Ancient Greek mathematics

Ancient Greek mathematics talks about the math ideas and books from Ancient Greece during classical and late antiquity. This was mostly from the 5th century BC to the 6th century AD. Greek math experts lived in cities around the Mediterranean Sea, from Anatolia to Italy and North Africa. They shared Greek culture and the Greek language.

One big difference between Greek math and older math was that Greeks saw math as a theory. They used deductive reasoning in proofs. The first full book on this was Euclid's Elements, written in the Hellenistic period. Famous math experts like Archimedes and Apollonius lived during this time too.

The work of ancient Greek math experts was copied and translated into Arabic and Latin. This helped math grow in the Islamic world and in Europe during the Middle Ages. In the Renaissance, books by Euclid, Archimedes, and others helped shape early modern math. Some problems from Greek math were only solved much later, leading to new kinds of math like non-Euclidean geometry.

Etymology

The Greek word mathēmatikē means "lesson." It comes from a verb that means "I learn." In ancient times, subjects like arithmetic, geometry, astronomy, and harmonics were special types of learning. These four subjects were later called the quadrivium. The mathematician Geminus of Rhodes split them into two groups: things we can think about (arithmetic and geometry) and things we can see or measure (astronomy and harmonics). He also added subjects like mechanics, optics, geodesy, and logistics. These are now part of physics or applied mathematics.

Origins

The start of Greek mathematics is still unknown. Early cultures in Greece, such as the Minoan and Mycenaean, had writing but no math books have been found. Before the Greeks, places like Babylon and Egypt used math mainly for measuring land and keeping records. When writing returned to Greece around the 7th century BC, new math ideas began to grow. We learn about early Greek math from later writers, like Plato and Aristotle, who talked about math from the 4th century BC.

Ancient Greeks often said that thinkers like Thales of Miletus and Pythagoras of Samos began Greek math, but we don’t have their writings to prove it. Real progress in writing about math began in the 5th century BC. For example, Hippocrates of Chios wrote the first known book called Elements, and tried to solve hard problems. Other math thinkers, such as Philolaus of Croton and Antiphon, also studied geometry and numbers. Later, thinkers like Plato helped share math ideas.

Hellenistic and early Roman period

Ancient Greek mathematics grew a lot during the Hellenistic and early Roman periods. After Alexander the Great's travels, Greek culture and language spread far, mixing with other traditions and creating new learning places. One of the most important was the Mouseion in Alexandria.

Great mathematicians like Euclid, Archimedes, Apollonius, and Ptolemy made many discoveries. Euclid put many math ideas together in his book Elements, which became very important for geometry. Archimedes found clever ways to measure shapes and even very large numbers. Trigonometry began to develop, helping astronomers learn more about the stars and planets.

Late antiquity

Mathematicians in the later Roman era were mostly known for writing about earlier work. Their writings helped save important ideas from books that were lost.

Diophantus, who lived around the 3rd century AD, wrote the Arithmetica. This book had 290 algebra problems. Only some of the book remains today. Pappus of Alexandria wrote the Collection. This was a review of earlier math in eight books. Some of these books still exist. He talked about topics like doubling the cube and squaring the circle.

Many mathematicians from this time wrote commentaries. These were explanations of earlier works. The commentaries often saved information from books that are now lost.

Reception and legacy

Many old math books from Ancient Greece are lost, but we still know about many Greek mathematicians because other people wrote about their work. Some mathematicians whose work we still know about include Euclid, Aristarchus of Samos, Archimedes, Apollonius of Perga, Hipparchus, Diophantus, Ptolemy, and Pappus of Alexandria.

Even though many of the original Greek math books are gone, we have copies from later times. Some of the oldest pieces of Greek math are from the 3rd century BC. These include parts of Euclid’s Elements found on pieces of pottery. Many of the Greek math books we have today were copied much later, during the Byzantine Empire and the Islamic Golden Age. These copies helped keep Greek math ideas alive for future generations.