Nice to see that the article mentions the Polish Bombe upon which Turing's work was based. Even so, by now Turing's accomplishments are hardly unknown, and the work of the Poles probably deserves more attention (getting the Bombe from Poland to England as Poland fell to the allied Nazis and Soviets would probably make a good story too.
I have always been a huge fan of Alan Turing and could not respect him more, but keep in mind that he was part of a team. The story of Enigma is really a story about a whole spectrum of people, many of whom also played very significant roles and don't get the recognition they deserve.
When it comes to breaking the Enigma Machine, the guy who actually did is a polish mathematician named Marian Rejewski.<p>All credits to Alan Turing. But in all fairness its Marian Rejewski who did it.
For those interested in learning more, Simon Singh's "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography"[1] has a great chapter explaining in detail the creative breakthroughs that allowed Turing to break the Enigma machine when it was stumping pretty much everyone else at Bletchley Park.<p>--<p>[1] <a href="http://www.amazon.com/Code-Book/dp/0385495323" rel="nofollow">http://www.amazon.com/Code-Book/dp/0385495323</a>
This guy did a comprehensive job at digesting the material available, had a professional speaker do the audio book, ebook and so forth and gives it all away for free:<p><a href="http://www.bletchleypark.at" rel="nofollow">http://www.bletchleypark.at</a><p>the audio book is really cool and can be completed in one or two car rides home, loved the compact format. wish more folks would make these little historical snippets (other than wikipedia).
The first half of our initial Haskell module covered breaking the enigma machine, it was great fun and the lecturers made sure to give the back story in detail covering both the british and polish efforts (probably in an attempt to make the module appear 'cooler'). It was a great module and I have the upmost respect for Turing and the unsung Polish efforts made in breaking it.
Numberphile did two episodes on the Enigma machine, with some practical demonstration and a basic discussion of the mathematics involved.<p><a href="http://www.youtube.com/watch?v=G2_Q9FoD-oQ&feature=share&list=UUoxcjq-8xIDTYp3uz647V5A" rel="nofollow">http://www.youtube.com/watch?v=G2_Q9FoD-oQ&feature=share...</a>
Speaking of those who didn't get credit...<p>I couldn't find it during my lunch break, but I saw a documentary about another code breaker/breaking team at Blechley Park during the same period who worked on another German code (more secret than the Enigma that Turning worked on). One of the fellows made the first electronic computer as I recall. It was all kept secret and the code breaker unheralded until just recently.
I don't understand how the combinations of the 26 letters of the alphabet minus the 6 we don't care about (bc we only want 10 pairs) becomes 26!/6!<p>Why does the division make sense here?