In World War II, the Allies faced a dilemma. The German Enigma machine created encrypted messages, and the Germans changed the code every day. Even if a code was broken, that solution was only good for that one day's transmissions. But eventually, Bletchley Park cryptographers—most notably Alan Turing—did solve the puzzle, building a giant computer called the Bombe to calculate solutions. So what were the cracks in the Enigma code?

In this video, Numberphile digs into how the Enigma cipher worked, and initially how the daily codes were broken manually using guesswork, inference, and brute force. It's a fascinating exercise, relying on a few key bits of information: In the Enigma cipher, letters never become themselves when encrypted; the first transmissions of the day were often weather reports (this was a procedural flaw more than a technical one); and many messages ended with similar phrases (again, a procedural issue, but handy when looking at a large volume of encrypted text). By making some educated guesses—like guessing that the word "weather" or "Hitler" might appear—a skilled cryptographer could manually break an Enigma code.

But Turing's solution turned this manual exercise into a transcendent moment for computers. If you're unfamiliar with Enigma, watch this explainer first. Then tune in to the mathematical discussion below to understand how Turing's machine was able to break Enigma codes in under 20 minutes every day. Enjoy:

If you're not able to view video at the moment, this Open Culture article is a great text-based explanation.