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Olga Taussky Todd (born Taussky) was the first woman to obtain a PhD in mathematics in Wien. She was a student of K. Menger, H. Hahn and a fellow student of Goedel. See e.g. biography for more information.
Definitely leaving Wien after the Anschluss, Olga Taussky found a new home in the US, where she worked at the IAS in Princeton and emerited at CalTech. There has been a big conference in her honour by the US Association of Women in Mathematics - see this link for more info and more links.
Since Olga was born in 1906 (in Olmütz, a place in Bohemia, then Austria, now Czech Republic) , the new programme ( Call for Olga Taussky Pauli Fellowships ) starts for her 100th birthday, bringing excellent women in mathematics and related sciences to Wien, also under the name of Pauli - who would certainly have liked this idea.