c.6th Century B.C.
According to tradition, Theano was the wife of Pythagoras. Some sources claim that she and her two daughters carried on the Pythagorean School after the death of Pythagoras and that she wrote treatises on mathematics, physics, medicine, and child psychology. McLemore writes that her most important work was the principle of the "Golden Mean." In addition, Damo (ca. 535-475 BC), the daughter of Pythagoras and Theano, is said to have published her father's treatises on geometry as well as treatises on the construction of a regular tetrahedron and the construction of a cube. But discerning what Theano actually did is extremely difficult. As stated in the article in the Biographical Dictionary of Women in Science,
That Theano continued to operate the school of Pythagoras after his death is often affirmed but not confirmed. Thus, it can only be stated that, according to tradition, Theano was a mathematician, a physician, and an administrator—someone who kept alive an important training ground for future mathematicians.
Michael Deakin has written an extensive article examining how much of the claim that Theano was the first woman to play an active role in mathematics can be supported by historical resources. He says, for example, that "The most we can say about the claim that she wrote a book on [the golden ratio], is that she may have done. It was the sort of thing she might have done, but there is absolutely no evidence whatsoever that she actually did."