For all of you who absolutely detest math, this is the man you have to thank.   Al Khwarizmi is dubbed the  "Father of Algebra" .  Born in approximately 780 in the town of Khiva in then Persia (now Uzbekistan) .  His family moved to Baghdad shortly after his birth.  No one really knows what language is his native language, but he most likely spoke  Arabic and an archaic version of Persian.  
 
The common mathematical term that we all know and love, Algebra, actually is originated in Khwarizmi's book entitled  Al-Jabr  wa- al Muqabilah.  The title literally translates to "calculation by completion and reduction" 

 al-Khwarizmi introduces the main topic of this first section of his book. His equations are linear or quadratic and are composed of units, roots and squares. For example, to al-Khwarizmi a unit was a number, a root was x, and a square was x². However, although we shall use the now familiar algebraic notation in this article to help the reader understand the notions, Al-Khwarizmi's mathematics is done entirely in words with no symbols being used.

He first reduces an equation (linear or quadratic) to one of six standard forms:

1. Squares equal to roots.
2. Squares equal to numbers.
3. Roots equal to numbers.
4. Squares and roots equal to numbers; e.g. x² + 10 x = 39.
5. Squares and numbers equal to roots; e.g. x² + 21 = 10 x.
6. Roots and numbers equal to squares; e.g. 3 x + 4 = x².

The reduction is carried out using the two operations of al-jabr and al-muqabala.  For example, using one of al-Khwarizmi's own examples, "al-jabr" transforms
 x² = 40 x - 4 x² into 5 x² = 40 x. The term "al-muqabala" means "balancing" and is the process of reducing positive terms of the same power when they occur on both sides of an equation. For example, two applications of "al-muqabala" reduces 50 + 3 x + x² = 29 + 10 x to 21 + x² = 7 x

Al-Khwarizmi then shows how to solve the six standard types of equations. He uses both algebraic methods of solution and geometric methods. For example to solve the equation x² + 10 x = 39 he writes 

... a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5 leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square.

The geometric proof by completing the square follows. Al-Khwarizmi starts with a square of side x, which therefore represents x². To the square we must add 10x and this is done by adding four rectangles each of breadth 10/4 and length x to the square (Figure 2). Figure 2 has area x² + 10 x which is equal to 39. We now complete the square by adding the four little squares each of area 5/2 5/2 = 25/4. Hence the outside square in Fig 3 has area 4 25/4 + 39 = 25 + 39 = 64. The side of the square is therefore 8. But the side is of length 5/2 + x + 5/2 so x + 5 = 8, giving x = 3.

Al Khwarizmi, aside from creating the mathematical equation for completing  the square, Khwaizmi also developed a mathematical way to mulitply the expression  (a + b x) (c + d x)

We study his works in Algebra and we refer to them as quadratic and linear equations. We also do not give credit for Al- Khwarizmi for his use of the place holder 0. Prior to Al-Khwarizmi the  was in the place of the 10 algorithmically, Khwarizmi saw the need for a number 0 particularly with roots, so instead Khwarizmi place the zero in front of the 1.

We now know that Al-Khwarizmi is a brilliant mathematician, but did you also know he was considered a great contributor to the world of Geography? It's true, Khwarizmi built on the work of Ptolomy in Khwarizmis' book. Khwarizmi constructed maps based on latitudes and longitudes.

On top of all that Al- Khwarizmi was also an astrologer, no, not astronomer. He actually wrote horoscopes for prominent political figures. He also wrote many books on the sundial, astrolabe, and different calendars.

Web Citations:
O'Conner, JJ, Robertson, EF
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html
*picture and diagram also courtsey of the web page

Conger, Heather, Overbay, Shawn, Schorer, Jimmy. Al-Khwarizmi
http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html

Turner, Howard, Science in Medieval Islam. University of Texas Press 1995

**Authors Notes

I afirm the credibility of my websources due to the scholarly nature of the articles. The mathematical equations and explainations are taken directly from the O'Conner and Robertson website. 

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