We have all heard of the various famous
Greek mathematicians such as Pythagoras (Pythagorean Theorem), Euclid (Euclidean
Geometry) or Archimedes who are giants in their field, but who has heard of the
name Al-Khwarizmi, the master mathematician from the Muslim world?

### Who was Khwarizmi?

Muḥammad ibn Mūsā al-Khwārizmī was born in Central Asia, Khorasan province in 780 CE, just a little over 100 years after the birth of the new Islamic Civilization. Al-Khwarizmi showed early on that he had considerable talents and usually was the most intelligent person in the room. As a result, most of his work was conducted in isolation. In the 9

^{th}Al-Khwarizmi was summoned to Baghdad by the Caliph Al-Mansur to work in the House of Wisdom. For the first time in his life is surrounded by giants, people who would be considered his intellectual equals and they pushed him and stretch his mental capacity.

Muslim thinkers at the House of
Wisdom during Khwarizmi’s time were busy translating everything they could get
their hands on from the Greeks, Persians and Indians. By the time Al-Kwarizmi is
born, much of the ancient work had been translated or was being translated. The
knowledge gleaned from these texts had a profound influence on Muslims thinkers
in general but on Al-Khawrizmi in particular.

Al-Khwarizmi’s first gift to the Caliph was the creation of the Arabic numeral system. Prior to Al-Khwarizmi, numbers were written out in words for example 1269 would be written One Thousand Two Hundred Sixty Nine. This system worked for the level of math practiced up until that point but in order to develop more advanced topics a different system was needed.

### Creation of the Modern Numeral System

Al-Khwarizmi’s first gift to the Caliph was the creation of the Arabic numeral system. Prior to Al-Khwarizmi, numbers were written out in words for example 1269 would be written One Thousand Two Hundred Sixty Nine. This system worked for the level of math practiced up until that point but in order to develop more advanced topics a different system was needed.

Al-Khwarizmi read many Hindu texts. He was influenced
by Hindu mathematician who had
already developed a numeral system one through nine and they had introduced the

*concept*of zero. But it was Al-Khwarizmi who recognized the*zero as a number*and included it in the Hindu system to create the Arabic numeral system. Introducing the Hindu numeral system and placing the zero at the center of his mathematical universe was a revolutionary concept that allowed for more abstract and complex computation that was not possible previously. This by itself would have placed Al-Khwarizmi in the pantheon of mathematicians, but he had another major contribution to make.

*A page of the Liber Abaci written by Leonardo of Pisa showing the*

*Arabic Numerals (In the margins on the right) .*

*This book introduced the Arabic numeral system to Europe.*### Invention of Algebra

Prior to the Greeks, mathematics involved trial and error to establish the “rule of thumb”. Once the rule was established, everyone would use it without understanding why. With the arrival of the Greek mathematicians, a level of sophistication was added that did not exist previously. They used logic to derive their conclusions and mathematical rigor to prove them. The mathematics practiced by the Greeks was physical and used to solve real world practical problems such as the distance around the amphitheater or the volume of liquid in a container. The Greeks called this “geometria” or geometry which means “measurement of the Earth”. The advancements made with the arrival of the Greeks were a major jump in the field of mathematics and they were held in high esteem, past and present, for their work.

When Al-Khawizimi introduced Algebra
(Al-Jabr), it was a revolutionary move away from the Greek concept which was
essentially geometry. It was no different than when the Greeks introduced logic
into their concept of mathematics.

**ax**

^{2}+bx+c=0

**Al-Khwarizmi provide an exhaustive**

**account of solving a polynomial equation**

**up to the second degree**

Algebra added a level of
abstraction that did not exist before. Geometry is a physical problem such as “how
much water is in the container” but algebra is abstract; “if a person invests
$100 in the stock market today and the investments grows at 7% over 10 years
how much would the investment be worth in 10 years?” Al-Khwarizmi created a
whole new field that was much broader in scope and he provided generic rules
which would allow the concept to develop further.

The introduction of Algebra allowed future Muslim
mathematicians to turn their intellect to solving equations just for the sake
of solving equations, even though they had no physically application (at least
the time) such as where does a line intersect a parabola? This is what we would
call today pure mathematics. This is a line of study that did not exist before
Al-Khwarizmi or it was limited in scope. It is these abstract ideas that allow
engineers today to build skyscrapers, mile long bridges and security encryption
equations.

**A page from Al-Khwarizmi's book on Algebra,**

**The Compendious Book on Calculation by Completion and Balancing**

**(Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala)**
Al-Khwarizmi book on Algebra

*,*The Compendious Book on Calculation by Completion and Balancing*(Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala)*and on numerals,*Al-Khwarizmi on the Hindu Art of Reckoning**were not introduced to Europe until the 12*^{th}century. His books became the core university mathematics and astronomy textbooks in Europe and the Muslim world well into the 16^{th}century.
The name “Algebra” was taken from the title
of his book al-jabr.

The term “Algorithm” was taken from his name which
is Latin for Al-Khwarizmi (or Algoritmi).

Europeans would honor and dignify all of
their calculations with the foot note “dixit Algoritmi” or “so says Al-Khwarizmi”
meaning they have based their calculations on faith based on the teachings of
the Persian master.

Al-Khwarizmi is a giant in the field of mathematics.
He absorbed the knowledge of the ancient masters from Greece, Persia and India;
He added his own original research and elevated the entire field to a new plane
of existence. We owe Muḥammad ibn
Mūsā al-Khwārizmī a debt of
gratitude.

Note 1: In 1976, In recognition of the
accomplishments of Muḥammad ibn
Mūsā al-Khwārizmī, the Working Group for Planetary System Nomenclature (IAU/WGPSN) named
moon crater 7.0N, 107.0E Al-Khwarizmi
in his honor.

Note 2: There is a debate among
scholars whether Al-Khwarizmi invented Algebra or Diophantus (in

*Arithmetica*) several centuries earlier, but all agree that Al-Khwarizmi work is distinct and it was he who established it as a separate field of study from geometry and created the rules that govern it.**-- End --**

**Read my Amazon book reviews on Islamic history**: http://www.amazon.com/gp/cdp/member-reviews/AN725PJ87OGEM/ref=cm_pdp_rev_all?ie=UTF8&sort_by=MostRecentReview

**Sources:**

Morgan, Michael Hamilton. Lost history – The Enduring Legacy of Muslim
Scientists,

Thinkers and Artists. Washington D.C.: National Geographic Society 2007.

Venkatesan, Vijay. “The
Second Father of Algebra - Muḥammad ibn Mūsā al-Khwārizmī.” Catalyst:
Rice Undergraduate Science & Engineering Review. Onkur Sen, Savina Venkova, and Juhye Lee. March
13, 2012, Rice Student Activities President’s Programming Fund, Dr. Anne Chao, The Dr. Bill Wilson Student Initiative Grant, Faculty Sponsor Dan Wagner, George R. Brown School of Engineering. Dec 9, 2013 <http://catalyst.rice.edu/discoveries/2012/03/13/>

Thinkers and Artists. Washington D.C.: National Geographic Society 2007.

“The genius
of Al Khwarizmi.” Arab Science A Journey of Innovation. 2009 Qatar Foundation.
Dec 9, 2013 <http://www.grouporigin.com/clients/qatarfoundation/chapter2_1_2.htm>

Reidel, D. “IAU Transactions XVIB.” The
Moon Wiki. Nov 14, 2010. Dec 12, 2013 <http://the-moon.wikispaces.com/IAU+Transactions+XVIB>

“History of
mathematics.“ Wikipedia. Dec 11, 2013. Dec 11, 2013 <http://en.wikipedia.org/wiki/History_of_mathematics>

“Muḥammad
ibn Mūsā al-Khwārizmī.” Wikipedia. Dec 12, 2013. Dec 12, 2013 <http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB>

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