Vigenère’s work culminated in his Traicté des Chiffres (A Treatise on Secret Writing), published in 1586. Ironically, this was the same year that Thomas Phelippes was breaking the cipher of Mary Queen...
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...
There exists no purer concentration of Americanism than among the First Americans. The Navajos were so eager to fight that some of them lied about their age, or gorged themselves on bunches of bananas...
The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is n...
The first known European book to describe the use of cryptography was written in the thirteenth century by the English Franciscan monk and polymath Roger Bacon. Epistle on the Secret Works of Art and...
The Last Theorem is at the heart of an intriguing saga of courage, skulduggery, cunning, and tragedy, involving all the greatest heroes of mathematics.
Stát, který věří, že není správné číst cizí dopisy, časem začne věřit i tomu, že jeho korespondenci také nikdo nečte...
Pythagoras, the teacher, paid his student three oboli for each lesson he attended
One way to solve an encrypted message, if we know its language, is to find a different plaintext of the same language long enough to fill one sheet or so, and then we count the occurrences of each let...
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...
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...
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...
Although this may seem a paradox, all exact science is dominated by the idea of approximation.
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...
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...