Theano (born c. 546 B.C.), the wife of the Greek mathematician and philosopher Pythagoras, ran the Pythagorean school in southern Italy in the late sixth century B.C. following her husband's death. She is credited with having written treatises on mathematics, physics, medicine, and child psychology. Her most important work is said to have been an elucidation of the principle of the Golden Mean.

Theano's husband, Pythagoras (c. 582--500 B.C.), was inspired one of the most influential sects in the ancient world. Best known for devising the Pythagorean Theorem---which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse---Pythagoras was considered the greatest scientist of antiquity by classical Greek scholars and is considered to have been the first mathematician. However, given that Pythagoras lived seven generations before Plato, most of the information about him comes from fairly late sources---a few as late as the third century A.D. Another problem is that some of these sources are of doubtful reliability. However, references to Pythagoras's ideas can be found in earlier writings, including those of Empedocles, Heraclitus, Herodotus, Plato, and Aristotle.

Influenced by Her Husband

Theano's husband is believed to have been born on the large island of Samos, just off the coast of Asia Minor. Pythagoras reportedly left the island when he was 18 and began traveling throughout the Mediterranean world to study with a variety of teachers, including Thales in Miletus. According to some accounts, he also spent time in Egypt, Babylon, Crete, and Sparta. He is believed to have moved to the Greek colony of Croton in southern Italy around 531 B.C., at the age of about fifty-six.

In Croton Pythagoras established a quasi-religious society dedicated to mathematical and philosophical speculations about the nature of the universe. He is reported to have taught purification of the spirit through study and proper diet and to have urged self-control and self-awareness through meditative techniques. However, because the Pythagorean community swore its members to secrecy very little about the society was made public during Pythagoras's lifetime.

There is, however, evidence that Pythagoras's academy accepted men and women on an equal basis. By some accounts there were at least 28 women teachers and students in the school, which is said to have eventually numbered some 300 adherents. Concerned with the quasi-religious, quasi-political study of mathematics and philosophy, the academy's religious ideas tended to be mystical, while its approach to natural philosophy was entirely rational.

Theano

Peter Gorman, writing in Pythagoras: A Life, cited Porphyry's account of Pythagoras's arrival in Croton. According to Porphyry, Pythagoras was at that time "tall," with "great charm and elegance in his voice." The mathematician reportedly spoke to the council of elders at Croton "with many fine words" and later addressed the school children and, finally, the women. Porphyry added: "One of the women is especially famous, Theano by name."

According to Gorman, Theano was the daughter of the Orphic disciple Brontinus. The Orphics were members of a religious group that centered its beliefs around the death and resurrection symbolism in the Egyptian deity Osiris. The Orphics further believed in reincarnation and an afterlife spent with the gods. Like the Orphics, the Pythagoreans owed many of their beliefs to Egyptian mythologies, so it is not surprising that Brontinus eventually became a disciple of Pythagoras. More significantly for the historical record, he would eventually become Pythagoras's father-in-law.

Brontinus's daughter---and Pythagoras's future wife---Theano also became Pythagoras's student. Pythagoras was reportedly Theano's senior by 36 years. According to Gorman, Theano would later bear Pythagoras a daughter named Damo and a son named Telauges. By other accounts, Pythagoras and Theano had three daughters, Damo, Myria, and Arignote, and two sons.

Theano is said to have eventually become a teacher of mathematics at the school in Croton. Legend has it that Pythagoras ran his school without discrimination based on gender. If true, this policy would have set him apart from his contemporaries, who granted no educational or political rights to women. In Pythagoras's time, women were usually considered property and relegated at best to the roles of housekeeper or spouse.

According to some of Pythagoras's earliest biographers, the philosopher and mathematician had other female students besides Theano. One source identifies a woman by the name of Aristoclea as a member of the early community. A third-century A.D. source lists 16 women who belonged to Pythagoras's school. Some historians have argued that the survival of these womens' names so long after Pythagoras's lifetime attests to the importance of women scholars in his school.

Death of Pythagoras

After Pythagoras's academy gained control of the local government of Croton, the local populace grew to resent the Pythagorean aristocracy and destroyed the school. The teachers and students were reportedly either killed or exiled. By some accounts Pythagoras himself was killed during this uprising.

Surviving the attack, Theano reportedly ran the dispersed Pythagorean School following her husband's death with the assistance of two of her daughters; in fact, one source says that Theano's daughter Damo was responsible for safeguarding her father's writings following his death. Theano has been credited with writing treatises on mathematics, physics, medicine, and child psychology, and there are reportedly references to her work in the writings of Athenaeus, Suidas, Diogenes Laertius, and Iamblichus.

Theano and her daughters acquired reputations as excellent physicians. According to the Pythagoreans, the human body is a miniature copy of the universe as a whole. In a debate with the physician Euryphon on the nature of fetal development, Theano and her daughters reportedly prevailed with their argument that the fetus is viable after the seventh month.

Offshoots of the Pythagorean academy continued for some 200 years after its founder's death. In the fifth century B.C. there were reportedly still several prominent women members of the Pythagorean school.

Theano's Writings

There were reportedly many individuals---both teachers and students---living communally at Pythagoras's school. Because all writings were published under Pythagoras's name, it is difficult to determine who was actually responsible for which work. However, given that Theano was a member of the Pythagorean academy, certain facts of her existence can be taken for granted.

There are no surviving written works by any of the Pythagoreans; all that is known of them comes from the writings of others, including Plato and Herodotus. Whenever one refers to the writings of Pythagoras or his students, one is in fact referencing a body of work that was done between approximately 585 B.C. and 400 B.C. The discoveries of the Pythagoreans were considered to be the common property of all members of the school, which was organized along the lines of a brotherhood or secret society.

According to one source, Theano's principal works included a Life of Pythagoras, a Cosmology, The Theorem of the Golden Mean, The Theory of Numbers, The Construction of the Universe, and a work titled On Virtue. None of the primary sources that remain, however, reveals anything of her personality.

Theano's most important work is said to have been the principle of the Golden Mean. Like the geometrical constant pi, the Golden Mean is an irrational number that shows up in many relationships in nature. Its decimal value is approximately 1.6180. In geometry, a "golden" rectangle is one whose sides are related by the Golden Mean ratio, for example 13:8. Both the ancient Greeks and Egyptians designed buildings and monuments with proportions based on the Golden Mean. It is now known that some growth patterns observed in nature occur in accordance with the Golden Mean, examples being the spirals in the nautilus shell and the ratio of clockwise to counterclockwise spirals in a sunflower.

In a treatise on the construction of the universe attributed to Theano, she reportedly argues that the universe consists of ten concentric spheres: the Sun, the Moon, Saturn, Jupiter, Mars, Venus, Mercury, Earth, Counter-Earth, and the stars. The Sun, Moon, Saturn, Jupiter, Mars, Venus, and Mercury move in orbit about a central fire. The stars are fixed and are not considered to move. In Theano's theory, the distances between the spheres and the central fire are in the same arithmetic proportion as the intervals in the musical scales.

The Pythagorean mathematical investigations into the relation between numerical ratios and musical intervals reportedly extended to other areas as well. According to one tradition Pythagoras could cure ailing psyches with his music.

In the Pythagorean school, matter was held to be discontinuous. According to Aristotle, the Pythagoreans believed numbers to be the ultimate component of material objects. Because astronomy and music are ultimately reduced to arithmetic and geometry in the Pythagorean framework, even those disciplines were considered to be mathematical subjects. Thus numbers for the Pythagoreans played much the same role that atoms do in modern scientific theory. Significantly, the Pythagorean cosmology, with later modifications by Plato, Eudoxus, and Aristotle, formed the basis of natural philosophy during the Middle Ages.

A Second Theano

The confusion surrounding Theano's life is compounded by the existence of a second Pythagorean woman of the same name who reportedly lived in the fourth century B.C. According to a tenth-century source known as the "Suda," this Theano was a Pythagorean woman from Metapontum, a town along the coast of southern Italy not far from Croton.

Based on this Theano's surviving writings, it would appear that women were still influential participants in the Pythagorean school in the fourth century. In fact, a literature directed to female readership had evolved by then. Some historians have speculated, however, that the writings attributed to this Theano were actually written by men, using the name of Pythagoras's wife as a pseudonym.

Further Reading

• Alic, Margaret, Hypatia's Heritage: A History of Women in Science from Antiquity to the Late Nineteenth Century, Women's Press, 1986.
• Gorman, Peter, Pythagoras: A Life, Routledge & Kegan Paul, 1979.
• Kline, Morris, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972.
• Olsen, Kirstin, Chronology of Women's History, Greenwood Press, 1994.
• Snyder, Jane McIntosh, The Woman and the Lyre: Woman Writers in Classical Greece and Rome, Southern Illinois University Press, 1989.