Eudoxus of Cnidus

 

Lived c. 400 — c. 347 BC

Eudoxus made momentous advances in mathematics; he was the world’s greatest mathematician before Archimedes.

Eudoxus founded mathematical astronomy when he created the first mathematical model of the universe, expressing the movement of the heavens in the language of spherical geometry. In doing so he turned physical reality into something more abstract offering a new vantage point from which we could study the universe.

Eudoxus was responsible for the far-reaching theory of proportion expounded in Book V of Euclid’s Elements: Eudoxus gives the first rigorous definition of what today we call real numbers – the set that includes both rational and irrational numbers.

Eudoxus developed the method of exhaustion, giving future mathematicians such as Archimedes a potent tool to calculate areas and volumes. A forerunner of integral calculus, the method of exhaustion allowed Eudoxus to prove the formulas for cone and pyramid volumes. It is the basis of Book XII of Euclid’s Elements.

• Eudoxus learned mathematics in the school of Archytas, one of the greatest mathematicians of his day, in Tarentum, now in southern Italy.
• He learned the art of healing in the school of Philistion of Locri in Sicily.
• At age 23, he visited Athens to attend lectures by Plato. To save money he roomed in the port of Piraeus and made a 14 mile round trip on foot each day of his two month stay.
• Back in Cnidus he raised money from his friends to travel again – ancient crowdfunding! His friends recognized something in the young man that made him worthy of their trust and support.
• In about 381 BC, Eudoxus traveled to the city of Heliopolis in Egypt for 16 months. There he was taught astronomy by Egyptian priests in their observatories. Like them, he shaved off ALL of his hair, including his eyebrows.
• The next stage of his odyssey took Eudoxus to the shores of the sea of Marmaris and the city of Cyzicus, whose ruins lie in modern Turkey. He was now regarded as a wise teacher.
• From Cyzicus he traveled south to the city of Mylasa and joined the court of King Mausolus. The king ruled over the region of Caria, which included Eudoxus’s hometown. King Mausolus became eternally famous when the astounding mausoleum he built at Halicarnassus became one of the seven wonders of the ancient world – we get the word mausoleum from the king’s name. Eudoxus now founded his own school.
• In about 368 BC, aged somewhere in the region of 32-42, Eudoxus took his school to Athens.
• From Athens, Eudoxus’s final move took him home to Cnidus. The people of his hometown quickly voted him into office as one of the city’s governors.
• At some point in his life Eudoxus married, but we do not know his wife’s name. He fathered a son: Aristagoras, and three daughters: Actis, Philtis and Delphis.
• None of Eudoxus’s work survive. We know some of his achievements because of acknowledgements, citations, and references made by the likes of Aristotle, Archimedes, and Hipparchus.

The End

Eudoxus died at age 53, leaving a legacy of major progress in mathematics. He does not seem to have been born wealthy, but as a young man he was regarded so highly that his friends raised money to send him on travels in search of knowledge. In middle-age, he remained popular enough to be elected to serve as a governor when he returned to his hometown.

Aristotle was alive in the same era as Eudoxus, therefore what he said about his character is likely to be true: