Bates graduated with a First in Mathematics from University of Manchester in the summer of 1949.[2] She was taken on as a research student by Alan Turing, and shared an office with him and Cicely Popplewell.[3] In 1950 Bates submitted an MSc thesis entitled "The mechanical solution of a problem in Church's Lambda calculus".[4] This thesis documents a successful attempt to carry out higher-order logical reasoning on the extremely primitive Manchester Mark I electronic computer.[3][2]
When the Manchester Mark I was commercialised by the local electronics firm Ferranti, Bates moved to work with them as a programmer. Whilst at Ferranti she composed several sections (some uncredited) of Vivian Bowdon's Faster Than Thought, a popular introduction to electronic computing.[2][5]
In 1952, Bates went to work on the FERUT, the Ferranti Mark I installed at the University of Toronto.[2] In 1955, Bates was pictured supervising the FERUT when it carried out the first automated remote access to a computer.[6][7]
In 1979, Bates was working as a 'futurist' at a US military think tank.[8]