Aristotle

Aristotle portrait
Aristotle

There was no other ancient thinker who held a greater influence over European medieval intellectual life more than Aristotle (384 – 322 BCE).  It’s easy to see why, giving his prolific writings and interests in a wide range of topics that included physics, cosmology, biology, zoology, geology, psychology, mathematics, logic, metaphysics, politics, ethics, justice, and rhetoric – to name a few.  Over 150 books are attested to be authored by Aristotle, although only 30 or so of his works survive to the modern day.

Aristotle was born in Stageria, Macedon, was orphaned at an early age and raised by his uncle.  At age 17 he went to Athens and joined Plato’s Academy where he spent 20 years studying and earning his reputation as one of Greek’s great philosophers.  After his time at The Academy he ended up in King Philip of Macedon’s court, where he tutored his 13 year old son, Alexander, who grew up to be Alexander The Great.  During his time at the Macedonian court Aristotle also tutored two future kings and successors to Alexander’s empire, Ptolemy and Cassander.

When Aristotle did not receive headship of the Academy in Athens due to political reasons, he started his own establishment around 335 BCE with encouragement from Alexander called The Lyceum.  It is during his time at The Lyceum, from around 335 BCE to 323 BCE, when he composed most of his works.  Aristotle was forced to leave The Lyceum and Athens again due to political reasons after Alexanders death.  He died shortly after by natural causes.

Aristotle’s impact and legacy in western philosophy is immense. He was one of the first great figures in the history of science, influencing scientific thought for well over a millennia. Some of Aristotle’s works were preserved through the fall of Rome.  They were well read in Byzantium and in the Islamic empire but were virtually forgotten in Western Europe. Then, in the 13th century, much of his work was reintroduced into Western Europe through the work of Thomas Aquinas and others, and a synthesis of Aristotelian philosophy and Christian theology held supreme for over three centuries.  This Aristotelian influence was not to last forever as the dawn of the scientific revolution burst onto the world scene in the 16th century and permanently changed how humans viewed themselves and their world.

Pythagoras

Pythagoras portrait
Pythagoras

One of the most famous mathematicians of the ancient world was Pythagoras of Samos (570 – 495 BCE).  Much mystery surrounds the early life of Pythagoras and it is sometimes difficult to separate fact from legend.  It is believed that around the age of nine, Pythagoras may have traveled to Miletos where he was taught by the famous Greek philosopher Thales and his pupil Anaximander. Later on, around 535 BCE, it is likely that he traveled to Egypt and Babylon where he was taught geometrical principles that laid the foundation for many of his theorems.

In about 518 BCE Pythagoras settled in Cronton, a Greek seaport in southern Italy, where he founded a school dedicated to studying mathematics.  The school provided a way of life for him and his followers that included rules on diet and behavior, but also placed a primacy on mathematics and numbers.  They believed that everything in the universe was related to numbers.  Therefore symmetries and sequences held deep meaning where they turned up in nature, including in the study of music.  Since Pythagoras traveled widely in the ancient world it likely that he incorporated many ideas of the Egyptians and Babylonians into his school’s philosophy.  Indeed, the school was part philosophy, part mysticism, but its influence was profound and was clearly a source of inspiration for future generations of Greek mathematicians and thinkers.

During his lifetime Pythagoras made several discoveries in mathematics.  The one which he is most famous for and bears his name is the Pythagorean Theorem.  It states that for any right sided triangle the square of the length of the hypotenuse is equal to the sum of the square of the length of the two legs.  He is also alleged to have been one of the first people to teach that the Earth was a sphere.  The exact details of his death are unclear but his school expanded rapidly after 500 BC preserving his philosophy, ideas, and legacy for future generations.