Thales and Pythagoras: Ancient Greek Math Contributions

Introduction: Mathematics Arrives in Ancient Greece

In the 6th century BC, mathematics came to Greece and helped launch the next stage of mathematical evolution in the history of the West. Responsible for this movement were two people — first, Thales of Miletus; second, Pythagoras of Samos (Lewinter & Widulski, 2002). This paper explains the important contributions that these two mathematicians made during this period of ancient history and shows how they were received by the wider world.

While most people remember ancient Greece for introducing Socrates, Plato, and Aristotle to the world, the pre-Socratic mathematicians and philosophers Thales and Pythagoras actually helped set the stage for those later thinkers by advancing ideas and theorems that pushed the envelope of mathematical thought and philosophy. After all, it was Pythagoras and his school that coined the phrase "All is number" (NRich, 2011). This was, in fact, the motto of the Pythagorean School. Its members believed that the universe was explainable by numbers — that is, by mathematics.

Pythagoras and the Philosophy of Number

Where did Pythagoras get his ideas? At around the age of 20, he left Greece and traveled east to a place known as Miletus, in present-day Turkey. There he encountered an elder named Thales. Pythagoras learned a great deal about cosmology, geometry, music, astronomy, and philosophy — and at the center of all of it was the number. Mathematics explained so much of life and the world. However, in 525 BC, Pythagoras was taken prisoner and sent to Babylon. While there, he continued his studies and advanced his understanding of music and mathematics under the tutelage of the Babylonians (NRich, 2011).

Pythagoras was responsible for applying a qualitative nature to numbers, viewing some as perfect, others as incomplete, some as masculine, others as feminine, some as ugly, and some as beautiful (NRich, 2011). He was also the first to make distinctions between even and odd numbers, introduced the concept of prime numbers, and distinguished them from composite numbers. In Pythagoras's view, the number 10 was the greatest and most perfect number of all. He observed that 10 is the sum of the first four numbers, and that when these numbers — represented by dots — are arranged in a formation (one at the bottom, two atop one, three atop two, and four atop three), the resulting image is a perfect triangle.

The Pythagorean Theorem and Cosmological Discoveries

Pythagoras is best known for the Pythagorean theorem, a method he developed that proved the ancient Babylonian concept regarding how the sides of a triangle are related in terms of size (NRich, 2011). He also deduced that the earth was round and that the heavenly bodies were spherical and moved in circles. He returned to Greece and founded his school, which continued to focus on observing the natural world and explaining phenomena through mathematics rather than myth — which is why he was regarded as a philosopher. Aristotle viewed his teacher Thales as the first true philosopher of Greece, since Thales was the first to break with Greek mythology and attempt to explain the natural world by applying mathematical science (NRich, 2011).