[7] During that time, she attended meetings of the so-called Vienna Circle, the group of philosophers and logicians developing the philosophy of logical positivism.

Taussky, like Olga Hahn-Neurath and Rose Rand, was one of the first women to join the group, which included Otto Neurath, Rudolf Carnap, and Kurt Gödel and which was strongly influenced by Ludwig Wittgenstein.

Later, she started to use matrices to analyze vibrations of airplanes during World War II, at the National Physical Laboratory in the United Kingdom.

She also supervised Caltech's first female Ph.D. in Math, Lorraine Foster, as well as Hanna Neumann, Philip J. Hanlon, and Charles Royal Johnson.

Taussky received the Ford Prize for an article on sum of squares published in 1970 in American Mathematical Monthly.

She was a Fellow of the AAAS, a Noether Lecturer and a recipient of the Austrian Cross of Honour for Science and Art, 1st class (1978).