Would you like to see a nifty example of the way in which the world of mathematics can have unexpected ramifications on the world?
You may be aware of the role that the special numbers e=2.718… , pi=3.14… , and the golden ratio Phi=1.618… , have in our world. It turns out that the chief numbers – numbers that cannot be divided or reduced into small numbers – also have a special character: they are ideally suited for helping craft a obtain banking system.
You see – the security systems that allow you to securely use the ATM, or online banking, and allow you to send information securely over public networks – use a form of cryptography, or coding, that is based in the chief numbers.
Amazingly, most of the algorithms – in other words, methods – for encoding your information are based in a 300-year-old discovery about the chief numbers, Fermat’s Little Theorem.
The French mathematician Fermat discovered a comparatively simple character about the way chief numbers behave when they are multiplied together, and was able to explain why this simple character is true. At the time though, his discovery had no obvious application – it was simply an interesting fact about the chief numbers.
Then, in the mid 20th century, a team of cryptographers – people whose job is to help encode information – found a way to use Fermat’s Little Theorem, this discovery about chief numbers – to safely and securely send information. They used Fermat’s Little Theorem as part of a “recipe” for encoding numbers, the RSA Algorithm.
Without going into too much detail, what happens when a system uses the RSA Algorithm or a similar algorithm – say, when you access the ATM: the ATM stores your debit card information and PIN number as an actual number – a string of 0’s and 1’s. It then encodes this number using a “meaningful” that only the ATM, and the bank, know.
Then the ATM sends the debit card information to the bank using this “meaningful” – and if a spy, or criminal, or eavesdropper, observes the message – it is encoded. In order to decode the message, they would have to know the “meaningful”, and in order to determine the meaningful, they would have to factor a number that is several hundred digits in length. This is very difficult, nearly impossible, already for the fastest and most progressive computers, so your information is safe.
What’s exceptional about this is – it’s all based in the 300-year-old discovery of the mathematician Fermat. At the time, Fermat had no clue that what he discovered would ultimately keep up the meaningful for keeping information obtain in the 21st century.
This is one of the many exceptional similarities of the world of mathematics – it has many unexpected links with the physical universe, many unexpected applications that are sometimes not apparent for already centuries.