Archimedes and the Door of Science

Jeanne Bendick's biography presents the life and scientific contributions of Archimedes, the ancient Greek mathematician and inventor born in 287 B.C. in Syracuse, a city on the island of Sicily. Bendick traces his story from birth to death while explaining the scientific principles he discovered and the world that shaped his thinking.

Archimedes was the son of Phidias, an astronomer who studied the distances to the sun and moon, and a relative of Hiero II, the King of Syracuse. Bendick emphasizes that Archimedes had almost no prior scientific knowledge to build on beyond the geometrical principles of Euclid, the Greek mathematician, yet his ideas opened the door to modern science. His most important legacy, she argues, is a logical method of thinking about mathematics, proving or disproving ideas step by step.

Bendick devotes considerable attention to the Greek world in which Archimedes grew up. Greek culture prized curiosity, argument, and self-discipline. Boys received extensive education from age eight in geometry, literature, music, astronomy, and military tactics, while training physically at the palestra, an open area for wrestling, boxing, running, and swimming. Citizens were expected to vote, make laws, serve as jurors, and perform military service. Their leisure for learning depended on a society built on slavery: Most labor was performed by enslaved people. Even as a young man, Archimedes was so absorbed in study that he forgot to eat and had to be carried to the baths.

Archimedes traveled to Alexandria, Egypt, to study at the Museum, the first government-supported scientific institution in history. Alexandria, founded in 332 B.C. by Alexander the Great, housed the world's largest library. After Alexander's death, his general Ptolemy took control of Egypt and invited scholars to live and work at the Museum on paid salaries, freeing them to devote themselves entirely to ideas. The Museum produced three of the greatest mathematicians of the ancient world: Euclid, Archimedes, and his fellow student Apollonius. Archimedes studied under Conon of Samos, a mathematician and astronomer, and formed a lifelong friendship with Eratosthenes, who later became head of the library and accurately measured the circumference of the earth.

While in Egypt, Archimedes observed farmers carrying water by hand from the Nile River to their fields and designed the Archimedean screw, a wooden corkscrew-shaped device fitted inside a cylinder that raised water when turned by a handle. Still used more than two thousand years later for irrigation and drainage, this invention was also the ancestor of the propeller.

After returning to Syracuse, Archimedes spent his days drawing geometric diagrams in sand and conducting experiments. He and King Hiero carried on a running argument: Archimedes valued pure mathematical reasoning, while Hiero insisted that ideas were worthless until applied practically. Archimedes declared that if he had another earth on which to stand, he could move the earth itself. Hiero challenged him to move a massive three-masted ship that his dock workers could not budge. In a public demonstration, Archimedes used a system of ropes, wheels, and a helix (a large screw with a handle) to move the fully loaded ship with one hand. Bendick uses this episode to explain mechanics, the science of how forces act on objects, and notes that all mechanical devices are combinations of just two fundamental machines: levers and inclined planes.

The book recounts the famous story of King Hiero's crown: Hiero suspected his goldsmith of replacing some pure gold with cheaper silver. Archimedes obsessed over the problem until he was carried to the public baths, where he noticed water overflowing from an overfull tub as he stepped in. He realized that a submerged object displaces a volume of water equal to its own volume and leaped out shouting "Eureka!", Greek for "I have found it!" By submerging the crown and then a lump of pure gold of equal weight, he showed that the crown displaced more water, proving it contained silver. Because silver is less dense than gold, more was needed to match the weight, making the crown larger in volume.

This discovery led Archimedes to broader principles. He found that every substance has a unique density and defined specific gravity as the weight of a substance compared to the weight of the same volume of water. He formulated Archimedes' Principle: A body submerged partly or wholly in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. This principle explains why a steel ball sinks but a steel ship floats. Bendick notes that Archimedes' experiments founded the science of hydrostatics, the study of liquids at rest, and that no one added to its laws until the French scientist Blaise Pascal, roughly eighteen hundred years later.

Bendick also traces Archimedes' astronomical work. Ancient Greek astronomers had no telescopes, cameras, or computers, relying on tools like sundials, measuring rods, and water clocks. Archimedes estimated the sun to be at least 30 times larger than the moon and constructed an astronomical machine of concentric glass spheres turned by water power, demonstrating the motions of the sun, moon, and planets, including eclipses. This device was effectively the first planetarium.

Bendick discusses Archimedes' mathematical contributions. He measured a circle by enclosing it between two 96-sided polygons, establishing that pi, the ratio of circumference to diameter, lies between 3 10/71 and 3 1/7. In The Sand Reckoner, Archimedes demonstrated that numbers are infinite by calculating the number of grains of sand needed to fill the universe. His work on centers of gravity founded theoretical mechanics. His favorite discovery concerned the relationship between a sphere and a cylinder: When a sphere is enclosed in a cylinder whose height and base match the sphere's dimensions, the cylinder's volume and surface area are exactly one and a half times those of the sphere. He wanted this figure engraved on his tomb.

The book's final section concerns the siege of Syracuse. Under King Hiero, Syracuse had remained peaceful but was caught between Rome and Carthage, the two great powers fighting for control of the Mediterranean. Hiero persuaded Archimedes to design war machines, though Archimedes initially resisted, believing science should build people up rather than destroy them. After Hiero died in 215 B.C., political upheaval broke the city's alliance with Rome, and Rome sent forces under the general Marcellus. Drawing on the Roman historian Plutarch's account, Bendick describes how Archimedes' machines hurled massive stones, sank ships with iron claws, and repelled every assault. Marcellus, unable to breach the defenses, blockaded the city for three years. When the Syracusans grew careless during a festival, Roman soldiers crept over a poorly guarded wall.

Marcellus ordered his men not to harm Archimedes, but a soldier found the mathematician absorbed in a geometric diagram in the sand, unaware the city had fallen. When Archimedes refused to leave his work, the soldier killed him. Marcellus had the soldier executed, mourned Archimedes, and buried him with ceremony, placing on his tomb the figure of a sphere inscribed in a cylinder.

Bendick concludes by comparing the spread of Archimedes' ideas to ripples from a pebble dropped in a pond. He founded mechanics and hydrostatics, discovered buoyancy and specific gravity, established the laws of levers and pulleys, measured circles, and gave mathematicians a logical method of working. Some, she notes, consider him the greatest mathematician of all time.