Archimedes

Born: 287 BCE
Died: 212 BCE
Title: Greatest Mathematician of Antiquity

The Precursor of Calculus Across Time

If Euclid was a theorist, Archimedes was an "applied mathematician" and engineer with extremely formidable intuition. His thinking was nearly 2000 years ahead of its time.

Core Contributions - Deep Analysis

Method of Exhaustion

This is the prototype of the "integral" concept in calculus. To calculate the area of a circle or π, he inscribed and circumscribed regular polygons around the circle (from hexagons all the way to 96-gons). He calculated that the value of π lies between $3\frac{10}{71}$ and $3\frac{1}{7}$.

He was essentially using countless tiny line segments to approximate curves, which is precisely the core idea of modern calculus.

Sphere and Cylinder

He proved that both the volume and surface area of a sphere are $\frac{2}{3}$ of its circumscribed cylinder. He was very proud of this and requested in his will that this figure be engraved on his tombstone.

Large Number Counting

In The Sand Reckoner, he created a method to calculate the number of sand grains needed to fill the universe, proving that numbers could be infinitely large and could be systematically represented.

Tragic End

When the Roman army breached the city of Syracuse, Archimedes was drawing geometric figures in the sand. When a Roman soldier stepped on his diagram, he shouted: "Do not disturb my circles!" (Noli turbare circulos meos!) and was immediately killed by the soldier.

Legacy

Archimedes demonstrated that mathematics can precisely describe nature and solve complex problems. His Method of Exhaustion was a precursor to integral calculus, and his work in mechanics and hydrostatics laid the foundation for physics. He is considered one of the greatest mathematicians and scientists of all time.