Hippocrates of Chios - Biography

Hippocrates of Chios was a mathematician and astronomer in Ancient Greece, he lived between 470 BCE and 410 BCE. As the custom was, ‘Chios’ indicates the place of his birth, in the same way as ‘da Vinci’ simply meant that Leonardo was from Vinci. Born on the isle of Chios, Hippocrates began as a merchant, however after some incident he traveled to Athens, where he became a mathematician.

Hippocrates was not a novice of mathematics upon his arrival in Athens. He had, it is suspected at least, been the student of Oenopides (of Chios), a mathematician and astronomer. Moreover, in Hippocrates’ mathematical work there is evidence of Pythagorean influence. This claim is evidenced by the geographical proximity between Chios and Samos, which was the center of Pythagorean thought. Hippocrates has often been described as a ‘para-Pythogorean’. Hippocrates’ major accomplishment was the writing of Stoichia, i.e. The Elements. This work was the first systematically organized textbook on geometry. It contained the basic theorems of mathematics, and allowed, in principle at least, the entire ancient world to work on the basis of a common framework of basic theorems, concepts and methods. Such an act is the basis for the existence of a common law, which itself is the condition for scientific progress, or the progress in any field whatsoever.

Over the course of the century following Hippocrates’ death four other mathematicians wrote their own versions of Elements. Although each new version improved the terminology and structure of the textbook, it was Euclid’s Elements, that proved to be the culmination of Ancient Greece’s geometric knowledge, and the text which remained the standard textbook of geometry for many centuries.

Of this founding work only a single fragment remains. The fragment deals with Hippocratic lunes, or the Lune of Hippocrates, which was part of a research project on the calculation of the area of a circle, referred to as the ‘quadrature of the circle’. The strategy consisted in dividing the circle into crescent-shaped parts, with the hypothesis that their area was calculable. To calculate the are of a circle would then require nothing more then the sum of the crescents’ areas. This thesis, or approach, of squaring the circle was not discredited until the late 19th century. Only in 1882 by Ferdinand von Lindemann prove that the factor pi (π) is transcendental. Hippocrates is credited with two further noteworthy contributions to mathematics. The first of which is his resolution of the problem of constructing a cube root. A problem which, along with the quadrature of the circle, was considered one of the three great problems of ancient mathematics. Hippocrates also invented the method of reduction, which involves the transformation of specific mathematical problems in to a more general form, which is easier to solve, and can then be automatically provide a solution to the original more specific problem. The ‘reductio ad absurdum’ argument has also been traced to Hippocrates. The argument’s primary form involves disproving a proposition by assuming its premises and following their logical implications until an absurd consequence is reached. A subspecies of this argument is proof by contradiction, that is, a proposition is proved by showing that it is impossible for it to be false.

Anselm of Caterbury’s ontological argument for the existence of God was one of the first prominent applications of reduction ad absurdum in modern philosophy. In ancient philosophy, similar arguments to reductio ad absusrdum are not well hidden in the dialogues of Plato.

Hippocrates’ adventures into astrology, despite being of secondary interest in comparison to mathematics and geometry, proved nonetheless prophetic. His attempts to explain the phenomena of comets and the Milky Way led him to the conclusion that both were optical illusions, resulting from the refraction of solar light and moisture, exhaled by putative planets near the stars and sun. Certainly, it is an exaggeration to claim that Hippocrates was aware of the philosophical implications of such a statement, but the conclusion that light rays originated in the subject’s eyes and not in the object, which is thereby just a subjective projection, does place Hippocrates’ reflections in the realm of ‘Speculative Philosophy’.