The History of the “Algorithm” and “Algebra”

What is an “algorithm?”
Well, it is defined as:

a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

Who was Musa Al-Khwarizmi?
Musa Al-Khwarizmi was born about 780 C.E., and died about 850 C.E. He was a mathematician who, contrary to popular belief, pioneered Algebra (he was known as the “Father of Algebra” and pushed it forward, as well as defining the Algorithm.

How did he pioneer/invent Algebra?
He wrote al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah, which translates to The Compendious Book on Calculation by Completion and Balancing. He writes in his book a very interesting statement.

A square and twelve roots are twenty-eight numbers.

What does this mean? Well, if we look closely, A SQUARE, so X^2, and twelve roots, so 12X, are twenty-eight numbers, so =28! So the equation is X^2+12X=28! He solves this equation this way:
[Note: Solution is quoted from this article as I couldn’t find it myself]

Divide the 12 numbers by 4, you will get 3 numbers.
Multiply the 3 numbers by 3 numbers, you will get 9 numbers.
Multiply 9 times 4, you will get 36 numbers.
To 36 you add the 28 numbers from the original equation and you will thus get 64
Calculate the square root of 64, you will get 8.
From 8 you subtract one half of the roots (meaning X - 12 in our case). Subtract 6 from 8 and you will get 2.

And 2 is correct.

Let’s solve it by factoring. First, let’s move the terms to the left side of the equation.

1. Move terms to left side, to get X^2+12x-28=0.

2. What factors of -28 combine to get 12? 14 and -2. So, we have to create (x-2)(x+14)=0

Or, x=2, and x=-14. 2 is one of the answers. Wow.

But, how did the Algorithm come to be?
It’s… strange. But really cool. In the present day, we are familiar with the quadratic formula, which is a widely used tool for solving quadratic functions. However, back in Al-Khwarizmi's time, they only knew about positive numbers, which made it challenging for him to come up with a single method to solve all quadratic equations. As a result, he divided them into six types and developed a set of clear and organized steps for each type. This approach can be considered a true algorithm because it provides a systematic way to find solutions to quadratic equations. This is the story of the Algorithm and Algebra… but… wait. How did the name Algebra come along?
Well, his work was called al-Jabr wal-Muqābalah, which the first part, al-Jabr, over time, when westernized, turned into ALGEBRA!!
So there you have it.