Number theorists consider prime numbers to be the most important numbers of all because they are the atoms of mathematics. Prime numbers are the numerical building blocks because all other numbers can...
Major General Howard Conner, without the Navajos, the marines would never have taken Iwo Jima.
It has been said that the First World War was the chemists’ war, because mustard gas and chlorine were employed for the first time, and that the Second World War was the physicists’ war, because the a...
In June 1991 he took the drastic step of asking a friend to post PGP on a Usenet bulletin board. PGP is just a piece of software, and so from the bulletin board it could be downloaded by anyone for fr...
If each battalion in the Pacific employed a pair of Native Americans as radio operators, secure communication could be guaranteed. This would be much simpler than a mechanical encryption device and mu...
French listening posts learned to recognize a radio operator’s fist. Once encrypted, a message is sent in Morse code, as a series of dots and dashes, and each operator can be identified by his pauses,...
By depriving Rejewski of the keys, Langer believed he was preparing him for the inevitable time when the keys would no longer be available. He knew that if war broke out it would be impossible for Sch...
Babbage’s successful cryptanalysis of the Vigenère cipher was probably achieved in 1854, soon after his spat with Thwaites, but his discovery went completely unrecognized because he never published it...
Al-Kindi's technique, known as frequency analysis, shows that it is unnecessary to check each of the billions of potential keys. Instead, it is possible to reveal the contents of a scrambled message s...
Turing knew of Babbage’s work, and the universal Turing machine can be seen as a reincarnation of Difference Engine No. 2. In fact, Turing had gone much further, and provided computing with a solid th...
Pythagoras, the teacher, paid his student three oboli for each lesson he attended
On a fatal day, in the holy season of Lent, Hypatia was torn from her chariot, stripped naked, dragged to the church, and inhumanely butchered by the hands of Peter the Reader and a troop of savage an...
It is the same with life. Some are influenced by the love of wealth while others are blindly led on by the mad fever for power and domination, but the finest type of man gives himself up to discoverin...
He took the messages to a local brewer, who wrapped them in a leather packet, which was then hidden inside a hollow bung used to seal a barrel of beer. The brewer would deliver the barrel to Chartley...
Even after Pythagoras’s death a member of the Brotherhood was drowned for breaking his oath—he publicly announced the discovery of a new regular solid, the dodecahedron, constructed from twelve regula...
Many shipwrecks and engineering disasters were blamed on faulty tables. These mathematical tables were calculated by hand, and the mistakes were simply the result of human error. This caused Babbage t...
Like Turing and the cryptanalysts at Bletchley Park, the Navajo were ignored for decades. Eventually, in 1968, the Navajo code was declassified, and the following year the code talkers held their firs...
It requires a great deal of time, effort and money to create a random key. The best random keys are created by harnessing natural physical processes, such as radioactivity, which is known to exhibit t...
Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a p...
Proof is what lies at the heart of maths, and is what marks it out from other sciences. Other sciences have hypotheses that are tested against experimental evidence until they fail, and are overtaken...