The Strangest Mathematician in History: Archimedes
Archimedes—a name synonymous with genius—is celebrated as one of the most brilliant mathematicians and inventors in history. From running naked through the streets shouting “Eureka!” to defending his city with ingenious war machines, Archimedes’ life is a tapestry of remarkable discoveries and eccentric tales. His contributions not only shaped the ancient world but also laid the foundation for modern science and mathematics. This article delves into the life, achievements, and legacy of this extraordinary figure.
The Eureka Moment
One of the most iconic stories about Archimedes involves the moment he discovered the principle of buoyancy. The tale begins with King Hieron II of Syracuse, who suspected that a goldsmith had adulterated his crown with silver. The king tasked Archimedes with determining the crown’s purity without damaging it.
The breakthrough came when Archimedes stepped into a full bathtub and observed water spilling over the edge. He realized that the volume of water displaced must be equal to the volume of the submerged object. Using this principle, he compared the crown’s displacement with that of a pure gold bar of the same weight. When the crown displaced more water, it revealed that it was not pure gold. This discovery not only solved the king’s dilemma but also provided the foundation for understanding buoyancy, revolutionizing fields ranging from shipbuilding to material science.
Early Life and Education
Born around 287 BCE in the prosperous Greek city-state of Syracuse, Archimedes was fortunate to live during a rare period of peace under King Hieron II’s reign. His insatiable curiosity led him to Alexandria, the intellectual hub of the Hellenistic world. There, he studied under the successors of Euclid and immersed himself in the wealth of knowledge housed in the Great Library.
Archimedes’ Mathematical Masterpieces
Among Archimedes’ many mathematical achievements, he considered his study of spheres and cylinders to be his greatest. He discovered that the volume of a sphere is two-thirds that of a cylinder that perfectly encloses it, and the same ratio applies to their surface areas. This finding was so significant to him that he requested it be engraved on his tombstone.
Archimedes also advanced the understanding of π (pi). Using inscribed and circumscribed polygons, he calculated that π lay between 3.1408 and 3.1429, an astonishingly accurate estimation given the tools of his time. This iterative approach laid the groundwork for modern numerical methods.
His playful side emerged in his “Cattle Problem,” a complex brain teaser that challenged mathematicians to calculate the number of cattle in Helios’ mythical herd under intricate constraints. It wasn’t fully solved until the advent of computers in the 20th century, underscoring its complexity.
Conquering Big Numbers
Archimedes’ fascination with large numbers led him to address the question of how many grains of sand it would take to fill the universe. Using a revolutionary system of “orders of magnitude,” he introduced a way to represent extremely large numbers. This innovation allowed him to estimate that 10^63 grains of sand could fill the known cosmos. While modern science reveals this figure to be vastly underestimated, the exercise demonstrated Archimedes’ ability to think on an astronomical scale.
The Palimpsest and Lost Works
Many of Archimedes’ works were nearly lost to history. Written on fragile papyrus, they deteriorated over time. In the 10th century, a Byzantine scribe transcribed seven treatises onto parchment. However, by the 13th century, the parchment was scraped clean and reused for a Christian prayer book. Known as the Archimedes Palimpsest, this manuscript was rediscovered in 1906. Advanced imaging techniques have since revealed hidden texts, including his treatise on the law of the lever, which explains how small forces can lift massive weights. This principle underpins countless engineering applications today.
Engineering Marvels and War Machines
Archimedes applied his mathematical genius to practical challenges, particularly during the Roman siege of Syracuse in 213 BCE. His inventions included a “claw” mechanism that lifted and capsized enemy ships and possibly reflective devices to disorient Roman sailors. These innovations were so effective that they inspired myths of Archimedes using mirrors to set ships aflame.
Despite his efforts, Syracuse fell in 212 BCE. Legend has it that Archimedes was killed by a Roman soldier while engrossed in a mathematical problem. His last words, “Do not disturb my circles,” reflect his unwavering dedication to his work.
Legacy
Archimedes’ discoveries laid the groundwork for countless advancements in science, mathematics, and engineering. His methods prefigured calculus, and his inventions influenced technologies that shaped civilizations. Today, his genius continues to inspire, reminding us of the boundless potential of the human mind.
