Archimedes
Life
The surviving works are more remarkable than the legends. Archimedes used exhaustion and mechanical reasoning to study spheres, cylinders, parabolic areas, and bounds for π; his results anticipate parts of later integration without being modern calculus. His work on floating bodies survives, while the bath, burning-mirror, and last-words stories come from much later accounts. The rediscovered Archimedes Palimpsest revealed more of how he reasoned.
Decisive moments
The mathematics of buoyancy and the “Eureka” tradition
SyracuseOn Floating Bodies preserves mathematical results about equilibrium in fluids. The crown, bath, and naked run are a famous story recorded later by Vitruvius.
Exhaustion — treating curves rigorously
He repeatedly inscribed and circumscribed figures to trap areas and volumes within bounds. The idea anticipates later integration, but it did not use modern definitions of infinitesimals or limits.
The fall of Syracuse — several versions of the end
Later sources agree that a Roman soldier killed him during the capture of Syracuse, but differ over what he was doing and what, if anything, he said.
If this person hadn't existed
This is a thought experiment about influence, not a verified historical fact.
Archimedes was not a necessary single cause of calculus. His rigorous examples nevertheless show how far ancient mathematics reached in problems of curved area and volume. Without the surviving texts, it would be much harder to see the depth of pre-Newtonian reasoning about such problems.
Key achievements1
Calculation of Circle Area
BC 250Calculated the area of a circle using the method of exhaustion, a forerunner of integration.
Places of activity
Syracuse
Mathematical research and inventions
Influence network
Beyond MathVoyage
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