The Enigma Machine: How Alan Turing Helped Break the Unbreakable Nazi Code

Especially Polish scientists who broke the Enigma first,and when the war was imminent gave their knowledge to the British team, without which it would be impossible to crack the Enigma completely. It annoys me that they are so rarely mentioned.

http://www.codesandciphers.org.uk/virtualbp/poles/poles.htm

Neither Rejewski nor Turing broke Enigma alone, to give either complete credit without crediting the other is a gross and false simplification. On the whole Turing's work was more significant and ultimately more fruitful but both deserve to be mentioned whenever the subject of breaking Enigma comes up, though others such as Henryk Zygalski and Dilly Knox probably deserve a bit of a mention too.

From what I remember from the excellent Turing's biography by Andrew Hodges, the Polish broke the first (pre-war) version of the Enigma and Turing broke a newer version (naval Enigma which gave away positions of U-boats)

I'm slightly confused by his description of:

"Oh, but it’s clever, you see, because the Enigma machine [...] translates ordinary messages into code through an ingenious method by which no letter in the code ever repeats, making it almost impossible to decode in the ordinary ways."

Since it used a standard alphabet of symbols, and messages >26 chars exist, that statement is wrong. I presume he actually means that plaintext symbols will not code consistently to the same ciphertext symbols (i.e. not a simple substitution cipher), due to the rotation of the rotors.

But it's also not entirely far from another very interesting property (and one which significantly aided in the breaking of the code), by which no plaintext symbol can ever map to itself (due to the reflector design)

You mean the two videos embedded in TFA?