Bill Tutte
The chemist who worked out the internal wiring of a German cipher machine without ever seeing one, or even a photograph of one.
William Thomas Tutte (1917–2002) read chemistry at Cambridge, switched to mathematics, and was recruited to Bletchley Park in 1941. He was put on Tunny, the teleprinter cipher used by the German high command, where the only usable material was a single 4,000-character message that a careless operator had sent twice on the same key setting in August 1941. Through the winter of 1941–42 Tutte wrote the key stream out on squared paper in rows of varying length, hunting for repeats.
A period of 41 fell out. From that one observation he derived, step by step, the entire logical structure of the Lorenz SZ40: twelve wheels, their sizes, how they stepped and how their outputs combined. Britain would not lay eyes on the machine until the war ended. Tutte's statistical method — the "1+2 break-in" — was far too slow by hand and had to be mechanised, which is the whole reason Heath Robinson and then Colossus were built. Afterwards he essentially founded matroid theory at Waterloo.