Hodges was born in London. Since the early 1970s, Hodges has worked on twistor theory, which is the approach to the problems of fundamental physics pioneered by Roger Penrose.
Hodges is best known as the author of Alan Turing: The Enigma, the story of the British computer pioneer and codebreaker Alan Turing. The book was chosen by Michael Holroyd as part of a list of 50 'essential' books (that were currently available in print) in The Guardian, 1 June 2002.
Hodges is also the author of works that popularize science and mathematics.
He is a Tutorial Fellow in mathematics at Wadham College, Oxford University. Having taught at Wadham since 1986, Hodges was elected a Fellow in 2007, and was appointed Dean from start of the 2011/2012 academic year.