The term algorithm derives from the name of Muhammad in Musa al’Khwarizmi, a ninth-century Persian mathematician. His latinized name, Algoritmi, meant “the decimal number system” and was used in this meaning for centuries. The modern notion of algorithm emerged in English in the nineteenth century, and became more commonly used since the 1950s, triggered by the emergence of first commercially available computers.
The first algorithms were captured on paper in Ancient Greece. Scholars such as Nicomachus of Gerasa or Euclid were then creating the building blocks of modern mathematics. To ease understanding and applicability of their ideas, they expressed many of them as step-by-step actions.
Nicomachus of Gerasa introduced the Sieve of Eratosthenes. The Sieve is used to this day by students learning to write efficient computer code. It helped simplify the process of identifying prime numbers. Prime numbers are natural numbers, greater than one, that cannot be formed by multiplying two smaller natural numbers. For instance, four is not a prime number because it can be formed by multiplying two by two. Five, in contrast, is a prime number, because no natural numbers, smaller than five, can be multiplied to form five. While it is not too hard to identify the first few prime numbers (for instance 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29), finding large prime numbers takes a lot of time. And large prime numbers are essential in cryptography. The Sieve of Eratosthenes gives step by step instructions for quickly removing all non-prime numbers from a defined set of numbers (for instance between 1 and 10,000) until only prime numbers are left. Today, there are numerous algorithms available, that simplify the task of identifying such numbers. The Sieve of Eratosthenes started a whole family of algorithms that have the same goal and are becoming better (quicker, or requiring fewer steps) at detecting prime numbers.
Euclid, the other scholar mentioned above, much better known than Nicomachus these days, introduced an algorithm for identifying the greatest common divisor of two numbers. Again, not always an easy task, but essential in many situations. Euclid’s algorithm helped to make this calculation easy. Why is Euclid’s algorithm helpful? Imagine you have a room with the exact size of 612 by 2006 centimeters that needs a new floor. Euclid’s algorithm will help you find the size of the largest square tiles that would neatly cover the floor. The answer, given by the algorithm, is 34 cm by 34 cm, resulting in a layout of 18 by 59 tiles. Of course, every tiler will tell you that the answer is wrong and that you have no idea what you’re doing because the algorithm doesn’t consider the grout width and leaves no space for it. Fear not: this can be calculated too, and neatly expressed as an algorithm.
Credit : Towards Data Science
Picture Credit : Google
