History of Mathematics Pythagoras and Theano

Some years ago, I wrote a biography of Hypatia of Alexandria, the first female mathematician of whose life and work we have a good body of reliable evidence.  (See my Hypatia of Alexandria: Mathematician and Martyr, Prometheus Press, 2007.)  But I kept coming across references to an earlier woman mathematician, Theano.  For example, Nicephorus Gregoras, a 14th Century Church historian, described a woman, whose mathematical ability he wished to praise, as "another Theano or another Hypatia".  I decided to see what I could learn of this other (earlier) female mathematician.  So in this column and my next I want to share what I did learn, to indicate the difficulties in discovering much more, and to use the opportunity to explore some interesting Mathematics along the way.
We learn that Theano was an associate (very possibly the wife) of a much better-known mathematician, Pythagoras, and in order to find out about Theano, we need first to learn of Pythagoras. Now Pythagoras himself, although his name is of course extremely familiar, is actually a rather shadowy figure. There is an accessible article on the Wikipedia website, and you will find another at