Mathematics in Ancient Greece

Mathematical Happenings between Ancient Egypt and the 11th Century: Thales and Pythagoras Inspire the Grecian World
In the 6th century, 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 will explain the important contributions that these two mathematicians made in this period of ancient history and show how they were received by the 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 to set the stage for the future philosophers by advancing the ideas and theorems that would push the envelope in terms of mathematical thought and philosophy. After all, it was Pythagoras and his school that coined the phrase, “All is number” (NRich, 2011). “All is number” was, in fact, the motto of the Pythagorean School. The members of this school believed that the universe was explainable by numbers—i.e., mathematics.
Where did Pythagoras get his ideas? At around the age of 20, he had 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’ view, the number 10 was the greatest and most perfect number of all. Why? He saw that 10 was the sum of the first four numbers and that when these numbers, represented by dots, were placed in a formation, one at the bottom, two atop one, three atop two, and four atop three, the resulting image was a perfect triangle.
Pythagoras is best known for the Pythagorean theorem, which was a method he developed that proved the ancient Babylonian concept regarding how parts of triangles are related in terms of size (NRich, 2011). Pythagoras 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 with the use of mathematics instead of myth—which is why he was considered a philosopher. Aristotle viewed his teacher Thales as the first true philosopher of Greece, as Thales was the first to break with Greek mythology and begin to try to explain the natural world by applying mathematical science (NRich, 2011).
Thales left his mark on Greece prior to Pythagoras coming into his own. Indeed, it was Thales who drew Pythagoras eastward to learn from the master. Thales’ theorem involved geometry and stated that three points on a circle will form a right angle. It may not seem that significant, but it actually was. It assisted architects in creating beautiful buildings and works of art by finding the center of a circle (Rusu, 2015). He showed that a circle is bisected by its diameter, that the angles at the base of an isosceles triangle are equal, and more. Thales was able to predict the solstice and the seasons, dividing them into a number of days that totaled 365 (Rusu, 2015)—which means today’s concept of the calendar really owes a lot to Thales.
It was Thales who attracted Pythagoras and together these two lit the ancient Grecian world aflame with a desire for ever more knowledge about the natural world, how to use mathematics to solve problems, how to apply geometry to art and architecture, and how math applied to music and the creation of beautiful melodies in a perfect rhythm and harmony. Pythagoras was ever grateful to Thales and Thales for his own part owed a lot to his Eastern brethren. Thales was the “father of proof” as Lewinter and Widulski (2002) point out, and Pythagoras was his child, giving to the world his own ideas—from number theory to music theory to proofs such as the angle of a sum of a triangle being 180 degrees (Lewinter & Widulski, 2002).
In conclusion, Thales and Pythagoras were the first two great mathematicians to readily identify how numbers and geometry played a part in the natural world and how they could be applied by people to interact with that world, embrace it, learn from it, and use the principles that the world reflected to produce great works of art and beauty to further enhance men’s minds and uplift their hearts. Thales set the stage for Pythagoras, who went on to learn even more deeply of the mathematical sciences, showing how number was pivotal in the creation of music. The later Greek philosophers, especially Aristotle, recognized the value of Thales in the West, and upheld him as one of the first Sages of Greece.
References
Lewinter, M. & Widulski, W. (2002). The saga of mathematics. Upper Saddle River,
NJ: Prentice-Hall.
NRich. (2011). All is number. Retrieved from https://nrich.maths.org/2572
Rusu, L. (2015). How Thales of Miletus changed the world. Retrieved from
https://www.zmescience.com/other/science-abc/thales-milet-changed-world/