Hippocrates of Chios Biography

World of Mathematics on Hippocrates of Chios

Hippocrates of Chioswas a Greek merchant turned mathematician who wrote the first textbook on geometry. He is also noted for his efforts in elucidating the properties of circles and the quadrature of the lune. Despite turning to mathematics later in life, Hippocrates, who was also interested in astronomy, has been called the greatest mathematician of the fifth century B.C.

Hippocrates was born on the island of Chios but little else is known about his life. He is not to be confused with the more famous Hippocrates of Cos, who was born in the same century and is known as the father of medicine. According to information passed down by Aristotle, Proclus, Simplicius, and others, Hippocrates' first calling was as a merchant. However, unlike the famous Greek mathematician Thales, who made a fortune in commerce, Hippocrates' endeavors in trade led to his financial ruin.

It is speculated that Hippocrates was a thriving merchant until an unfortunate turn of events. According to one legend, he lost most of his wares when attacked by Athenian pirates near Byzantium. Another version points to dishonest customs men who threatened him with imprisonment and then bilked him of almost everything he owned. Hippocrates is said to have traveled to Athens to recoup his losses in a court of law. Required to stay in Athens for an extended period of time, Hippocrates began to attend lectures on mathematics and philosophy. He eventually became proficient enough in mathematics to open his own school. Although Aristotle characterized Hippocrates as a "competent geometer," he also--perhaps unfairly--said Hippocrates lost his fortune because he was "stupid and lacking in sense."

Writes First Account of Elementary Mathematics

Hippocrates is believed to have been greatly influenced by the Pythagorean school of mathematics, named after the famed Greek mathematician and philosopher Pythagoras. Whether he came under this influence in his home of Chios, which is close to Samos where Pythagoras was born, or in Athens is debatable. Hippocrates' concept of proportion and his astronomical theories are both related to the Pythagorean school of thought.

Fortunately, Hippocrates' misfortunes in commerce had a silver lining. Although the Pythagoreans believed it was taboo to earn money from their knowledge, Hippocrates was reportedly allowed to establish a school in Athens because of his financial troubles. Hippocrates went on to write the first mathematical textbook, called the Elements of Geometry. This work precedes the better known Elements written by Euclid more than a century later.

Although Hippocrates' book is lost, it had a profound influence on the mathematicians who followed him. Through his pioneering book, Hippocrates was the first to develop geometrical theorems from axioms and postulates in a scientifically precise and logical manner. His book may also have contained the first written accounts of Pythagorean mathematics since the Pythagoreans themselves did not believe in written texts. Although Euclid's book was far superior in its approach to geometry and went on to become the most famous textbook of all time, Euclid most certainly based some of his work on that of his predecessor, including much of what appears in Books I and II of his Elements.

Addresses Ancient Problems in Mathematics

One of the most famous problems faced by ancient Greek mathematicians was doubling the cube, also called the Delian Problem. According to one legend, the Delian Problem arose when a Greek concluded that a typhoid plague was a scourge sent by the god Apollo, who was displeased with his altar. Apollo ordered a second altar built in his honor that would be double in size but have the same cubical form as the first altar. Mistakenly, the Athenians thought the problem was solved simply by doubling each of the old altar's edges. As the legend goes, the plague continued and the problem of doubling the cube became a preeminent mathematical problem in ancient Greece.

In his attempts to solve the problem of doubling the cube, Hippocrates used the method of reduction. Although Plato developed a method of reduction for philosophical problems, Proclus credits Hippocrates as the first to use such an approach in geometry. Basically, this method operated by altering a difficult problem into a simpler form, solving this simpler form of the problem, and then attempting to apply the solution to the more difficult problem. In the case of the Delian Problem, Hippocrates proposed that a cube could be doubled by finding the two mean proportionals (geometric means) between two given lines or between a number and its double. While Hippocrates never completely solved the problem of doubling the cube, others followed up on his directive and went on to develop several solutions to this ancient geometric puzzle.

Besides his book, Hippocrates' most noteworthy contribution to ancient mathematics was his quadrature of the lune, a figure bounded by two crescent-shaped arcs of unequal radii. Hippocrates' interest in the quadrature of the lune probably stemmed from his attempt to solve another popular problem of ancient Greece, namely the squaring of the circle. Hippocrates' based his work on the theorem that the areas of two circles are the same as the ratio of the squares of their diameter, or radii. According to some accounts, Hippocrates falsely claimed that his work on the quadratures of lunes led him to discover how to square a circle.

Among Hippocrates' other contributions to mathematics were geometrical solutions to quadratic equations and an early method of integration. Through his theorems on circles, Hippocrates may have also introduced the indirect method of proof to mathematics, also known as the reductio ad absurdum. In essence, this approach first assumes the opposite of what is wanted to be proved is true. By proving the opposite to be false, the alternative is then considered true.

Develops Theories for Comets and the Galaxy

Like many of his contemporaries, Hippocrates was also enamored by the heavens. Chios had long been a center of astronomical studies, and Hippocrates is believed to have formed his own theories concerning comets and the galaxy. In keeping with the Pythagorean view of the heavens, Hippocrates believed that there was only one comet, which was a planet that appeared at long intervals. He added the belief that the comet's tail was a type of mirage caused by the comet taking up moisture when it neared the sun. Some ancient commentators also say Hippocrates created a similar theory to explain the appearance of the galaxy.

Since Hippocrates turned to math and astronomy rather later in his life, it is noteworthy that he apparently attained great renown in a relatively short period of time. Much of his work is known only through commentaries by later mathematicians and historians, like Simplicius, who based his work on the History of Geometry by Eudemus. As a result, certain claims pertaining to Hippocrates are difficult to substantiate, including that he was the first to use letters in geometric figures and that he established the technical meaning of the word "power," which is now used in algebra. However, his reputation as an excellent geometer who influenced the course of mathematical thought is well-founded. Nothing is known about his death.