  His first true home was at King's College, Cambridge University, noted for its progressive intellectual life centred on J. M. Keynes. Turing studied mathematics with increasing distinction and was elected a Fellow of the college in 1935. This appointment was followed by a remarkable and sudden début in an area where he was an unknown figure: that of mathematical logic. The paper “On Computable Numbers…” (Turing 1936–7) was his first and perhaps greatest triumph. It gave a definition of computation and an absolute limitation on what computation could achieve, which makes it the founding work of modern computer science. It led him to Princeton for more advanced work in logic and other branches of mathematics. He had the opportunity to remain in the United States, but chose to return to Britain in 1938, and was immediately recruited for the British communications war.