THALES OF MILETUS

Mathematics as we know it today, with theorems and proofs, began with the great Greek mathematician Thales of Miletus (ca. 624–548 BCE). Miletus was among the first free city-states within the larger Greek empire, which spanned much of the eastern Mediterranean from Anatolia to the south of Italy and Egypt, including the islands in between. Lying on the coast of Anatolia, Miletus was one of the oldest and most prosperous Greek settlements of the time.

Thales is often called the first philosopher. He is also known for his famous saying “Know thyself,” which was even engraved on the stone entrance to the cave of the Oracle of Delphi, a sacred site where the Greeks sought counsel from their gods. Additionally, Thales was one of the Seven Sages of Greece, though according to the historian Plutarch, he surpassed the others. In his book on Solon, another of the Seven Sages, Plutarch says this about Thales: “He was apparently the only one of these whose wisdom stepped, in speculation, beyond the limits of practical utility: the rest acquired the reputation of wisdom in politics.”

 

Like other young Greeks interested in philosophy and culture, Thales headed for Egypt, and when he arrived there, “he spent his time with the priests,” as Plutarch tells us. The priests taught him about Egyptian religion and philosophy, but he was also given the opportunity to practice some ingenious mathematics and subsequently to propose the first known theorem in history while visiting the pyramids.

Thales’ other theorems include the statement that the base angles of an isosceles triangle are equal and that a circle is bisected by a diameter. He provided a key link between triangles and circles by showing that every triangle corresponds to a circumscribing circle that touches all three points of the triangle. Thus he demonstrated that only one circle passes through any three points that are not all on the same straight line, and that the diameter of such a circle corresponds to the circumscribed triangle’s hypotenuse. Additionally, he showed that an angle formed by the extension of two segments from the two endpoints of a diameter to any point on a semicircle is a right angle.

In addition to being the first “pure” mathematician, in the sense that he proposed and proved abstract theorems, Thales was also the first Greek astronomer. One day Thales was so engrossed in observing the stars that he moved forward a few steps without looking and fell into a well. “A clever and pretty maidservant from Thrace” who passed by and helped him out of the well chastised him for “being so eager to know what goes on in the heavens that he could not see what was straight in front of him, nay, at his very feet!”

As an astronomer, Thales was so competent that he could predict solar eclipses. In fact, he is credited with predicting the total solar eclipse that took place in his part of Greece on May 28, 585 BCE. Greek mathematics historian Sir Thomas Heath explained that Thales’ prediction was probably based on the fact that the Babylonians, who had been recording solar eclipses for centuries, knew that eclipses recur after a period of 223 new moons. Presumably, there had been a record of an eclipse in that area that had taken place 223 moons, or about eighteen years, earlier. This piece of information was probably transmitted to Thales through his intellectual connections in Egypt. He is also known to have studied the equinoxes and the solstices.