In a small but soon-to-be-revered town in Southern Italy, 2,500 years ago, a group of men and women gathered, united by the proposition that the universe is, at its base, Numbers. They were called the Pythagoreans, and their society would last for a millennium while their mathematical discoveries will be part of every geometry textbook in every school for as long as there are humans to read them. At the centre of that tight-knit society were two people: Pythagoras himself, and a woman named Theano.
Theano was one of seventeen early women Pythagoreans mentioned by name in the historical record, and the only one about whom we have anything approaching definite to say, for between the foundational Pythagoreans and us lie a number of bedevilling filters and documentational chasms. Firstly, the cult of silence that formed a central part of Pythagorean practice meant that few of the early practitioners set their thoughts to paper. Secondly, the appropriation of Pythagoreanism by later Platonic philosophers who cavalierly recast its origin in their own image means that we have to tread carefully in separating Pythagorean thought as it has come down to us from its various Platonic encrustments. Thirdly, the fifth-century BCE breakup of the Pythagoreans into two rival camps (the Aphorists and Scientists) and their mutual intellectual decimation makes it difficult to determine the original belief system of that first generation of thinkers. And lastly, the catastrophic loss of ancient sources during the Christian Era has reduced the original texts of those rare early Pythagoreans, who did write down their thoughts, to lists of titles recalled in sources from centuries later.
With so many conspiring sources muddying the historical waters, it is a wonder we know anything at all of Pythagoras and his generation, but some basics seem assured. That women were welcome to practise Pythagorean philosophy and to attain some renown thereby is clear from the number of sources listing their names and works. The problem comes when we start speculating on the contents of their work for, to a Pythagorean, ‘philosophy’ meant a good deal more than it does to modern ears. An ancient philosopher pondered questions of ethics, metaphysics, natural science, rhetoric and mathematics as part of their calling, and a Pythagorean philosopher in particular was a mixture of mathematician, theologist and ethicist which is difficult to separate into its component parts.
Pythagoreans celebrating the Rising Sun, by Fyodor Bronnikov (1827-1902)
When Pythagoras journeyed through the Egyptian and Babylonian Empires seeking wisdom, he came in contact with principles of reincarnation, lifestyle and the sacredness of Number which he brought back to Greece and fashioned into an influential new philosophy that preached silence, lack of ostentation, a simple diet, the migration of the soul between bodies, the eternal recurrence of all things, and the basic numerical nature of the world. In devotion to this last point, the early Pythagoreans expanded the frontiers of Greek arithmetic and geometry, including work on triangular and polygonal numbers, the classification of odd and even numbers, the arithmetic, geometric and harmonic means, the nature of the irrational, and of course the Pythagorean Theorem.
Who among the Pythagoreans was responsible for which advances has been lost to time, and even the ascription of the Pythagorean Theorem to Pythagoras is more a matter of tradition than certainty. Theano comes down to us as the most eminent of the women Pythagoreans, but which mathematical areas she worked upon, it is at present impossible to say. But here is what we know …
Most sources say that Theano was the wife of Pythagoras and the daughter of Brontinus, but some hold that she was the wife of Brontinus and a gifted student of Pythagoras. The most detailed account, that of Iamblichos (c.245–c.325 CE) in his Vita Pythagorica, has her as Brontinus’s wife, but the fragmentary mentions of her in Eusebios of Caesaerea (fourth century), Theodoretos of Kyrrha (fifth century), and Timaios of Tauromenion (third century BCE) all have her as Pythagoras’s wife, while Diogenes Laertius (third century) says she could have been either man’s wife. Modern scholars are divided on the issue, with some maintaining that the confusion has arisen because there were in fact two people named Theano whose lives got conflated with the passage of time.
Those who say she was married to Pythagoras claim that, after his death, the Pythagoreans were held together by her and her children Telauges, Myia and Mnesarchos, thereby creating the first link of continuity that would allow Pythagoreanism to exist as a virtually secret society for years.
Lukianos of Samosata referred to her in the second century BCE as ‘the daughter of Pythagorean wisdom'. Areios Didymos, one century later, asserted that she was the ‘first Pythagorean woman to philosophise and write poetry’, while Censorinus wrote some 400 years after that, placing her authority next to that of Aristotle on a question of natal periods. Our first hint of what she might have written doesn’t emerge until Suda’s Lexikon of the tenth century CE, some 1500 years after her death. The titles he mentions as being written by Theano are Of Pythagoras; Of Virtue (for Hippodamos of Thurium); Apophthegmata of a Pythagorean; and Advice for Women.
Of the contents of the two Pythagorean volumes we can only speculate, but we do have three letters purported to have been written by Theano, two common anecdotes from her life, and three further letters of a more dubious provenance to get a sense perhaps of her style.
The three letters are missives of advice sent to friends, and thus contain no mathematics. What they do contain is a blunderbuss of Pythagorean life-counselling – reprimanding one friend for spoiling her children with luxuries when austerity and a love of the life of the mind are most likely to produce good children; advising another to treat her servants with kindness and consideration and avoid unnecessary luxury; and pushing a third to react with an air of calm to her husband’s infidelity because men are essentially short-sighted sexual fools from whom not much is to be expected.
The two anecdotes are repeated constantly in the sources, which is endlessly aggravating. ‘Hey, future generations, which would you rather have, accounts of the mathematical insights of the early Pythagorean women or this one story about Theano’s elbow? I can’t hear you, because you don’t exist yet, so I’m going to assume the elbow thing and go ahead and throw the rest of this stuff on the fire. You’re welcome.’
So, the elbow story.
Theano was walking along one day when her elbow came uncovered. Somebody commented that it was a beautiful elbow. She said, ‘Yes, but not a public one!’
That is the elbow story.
The other anecdote is a similar two-line exchange. Somebody asks Theano how long after sex it takes a woman to become pure. She supposedly answered, ‘With your husband, instantly, with somebody else, never.’
I have my doubts on those two – among the dubiously attributed letters by Theano and other women Pythagoreans there is an awful lot of, ‘A woman’s job is to please her husband,’ which doesn’t seem to jibe with the daring communal intellectual spirit of early Pythagoreanism, but which does jibe perfectly with the Christian Platonism tasked with transmitting the heritage of ancient Greece and which often transmuted it in the process.
At this far remove, with so few sources at our disposal, it is simply impossible to say what among the histories, whispers, letters, and anecdotes counts as the ‘real’ Theano. What is true is that, long ago, at the dawn of the Western intellectual tradition, a group of men and women gathered, spurred on by love of intellectual exchange, and the association that they formed was so compelling it stretched over centuries and millennia to prod us forward with its example. Here was Pythagoras, and there Theano, philosophers both, the heirs of Egypt and parents of us all.
FURTHER READING:
We are fortunate to have all the ancient fragments about Theano and the women Pythagoreans gathered in one easily obtainable source: Theano: Briefe einer antiken Philosophin. It is a Reclam edition, so it is very convenient for travel, and contains the original Greek and Latin next to the German translations. For more on the Pythagoreans and what we actually know about them, Penguin has a nice volume, Early Greek Philosophy, that includes sections on Pythagoras and the two schools emerging from him. On the mathematics side, Sir Thomas Heath’s classic 2 volume A History of Greek Mathematics (1921) is a through and through classic of mathematical history that belongs in every history of science collection.
This story is also one of the over one hundred tales of women mathematicians you'll find in my History of Women in Mathematics, from Pen and Sword Books!
This column was originally published as episode 136 of the Women In Science series, in 2018.
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