There was an alliance between the Polish, French, and British to work on the Enigma problem. Rejewski made a simple assumption about the connection between the

There was an alliance between the Polish, French, and British to work on the Enigma problem. Rejewski made a simple assumption about the connection between the keyboard and the rotors that turned out to be correct. The British did not think to make this assumption. Why, who knows. The brains of the British operation was Dilly Knox, who was smart but not a mathematician. Rejewski was a mathematician. Rejewski was aided by a French spy, though. It's not clear how far he would have gone without that. It's neat to try and play this game of "who was first" but I think ultimately you have to give credit to the team: it was Poland, England, and France, and they each had some contribution in the early days of Enigma. However, critical to note, this work had been going on before Turing got involved with GC&CS. The alliance began around 1931, and Turing got involved with GC&CS in 1938. The entire signals problem was also not constrained at all to Enigma. Turing worked extensively on that problem, but there were other cipher systems, like Tunny, that Turing had a much more limited role in, which was mostly a crypotanalysis result from Tiltman (the "1+2 break") and engineering work by Flowers, to create an almost-entirely-electronic vacuum tube computer (which he personally funded because Bletchely thought it was impossible).