Alan Turing’s 1936 paper On Computable Numbers,introducing the Turing machinewas a landmark of twentieth-century thought. It settled a deep problem in the foundations of mathematicsand provided the principle of the post-war electronic computer. It also supplied a new approach to the philosophy of the mind. Influenced by his crucial codebreaking work in the Second World Warand by practical pioneering of the first electronic computersTuring argued that all the operations of the mind could be performed by computers. His thesismade famous by the wit and drama of the Turing Testis the cornerstone of modern Artificial Intelligence. Here Andrew Hodges gives a fresh and critical analysis of Turing’s developing thoughtrelating it to his extraordinary lifeand also to the more recent ideas of Roger Penrose.