At Vienna Olga was taught by Furtwängler, Hahn, Wirtinger, Menger, Helly and others, while she was a fellow student of logician, Kurt Gödel. She wrote her thesis, just as class field theory was being developed, on algebraic number fields. She was awarded a doctorate in 1930.
Hahn recommended Taussky to Richard Courant and, in 1931 she was appointed as assistant at Göttingen. Working with Wilhelm Magnus and Helmut Ulm, she edited the first volume of David Hilbert's complete works on number theory.
While in Göttingen she edited Artin's lectures in class field theory (1932), assisted Emmy Noether in her class field theory and Courant in his differential equations course.
In 1932-1933 Taussky tutored in Vienna, then she spent a year at Bryn Mawr before taking up a research fellowship from Girton College, Cambridge in 1935. Hardy helped her to obtain a teaching post in a London college in 1937 where she soon met Jack (John Todd). They were married the following year.
During World War II Olga and Jack moved from place to place. While teaching near Oxford she supervised Hanna Neumann's D.Phil. thesis on combinatorial group theory.
In 1947 Olga and Jack when to the USA and worked at the National Bureau of Standards' National Applied Mathematics Laboratory. Here she worked with computers and has been described as a
computer pioneer ... who provided significant contributions to solutions of problems associated with applications of computers.In 1957 Olga and Jack both accepted appointments at the California Institute of Technology. She wrote:-
After many years of work mostly with applied mathematics, I was in the beginning rather uncertain about the teaching. But again it was the students who came to my assistance [as in the college in London]. It was clear to them that I had much mathematics to give them and they forced it out of me.Olga's honours and work is described as follows:-
Olga Taussky-Todd was a distinguished and prolific mathematician who wrote about 300 papers. Throughout her life she received many honors and distinctions, most notably the Cross of Honor, the highest recognition of contributions given by her native Austria. Olga's best-known and most influential work was in the field of matrix theory, though she also made important contributions to number theory.