Thales of Miletus

Thales of Miletus lived from 634 B.C. to 548 B.C. In his youth, he travelled extensively. He likely visited Egypt and Babylon, two ancient civilisations which were still in existence. Later on, he founded the Ionian School, the first of its kind in Greece. Among others, Pythagoras would attend this famous school.

We have some ideas about Thales' deeds, but we cannot be sure that everything written about him is true. It was reported that he predicted a solar eclipse in Greece in 585 B.C., but this may not have been possible because of the primitive state of astronomy in Greece at the time. It was also said that he made his fortune by buying all of the olive presses in Miletus and nearby Chios (see map at Antiquity Online), and at harvest time he rented out the olive presses at a high profit, thus making his fortune.

The later Greeks named Thales as the first of the seven wise men of Greece. He is the first person to have specific mathematical discoveries credited to him. These discoveries were:

• The diameter of a circle divides that circle into two parts of equal area.
• Two triangles are the same if they have two angles that are the same, and the lengths of the side between those two angles are the same.
• A triangle inscribed in a semicircle is a right triangle.
• An Isoceles triangle has two equal angles.

You might think that everyone knows that, for example, a circle's diameter divides it into two, and that these discoveries are all obvious. Indeed they are. However, Thales' great advancement was that he was the first person to realize that he could prove his discoveries by means of logical deductions. This advancement was unique in human history; while other civilizations, such as those in China, India, and Mesoamerica, developed advanced mathematics, none of them made much use of deductive proof, a technique that is important to modern mathematics.

Thales was also one of the first to look at the geometrical figures as abstractions rather than as real-world objects. While a line drawn in the sand may represent a line, it is not the line. A true "line" is an abstract concept of a geometrical figure that is infinitely long, infinitely thin, and perfectly straight, something that a line drawn in (for example) the sand could never be. These features of Thales' work are a step forward from all previous mathematical work, such as that of the Egyptians and Babylonians.