In his paper, “On Computable Numbers, with an Application to the Entscheidungsproblem” he introduced the concept of Turing Machines the first time and proved the limits of computation. Yet again, there was another proof made shortly before him by Alonzo Church. But he could convince the jury to publish his paper regardless. Turing Machines are to this day the central topic to study in theory of computation and formed the central concept of modern computers. For his PhD he left Great Britain and went to Princeton, continuing his studies in mathematics and additionally also cryptography. Afterwards, he returned to England and Kingston College. Next to a post-doctoral position he also started working part-time for the Government Code and Cypher School (GC&SC), the British Code breaking organization.
With the start of the second world war in 1939, he reported to Bletchley Park, the headquarters of the GC&SC during the war. Previously, Polish codebreakers had developed a machine (bomba kryptologiczna) which could decipher the German enigma code. After the Germans redesigned their enigma it became useless and Turing developed within weeks a more efficient machine, called the Bombe. It used a fraction of plain text to rule out all unlikely settings of the enigma wheels and left only a few combination to check. By the end of the war more than 200 Bombes were in use. During his time at Bletchley Park he was engaged to one of his fellow mathematicians, Joan Clarke. When admitting his homosexuality to her, she was not at all surprised, but it was Alan himself who decided to break the engagement and not marry her.
After the war he started designing the Automatic Computing Engine at the National Physical Laboratory, which would later become the first design of a stored-program computer. His colleagues doubted that they would be able to build a machine like this so they followed a way simpler approach. Eventually, they lost the race of building the first stored-program computer against the Royal Society Computing Machine Laboratory at Manchester University. He later accepted the deputy director position of that Laboratory and developed the first ever programming manual there. His programming system was used in Mark 1, the first marketable digital computer.