*Originally published Online on May 25, 2005*

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**INRTODUCTION:** It is mostly agreed that Khaarazmi (aka Kharazmi and in Arabic: al-Khwarizmi), Razi, Faarabi, Karaji, Pur-e-Sina or Avicenna, Biruni, Khayyam and Nasir-e-Tusi are the most famous scientists of ancient Iran. Each of these eminent figures made some important contributions to the different fields of science, which can be summarized as follows: Khaarazmi (790-850) was the greatest mathematician of his time and gave analytical and geometric solutions to quadratic equations. He is often cited as the Father of Algebra (in Persian and Arabic: Jabr). Razi (865-925) was a chemist, physician, and a philosopher. Faarabi (870-950) was a philosopher and a scientist. Karaji (953-1029) also known as Karkhi was a mathematician and an engineer. Pur-e-Sina (980-1037) was an eminent physician, philosopher, and a scientist. He was the author of about 450 books on a wide range of subjects. Many of those books concentrated on philosophy and medicine. He is considered by many to be the Father of Modern Medicine. Biruni (973-1048) was a scientist who contributed greatly to the fields of mathematics, philosophy, and medicine. He wrote many books in Persian. Khayyam (1045-1122) was famous during his lifetime as a mathematician and astronomer who calculated how to correct the Iranian Calendar, presently known as Jalali or Solar Calendar. Khayyam is famous today not for his scientific accomplishments, but for his literary works. He is believed to have written about a thousand four-line verses. In the English-speaking world, he is best known for his Quatrains (in Persian: Rubaiyat). Nasir-e-Tusi (1201-1274) is known to be a philosopher, mathematicians, astronomer, physician, and a prolific writer. He was also one of the founders of Trigonometry. In this article the life story and the scientific contributions of Khaarazmi, the very first Iranian scientist is reviewed and discussed.

**HIS LIFE:** Muhammad Musa Khaarazmi was born in 780 in Khaarazm in Khorasaan province of ancient Iran. Khaarazm, presently called Khiva (in Persian: Khiveh), is located in the south of Aral Sea and it is a city in Uzbekistan. It is also documented that he was born in the town of Kath (part of Khaarazm), which is now buried in the sand. His family name is also spelled as Khwarizmi, al-Khowarizmi, Khawarizmi, and others, which are most unlikely.

Very little is known about his early life, except for the fact that his parents had migrated to a place south of Baghdad where he accomplished most of his work between 813 and 833 when Chaliph Mamun of Abbasid dynasty was in power. He was a staff member of the Institute of Science and Research or the House of Wisdom (in Persian: Khaaneh-e-Hekmat or Daaneshgaah). Like all scientists in that Institution, Khaarazmi wrote his works in Arabic. The famous Iranian historian, Tabari, applies the epithet Magus (in Persian and Arabic: Majoos) when describing Khaarazmi, which indicates that he was possibly a Zoroastrian. In his academic life Khaarazmi wrote many scientific books. In one of those books he emphasized that he wrote his books to serve the practical needs of the people in regard to inheritance, legacies, partition, lawsuits and commerce. He also considered his work as worship to God. One may, therefore, conclude that the attitudes expressed by Khaarazmi are somewhat similar to the adage of the Zoroastrian religion: Good Thoughts, Good Words, and Good Deeds. Khaarazmi also wrote a book on the Jewish calendar entitled Istikhraj Tarikh-Alyahud (in Persian: Bar-resi-e-Taarikh-e-Yahood), and two books on the astrology. Khaarazmi died in 850.

**HIS SCIENTIFIC CONTRIBUTIONS:** Khaarazmi was probably one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics. He influenced mathematical thought to a greater extent than any other mediaeval writer. His work on Algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear (L) and quadratic equations (QE). The very name Algebra has been derived from his famous book Jabr-o-Mughabeleh (JOM). JOM or the book of Integration and Equation is a compilation of rules for solving L and QE, as well as problems of geometry and proportion. Its translation into Latin in the 12th century provided the link between the great Iranian and Hindu mathematicians and European scholars. Khaarazmi also developed the decimal system so that the overall system of numerals, Algorithm (a Latin derivative of Khaarazmi), is named after him.

It must be noted that in solving the standard types of equations, Khaarazmi used both algebraic and geometric methods. For example to solve the equation x square 2 + 10 x = 39 by using algebraic method he could write: 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 10 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 root in the problem before us is 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 64, which is 8, subtracting from it half the root or 5 leaving 3, namely 8-5=3. So x equals to 3. (According to Steve Meehan, a Canadian Engineer, x also equals to -13). Khaarazmi also presented the geometric proof of the same equation by using the method of completing the square.

Khaarazmi also developed several arithmetical procedures, including operations on fractions. It was through the works of this Iranian scientist that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages. He developed in detail trigonometric tables containing the sine functions, which were probably extrapolated to tangent functions by other scientists later on (See the Epilogues below). He also perfected the geometric representation of conic sections and developed the calculus of two errors, which practically led him to the concept of differentiation. He is also reported to have collaborated in the degree measurements, which were aimed at measuring the volume and circumference of the earth.In addition to his work on mathematics, Khaarazmi also produced tracts on astronomy and geography, many of which were translated into European languages and Chinese. In 830, he produced the first global maps, a mammoth work involving a team of seven geographers. Khaarazmi’s scientific accomplishments continue to affect the world today.

IRANIANS MUST BE NOW VERY PROUD AND HONORED TO HEAR THAT THEIR GREAT SCIENTIST, KHAARAZMI, HAS BEEN NAMED AS THE GRANDFATHER OF COMPUTER SCIENCES BY MANY INTERNATIONALLY ACCREDITED ACADEMIC INSTITUTIONS.

**Epilogues (Posted August 2012)**

1. Of course, we have no good record of what Muhammad Musa Khaarazmi looked like, but in 1983, the USSR issued a lovely stamp in honor of the approximately 1200th birthday of Khaarazmi, which is shown here

2. In mathematics, the trigonometric functions (circular functions) are functions of an angle.

The most familiar trigonometric functions are the sine, cosine, and tangent (View here)

3. Muhammad Musa Khaarazmi wrote also several other books including a treatise on the Hebrew calendar. It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall; calculates the interval between the Jewish era and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar materials are found in the works of Iranian scholar Abu Rayhaan Biruni and Jewish philosopher Moses Maimonides (View here)

4. It is reported that he was also known as Master Khaarazmi, in Persian: Shaikhol Raiis Khaarazmi (View here)

5. It is suggested that a very special day as the commemoration day for Muhammad Musa Khaarazmi, the First Irania Scientist, be designated by the UNESCO.

*Manouchehr Saadat Noury, PhD*

** References**

Boyer, C. B. (1991): “The Arabic Hegemony”, A History of Mathematics (Second Edition ed.), John Wiley & Sons, Inc.

Gandz, S. (1926): The Origin of the Term “Algebra”, ed., November issue of the American Mathematical Monthly 33 (9): 437–440.

Hughes, B. (1986): “Gerard of Cremona’s Translation of al-Khwarizmi’s al-Jabr”, ed., Mediaeval Studies.

Meehan, S. (2005): Personal Communication.

Saadat Noury, M. (2005): Various Notes and Articles on the History of Iran.

Saadat Noury, M. (2005): Online Articles on First Iranians

Toomer, G. (1990): “Al-Khwarizmi, Abu Jafar Muhammad ibn Musa”, ed., in Gillispie, Charles Coulston, Dictionary of Scientific Biography, New York, USA.

Wikipedia Encyclopedia (2005): Online Notes on Muhammad ibn Musa Khwarizmi (in English & Persian).

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