Pythagoras

Pythagoras an Ionian Greek philosopher and mathematician of the sixth century BC, remembered as the founder of a religious and philosophical movement that combined the study of number with the discipline of a way of life. Although he wrote nothing and his biography is obscured by legend, the Pythagorean school influenced mathematics, astronomy, music theory and the theology of later antiquity.

Life and the Pythagorean Community

Pythagoras was born on the island of Samos, probably around 570 BC, and according to ancient tradition travelled to Egypt and the Near East before settling in Croton, in southern Italy. There he founded a society that was at once a philosophical school, a religious brotherhood and a political faction. Members lived a common life governed by rules of diet, dress and silence.

The society at Croton exercised considerable political influence, and this eventually provoked hostility. A revolt against the Pythagoreans, the details of which are uncertain, dispersed the community and led to the death or exile of many members. The school nevertheless survived in other Italian cities and continued to develop its doctrines for several generations.

Pythagoras himself became a semi-legendary figure. He was credited with miracles, with a golden thigh, with the power of prophecy and with the recollection of former lives. Such stories make it impossible to reconstruct his biography with confidence, and scholars distinguish the historical teacher from the symbolic founder of the tradition.

Number as the Principle of Reality

The central Pythagorean doctrine is that number is the principle, or arche, of all things. The Pythagoreans observed that musical harmony depends on simple numerical ratios, that the movements of the heavenly bodies appear regular, and that many natural phenomena can be described in quantitative terms. From these observations they concluded that the world is ordered by number and can be understood through mathematics.

This insight gave rise to the first systematic attempt to explain reality in non-material terms. Instead of seeking a physical substance such as water or fire, the Pythagoreans proposed that the essence of things is numerical structure. The doctrine was immensely fruitful, and the mathematisation of nature that began with them remains a defining feature of Western science.

The Pythagoreans also developed a distinctive cosmology. They held that the earth is a sphere and, in some accounts, that it moves, and they introduced the idea of a central fire around which the heavenly bodies revolve. They connected the harmony of the cosmos with the harmony of musical intervals, speaking of the music of the spheres, a notion that influenced astronomy and poetry for centuries.

Mathematics, Music and Geometry

The school made lasting contributions to mathematics. The theorem that in a right-angled triangle the square on the hypotenuse equals the sum of the squares on the other two sides is associated with Pythagoras, though knowledge of the result may predate him. The discovery of irrational numbers, probably through the diagonal of the square, is also attributed to the Pythagorean tradition and is said to have troubled the community deeply.

In music theory the Pythagoreans showed that the consonant intervals correspond to simple ratios of whole numbers. The octave is 2 to 1, the fifth 3 to 2, the fourth 4 to 3. This discovery, that perceived beauty rests on mathematical proportion, was one of the great achievements of ancient thought and provided a model for the study of order in nature.

Geometry and number theory alike benefited from the Pythagorean habit of seeking general proofs rather than particular results. The idea that mathematical truths are necessary and eternal, independent of the world of the senses, shaped the epistemology of Plato and, through him, the whole tradition of rationalist philosophy. Mathematics became the paradigm of certain knowledge.

Religion and the Way of Life

Pythagoreanism was as much a religion as a science. The school taught the immortality and transmigration of souls, the kinship of all living things, and the need for purification of the soul through discipline and knowledge. The body was understood as a prison or tomb from which the soul must be released, and the practice of philosophy was a preparation for that release.

Members followed an ascetic regimen that included abstention from certain foods, notably beans, and rules about silence, self-examination and communal property. The purpose was to purify the soul and to attune it to the harmony of the cosmos. Novices were required to observe silence for a period and to accept the authority of the master before being admitted to the inner teachings.

The religious and the mathematical sides of Pythagoreanism were intimately connected in the belief that the purification of the soul is achieved through the contemplation of order and number. To understand the numerical harmony of the universe was, in this view, to become like it, and so to be freed from the cycle of birth. Philosophy, mathematics and salvation formed a single enterprise.

Influence on Later Thought

Pythagorean ideas entered the mainstream of Greek philosophy through Plato, who visited southern Italy and whose theory of forms and mathematical cosmology show clear Pythagorean influence. The Timaeus, with its mathematical account of the creation of the world, transmitted the doctrine to later antiquity, and the Neoplatonists developed it further into an elaborate metaphysical system.

In the Renaissance the rediscovery of Pythagorean number mysticism inspired thinkers such as Pico della Mirandola, Kepler and Newton, who sought mathematical order in the heavens and believed that God had created the world according to number, weight and measure. The idea that nature is written in the language of mathematics, so important to the scientific revolution, has Pythagorean roots.

Pythagoras remains a paradoxical figure, a mathematician who founded a religion and a religious teacher whose followers advanced the science of number. His name is attached to one of the most famous theorems in geometry and to a tradition that unites the study of the cosmos with the care of the soul. He is remembered as one of the founders of both Western mathematics and Western philosophy.

See also

• Plato
• Pre-Socratic philosophy
• Music of the spheres
• Irrational number