Pythagoras of Samos Biography

World of Mathematics on Pythagoras of Samos

Pythagoras' wide-ranging interests in mathematics, music, and astronomy mark him as a seminal figure in early western civilization's intellectual development. In the realm of mathematics, he developed the Pythagorean theorem and discovered irrational numbers. Pythagoras also founded a philosophical and religious school steeped in mysticism and secrecy which left its mark on poets, artists, scientists, and philosophers down to the 20th century.

Pythagoras was born about 580 B.C., probably in Samos, Greece, where he grew up. His father, Mnesarchus, may have been an engraver of seals or a merchant. Living in a prosperous seaport that was the center of learning and art during the Golden Age of Greece stimulated Pythagoras' thirst for knowledge. However, conflicting reports and the lack of written records leave much of his early life a matter of conjecture. Some reports indicate that he had at least two elder brothers, was a champion athlete, and a child prodigy.

Pythagoras is said to have studied in Greece under Creophilus and Pherecydes of Syros, and Thales of Miletus.In his early twenties, he traveled to Egypt, where he probably learned geometry and was initiated in Egyptian philosophy and science. Pythagoras then may have traveled to Babylon, or have been taken their as a prisoner of the Persians following their invasion of Egypt around 525 B.C. If Pythagoras did live in Babylon, he probably gained a more in-depth understanding of mathematics and geometry. For example, Babylonians had developed reciprocals and square roots for solving equations involved in mathematical astronomy.

While it is uncertain whether Pythagoras traveled further east, many see his philosophical foundations as being closely aligned to Eastern mysticism and philosophy. Pythagoras eventually returned to his home, only to find it ruled by the tyrant Polycrates. As a result, Pythagoras eventually moved to Croton in southern Italy, where he founded his famous school.

Establishes School of Philosophy and Science

Pythagoras established his school in Croton around 529 B.C. Focusing primarily on religion, philosophy, and mathematics, the school was known as a "homakoeion," meaning a gathering place for people to learn. The school's success can be attributed to the charismatic personality of Pythagoras. In a relatively short period of time, he established a large following, broken up into two groups--the "akousmatikoi," who primarily studied the philosophical teachings of Pythagoras, and the "mathematikoi," who focused on theoretical mathematics.

Students of Pythagoras' school, known as Pythagoreans, followed a number of strict rules. For instance, they were conscientious vegetarians, took a vow of silence for the first five years of their membership, and kept no written records. Liberal in nature, Pythagoras' school was open to everyone, including women, who it allowed to share in the instructing. Following Pythagoras' own belief in simplicity and disdain for worldly honors, Pythagoreans took no credit for their own work or discoveries, attributing all findings either to their master or the group.

Numbers were the very foundation of Pythagorean philosophy, which maintained that numbers were both mystical in nature and had a reality of their own outside of the human mind. Impressed by the ratios that existed in musical harmonies, astronomy, and geometrical shapes, the Pythagoreans developed a theory that all things, in essence, were numbers and related through numbers. Out of this belief, they developed certain representations for numbers: 1 was a point, 2 a line, 3 a surface, and 4 a solid. Moral qualities were also numbers, with 4 representing justice and 10 (known as the tetractys) representing the sum of all nature due to its being the sum of 1+2+3+4 (the point, line, plane, and solid).

While the Pythagoreans' mystical belief in numbers is largely ignored today, their belief that one could penetrate the secrets of the universe through numbers led them to conduct a careful study of mathematical theory, focusing on the principals of geometry.

Scientific Contributions in Math, Music, and Astronomy

The nonexistence of written records attributable to Pythagoras or his followers has made it difficult for historians to determine what contributions were made directly by Pythagoras himself. However, most historians agree that Pythagoras was likely responsible for several basic tenets in math and science today.

Although the Babylonians knew about the relationship between the legs of a right triangle and the hypotenuse centuries before the birth of Pythagoras, he was the first to provide a general geometric proof of this relationship. The theorem states that the square of the measure of the hypotenuse of a right triangle is equal to the sum of the squares of the two legs. Considering that deductive geometry was in its infancy, this theorem was remarkable for its time. Euclid, who Pythagoras strongly influenced, stated the theorem, which is called the Pythagorean theorem, in book one of his Elements.

The Pythagorean theorem also led to the discovery of irrational numbers, which is considered to be one of the greatest discoveries of mathematical antiquity. Pythagoras discovered that the hypotenuse of the isosceles right triangle with legs of unit length is equal to the square root of two, which cannot be accurately represented by a rational number (a number that can be expressed either as a whole number, integer, or fraction). The irrational number cannot be represented by any ratio of integers, and in its decimal form does not terminate and does not repeat a certain pattern. Interestingly, the discovery of irrational numbers led to the contradiction of many existing mathematical proofs and theorems. According to legend, the Pythagoreans viewed irrational numbers as symbolic of the unspeakable.

Pythagoras was also the first to discover the mathematical basis of music. For Pythagoras and his followers, music was more than entertainment; it was an integral part of their philosophy and religion. Music was also seen as having an almost mystical affect on humans in terms of soothing the psyche and the soul. Pythagoras found that strings of the lyre produced harmonious tones when the ratios of the lengths of the strings are whole numbers. As a result, Pythagoras discovered the numerical ratios which determine the concordant scale in music. This discovery strengthened the Pythagoreans' belief that all things are numbers and ordered by numbers. Perhaps the most famous outgrowth of this belief is Pythagoras' theory that the heavenly bodies in the cosmos are separated in regular intervals, like the law of harmony. As a result, Pythagoras believed in a vast universal or cosmic harmony (ratio), which led to his doctrine of the "Music of the Spheres."

In the realm of astronomy, Pythagoras was the first to declare the Earth spherical in nature. It is reported that he made this discovery when he noticed the round shadow thrown by the Earth on the moon during a lunar eclipse. Pythagoras also deduced that the sun, moon, and planets have movements of their own, that is, that they rotate on their own axes and orbit a central point. However, Pythagoras mistakenly identified this central point as Earth. Eventually, the Pythagoreans deduced that Earth orbited around another central point, but never identified this point as the sun. The Pythagoreans also correctly determined that the Earth's rotation around this "central point" took 24 hours.

The Later Years

In his own time and the first few centuries following his death, Pythagoras was revered by many, with some accounts of his deeds reaching mythic proportions (such as being able to walk on water). His influence can be found in such famous Greek scientists and philosophers as Euclid and Plato. However, Pythagoras was also viewed with disdain by some, primarily because of his philosophies (such as transmigration of the soul, or reincarnation), which resembled the philosophy of the Orient rather than the Greek philosophy of his day.

Although Pythagoras and his school prospered, their controversial philosophies and strong political influence created enemies. With the rise of the democratic party in southern Italy, Pythagoras and his students became the objects of persecution. The democrats considered the Pythagoreans as elitists who placed themselves above others and were also suspicious of their secret rites. This mistrust came to a head sometime between 500 B.C. and 510 B.C., resulting in the destruction of the Pythagorean school and campus. The exact fate of Pythagoras himself remains uncertain. According to some accounts, Pythagoras was killed during this attack. Other accounts indicate that he escaped and lived to be nearly 100 years old. In keeping with Pythagoras' mythic stature, he is also said to have ascended bodily into heaven.

Regardless of the fate of Pythagoras, his followers continued his teachings in other lands, eventually returning to Italy to reestablish the Pythagorean school in Tarentum. In terms of influence, the Pythagoreans outlasted all other philosophies of ancient Greece. They established a strong presence and/or influence both in Egypt and ancient Rome, where the Senate erected a statue in honor of Pythagoras as "the wisest and bravest of Greeks."