James Sanborn once stated: “What struck me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant and pure sciences. I have found that the ends for which these pure sciences are used are less elegant.” Sanborn's comment couldn't be truer; During World War II cryptography was used by both the Allies and the Germans to send secret messages back and forth. It was then that elegant science created inelegant machines, such as: Enigma, Lorenz Cipher and the Japanese “Purple”. This drastic advance in cryptanalysis changed the way mathematicians and scientists viewed cryptosystems. During World War II, the German Nazis triggered a boom in cryptanalysis by creating a revolutionary invention, known as the Enigma. The Enigma machine worked by having someone input a message and then (using permutations) mixing it up with the use of three or five rotors. To encrypt a message for a three-rotor Enigma, they used the following equation: ; where P is the plugboard transform, U is the reflector, and L, M, and R are the left, center, and right rotors. This encrypted message was then sent to a recipient who had to decipher the message by recreating the exact rotor settings from the sender's machine. However, the code, which has 158 quintillion different settings, was eventually cracked by the Allies and used against the Nazi Germans as an advantage. And to show how confident the Germans were in this machine, until recently they still had no idea that the Allies had cracked their code. Another popular encryption machine during World War II was the Japanese 97 - shiki O-bun In-ji-ki known by the United States as “Purple”. The machine... was made of paper... and from there small parts of the encrypted messages could be obtained, and it was only a matter of time before the Allies were able to decipher the complete messages. In conclusion, we looked at three machines that helped shape cryptography not only during World War II, but helped shape science as a whole for years to come. We have seen progress, in mathematics, in both encryption and decryption, in plaintext and in ciphertext. Enigma, although it began as an advanced eight-rotor three-rotor device, "Purple" was a finished product of years of experimental cipher machines, and the Lorenz Cipher, got its start from Vernam. Technology builds on each other and failures turn into successes, and although World War II was a dark time for our planet, the advances we have made since that time are things we still use and can from continue learning to this day..