any sphere is four times its greatest circle."
"Any solid lighter than a fluid will, if placed in the fluid, be immersed in it to such an extent that the weight of the solid will be equal to the weight of the fluid displaced."
"My mind is not limited by the bounds of the earth."
Details
General reflection on the power of mathematics.
Date: Undated, but from accounts of his life and work.
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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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