1) Abu Ja'far Muhammad ibn Musa al-Khwarizmi was an influential 9th century Persian mathematician, astronomer, and geographer who lived in Baghdad and made significant contributions to algebra, trigonometry, and geography. 2) He authored an influential book on algebra titled "The Compendious Book on Calculation by Completion and Balancing" which introduced the fields of algebra and algorithms to both the Western and Islamic worlds. 3) Al-Khwarizmi's work popularized the Hindu-Arabic numeral system, including the use of zero as a placeholder, and influenced mathematics in Europe for centuries as his books were widely used as textbooks until the 16th

1. Al-Khwarizmi: The Fatherof Algebra
Abu Ja’far Muhammad ibn Musa al-Khwarizmi, (780 –
850 CE), was the grandfather of computer science and
the father of Algebra.
He was the populariser of Arabic numerals, adopterof
zero (the symbol) and the decimal system, astronomer,
cartographer, in brief an encyclopaedic scholar.
Life:
He was born in a Persian[1][5] family, and his birthplace is given as
Chorasmia[9] by Ibn al-Nadim. Few details of al-Khwarizmi's life are
known with certainty. His name may indicate that he came from
Khwarezm (Khiva), then in Greater Khorasan, which occupied the
eastern part of the Greater Iran, now Xorazm Province in Uzbekistan.
Bayt Al-Hikmah (House of Wisdom):
Abu Jafar Muhammad
ibn Musa al-
Khwarizmi lived in
Baghdad in the early
ninth century.
Baghdad at that time
was a cultural
crossroads, and, under
the patronage of the
Abbassid caliphs, the
so-called House of
Wisdom at Baghdad produced
a Golden Age of Arabic science and mathematics. In Baghdad, scholars
encountered and built upon the ideas of ancient Greek and Indian
mathematicians.
(Illustration source: http://www.silk-road.com/maps/images/Arabmap.jpg)

2. Contributions:
The modern word algorithm is derived from the name, al-Khwarizmi, the
best mathematician of his age, thanks to his book, “al-Kitab al-mukhtasar
fi Hisab al-jabr w’al-muqabala”, (a bookshowing how to solve equations
and problems derived from ordinary life) which means “The
Compendious Book on Calculation by Completion and Balancing”,
which later evolved into algebra, was the first written text on the subject.
In al-Khwarizmi’s time, algebra was a practical system for solving all
kinds of problems “in cases of inheritance, contracts, surveying, tax
collection, legacies, partition, lawsuits, and trade, and in all their dealings
with one another, or where the measuring of lands, the digging of canals,
geometrical computations, and other objects of various sorts and kinds
are concerned.” Al-jabr was about removing the negative terms from an
equation, while al-muqabalameant “balancing” the values of an equation
across an equal sign.
It is the title of this text that gives us the word “algebra”. It is the first
bookto be written on algebra. In al-Khwarizmi’s own words, the purpose
of the bookwas to teach what was easiest and most useful in arithmetic,
such as what was constantly required in cases of inheritance, legacies,
partition, lawsuits, and trade, and in all their dealings with one another, or
where the measuring of lands, the digging of canals, geometrical
computations, and other objects of various sorts and kinds were
concerned.
This does not sound like the contents of an algebra text, and indeed only
the first part of the bookis a discussionof what we would today
recognize as algebra. However it is important to realize that the bookwas
intended to be highly practical, and that algebra was introduced to solve
real life problems that were part of everyday life in the Islamic empire at
that time.
After introducing the natural numbers, al Khwarizmi discusses the
solution of equations. Al Khwarizmi's equations are linear or quadratic
and are composed ofunits (numbers), roots (x) and squares (x2). He first
reduces an equation to one of 6 standard forms, using the operations of
addition and subtraction, and then shows how to solve these standard
types of equations. He uses bothalgebraic methods of solution and the
geometric method of completing the square.

3. The next part of al-Khwarizmi’s Algebra
consists of applications and worked
examples. He then goes on to look at rules
for finding the area of figures such as the
circle, and also finding the volume of solids
such as the sphere, cone, and pyramid.
The text bookof Algebra was intended to be
highly practical and it was introduced to
solve real life problems that were part of
everyday life in the Islamic world at that
time.
Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals. The
Arabic text is lost but a Latin translation, “Algoritmi de numero Indorum”
in English “Al-Khwarizmi on the Hindu Art of Reckoning” gave rise to
the word algorithm deriving from his name in the title as mentioned
earlier. Unfortunately the Latin translation (translated into English) is
known to be much changed from al-Khwarizmi’s original text (of which
even the title is unknown). The work describes the Hindu place-value
system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The first use of
zero as a place holder in positional base notation was probably due to al-
Khwarizmi in this work. Methods for arithmetical calculation are given,
and a method to find square roots is known to have been in the Arabic
original although it is missing from the Latin version.“… The decimal
place-value system was a fairly recent arrival from India and … al-
Khwarizmi’s work was the first to expound it systematically. Thus,
although elementary, it was of seminal importance.”
Khwarizmi developed detailed trigonometric tables containing the sine
functions which later included tangent functions. Khwarizmi’s bookon
arithmetic was translated into Latin and published in Rome in 1857 by
Prince Baldassare Boncompagni and appears as part 1 of a volume
entitled “Tratti d’ aritmetica”. The bookis titled as Algorithmi de numero
indorum which means “Khwarizmi concerning the Hindu art of
reckoning.” Many of his books were translated into Latin and used as a
principle mathematical text bookin European universities until the 16th.
century. Among them these two books had important place: “Kitab al-
Jama wal-Tafreeq bil Hisab al-Hindi”and “Kitab al-Jabrwa al-
muqabala.”
Khwarizmi’s contribution and influence are tremendous. Two important
books on arithmetic, Carmen de Algorismo and Algorismus vulgaris
which were written in 12th. and 13th. century respectively owe a lot to
the Khwarizmi’s bookand were used for several hundred years in
Methods for arithmetical
calculationare given, and
a method to find square
roots is known to have
been in the Arabic
original although it is
missing from the Latin
version.

4. Europe. Abu Kamil Shuja, an Islamic mathematician, whose work on
mathematics was based on Khwarizmi’s works kept the influence of
Khwarizmi on Leonardo of Pisa, a 13th. century scholar and up to Middle
Ages and during the Renaissance
Al Khwarizmi’s Impact on Europe
In 1140 Robert of Chester (who read mathematics in Spain) translated
Khwarizmi’s bookinto Latin as Liber algebraeet almucabala,then
ultimately gave its name to the discipline of algebra. The Spanish Jew,
John of Seville, produced another Latin version.
When Khwarizmi’s work became known in Europe through Latin
translations, his influence made an indelible mark on the development of
science in the West. His Algebra bookintroduced that discipline to
Europe “unknown till then” and became the standard mathematical text at
European universities until the 16th. century. In the 16th. century it is
found in English as algiebarand almachabel and in various other forms
but was finally shortened to algebra.
Al Khwarizmi is one of the Muslim scholars who laid the foundations for
Europe’s Renaissance and the Scientific Revolution.
Several of Al-Khwarizmi’s books were translated into Latin in the early
12th. century by Adelard of Bath and Gerard of Cremona. The treatises
on Arithmetic, Kitab al-Jam’a wal-Tafreeq bil Hisab al-Hindi, and the
one on Algebra, Al-Maqala fi Hisab-alJabr wa-al-Muqabilah,are known
only from Latin translations. Introduction of Arabic numerals provided a
pivotal advance over the cumbersome Roman numerals. This
development of a more convenient number system assisted progress in
science, accounting and bookkeeping. Key to this was the use of the
number zero, a conceptunknown to the West. The use of this number
system (Arabic numerals) spread throughout the Muslim world over the
next two centuries, assisting the development of science. The Arabic
numeral system was first mentioned in Europe around 1200 CE, but
Christian adherence to the Roman system hindered its use and
introduction. It was only fully accepted in Europe after it was adopted by
the Italian traders in the Renaissance of the 16th century, who followed
the practice of their Arab trading partners.
Sources:

5. - wikipedia.org
- Pioneers ofIslamic History by Dr.Ibrahim B. Syed.