Gordon Welchman

William Gordon Welchman (15 June 1906 – 8 October 1985) was an English mathematician. During World War II, he worked at Britain's secret decryption centre at Bletchley Park, where he was one of the most important contributors. In 1948, after the war, he moved to the US and later worked on the design of military communications systems.

Gordon Welchman was born the youngest of three children in Fishponds, Bristol, to William Welchman (1866–1954) and Elizabeth Marshall Griffith. William was a Church of England priest who had been a missionary overseas before returning to England as a country vicar, eventually becoming archdeacon of Bristol. Elizabeth was the daughter of another priest, the Revd Edward Moule Griffith.

Welchman was educated at Marlborough College and then studied mathematics at Trinity College, Cambridge, from 1925 to 1928. In 1929, he became a research fellow in Mathematics at Sidney Sussex College, Cambridge. He became a fellow in 1932 and later dean of the College.

Just before World War II, Welchman was invited by Commander Alastair Denniston to join the Government Code and Cypher School in the event of war. GCCS established a centre ("Station X") for decryption and analysis of enemy (mostly German) encrypted messages at Bletchley Park (BP). Welchman was one of four early recruits to Bletchley, the others being Alan Turing, Hugh Alexander and Stuart Milner-Barry. They all made significant contributions at Bletchley and became known as "the wicked uncles". They were also the four signatories to a letter to Winston Churchill in October 1941, asking for more resources for the code-breaking work. Churchill responded with one of his "Action This Day" memoranda.

Much of Welchman's work at Bletchley was in "traffic analysis" of encrypted German communications. This was the collection and analysis of data about which enemy units sent and received messages, including where and when. Such metadata analysis can reveal a lot about enemy organisation, movements and activities, even when the content of the messages remains unknown. Welchman is credited with developing this technique.

However, Welchman's main contributions were to the process of breaking the German Enigma machine cipher (cryptanalysis of the Enigma). Welchman became head of Hut Six, the section at BP responsible for breaking German Army and Air Force Enigma ciphers.

Polish cryptanalysts had developed the bomba, an electromechanical device for finding the Enigma settings used by German operators; Turing improved the Polish design. Welchman invented the "Diagonal Board", an addition which made the British Bombe immensely more powerful.

The Diagonal Board exploited the self-reciprocity of the plugboard element of the Enigma; that is, if on the plugboard, letter B is Steckered (plugged) to letter G, then G is also Steckered to B. If 26 rows of 26 way connectors are stacked up, then any connection point can be referenced by its row letter and column letter. A physical piece of wire can now connect (row B element G) to (row G element B.) Each such wire runs diagonally across the board; thus its name.