Joan Elisabeth Lowther Clarke was born on 24 June 1917 at 45 Idmiston Rd, Dulwich and baptised at All Saints Church, Dulwich on 29 July. She attended Dulwich High School for Girls (now Rosemead) and won many prizes, including the Elsie Clarke prize for mathematics in 1934. She lived for over ten years at 193 Rosendale Rd and it was here that she developed her love of mathematics. In 1936 she  won a scholarship to study mathematics at Newnham College, Cambridge where she achieved a double first and was awarded the Philippa Fawcett prize and the Helen Gladstone scholarship for a fourth year of studies. She had to wait until 1948, when Cambridge finally allowed women to graduate, to receive her degree.

In 1939 she was a nursing auxiliary with the Red Cross and living with her parents at 193 Rosendale Road but the following year she joined Bletchley Park, where she was the only woman in Hut 8 working on the Naval Enigma Code. One of the three men working there was Alan Turing, who was a friend of her brother’s and whom she had met at university; for a brief period in 1941 she was engaged to him. 

After the war Joan was awarded an MBE. She worked for GCHQ where she met Lieutenant-Colonel John Kenneth Ronald Murray, a retired army officer. They married in 1952 and had no children. Joan retired from GCHQ in 1982 and died on 4 September 1996, aged 79.