Would you wish to see a nifty instance of the way in which through which the world of arithmetic can have surprising ramifications on the world?
You could concentrate on the position that the particular numbers e=2.718… , pi=3.14… , and the golden ratio Phi=1.618… , have in our world. It seems that the prime numbers – numbers that can’t be divided or lowered into small numbers – even have a particular property: they’re ideally fitted to serving to craft a safe banking system.
You see – the safety methods that permit you to securely use the ATM, or on-line banking, and permit you to ship data securely over public networks – use a type of cryptography, or coding, that’s primarily based within the prime numbers.
Amazingly, a lot of the algorithms – in different phrases, strategies – for encoding your data are primarily based in a 300-year-old discovery in regards to the prime numbers, Fermat’s Little Theorem.
The French mathematician Fermat found a comparatively easy property about the way in which prime numbers behave when they’re multiplied collectively, and was in a position to clarify why this straightforward property is true. At the time although, his discovery had no apparent utility – it was merely an attention-grabbing truth in regards to the prime numbers.
Then, within the mid twentieth century, a staff of cryptographers – folks whose job is to assist encode data – discovered a manner to make use of Fermat’s Little Theorem, this discovery about prime numbers – to soundly and securely ship data. They used Fermat’s Little Theorem as a part of a “recipe” for encoding numbers, the RSA Algorithm.
Without going into an excessive amount of element, what occurs when a system makes use of the RSA Algorithm or an analogous algorithm – say, once you entry the ATM: the ATM shops your debit card data and PIN quantity as an precise quantity – a string of 0’s and 1’s. It then encodes this quantity utilizing a “key” that solely the ATM, and the financial institution, know.
Then the ATM sends the debit card data to the financial institution utilizing this “key” – and if a spy, or felony, or eavesdropper, observes the message – it’s encoded. In order to decode the message, they must know the “key”, and to be able to decide the important thing, they must issue a quantity that’s a number of hundred digits in size. This may be very tough, practically inconceivable, even for the quickest and most superior computer systems, so your data is secure.
What’s outstanding about that is – it is all primarily based within the 300-year-old discovery of the mathematician Fermat. At the time, Fermat had no clue that what he found would ultimately maintain the important thing for maintaining data safe within the twenty first century.
This is among the many outstanding properties of the world of arithmetic – it has many surprising hyperlinks with the bodily universe, many surprising purposes which might be generally not obvious for even centuries.
