Forgotten Math Heroes

Today science, especially mathematics, is qibla to Western countries (Europe and America). We hardly ever hear of mathematicians who come from Eastern countries (Muslim Arabs, Indians, Chinese). The most popular we hear as Muslim Arab mathematicians who contribute to the development of mathematics are Al-Khawarizmi, known as the father of Algebra, introducing zeros (0), and translators of ancient Greek works.

Is it true that only the contribution of eastern countries (especially Muslims) to the development of mathematics?

Zero story

The concept of zero numbers has evolved since ancient Babylonian and Greek times, which at the time was interpreted as the absence of something. The concept of zero numbers and their properties continues to evolve over time.

Until the 7th century, Brahmagupta, an Indian mathematician, introduced some of the properties of zeros. The properties are a number when summed with zero is fixed, so a number when multiplied by zero will be zero. However, Brahmagupta ran into difficulties, and tended in the wrong direction, when dealing with division by zero. It continued to be a research topic at the time, even up to 200 years later. For example, in 830, Mahavira (India) confirmed brahmagupta’s results, and even stated that “a number divided by zero is fixed”. Of course it’s a fatal mistake. However, this should still be highly appreciated for its current size.

Brilliant ideas from Indian mathematicians are further studied by Muslim and Arab mathematicians. This occurred in the early stages when mathematician Al-Khawarizmi examined the Hindu (India) calculation system describing the place value system of numbers involving numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Al-Khawarizmi was the first to introduce the use of zeros as a place value in base ten. This system
referred to as the decimal number system.

Dark Ages

In fact the stagnation of science never happened, what happened was the transfer of science centers. History
noting that after Greece collapsed, a new era emerged, namely the era of Islamic glory in arab lands. This resulted in the development of culture and science centered and dominated by Muslim-Arabs. What is meant by Arabia here covers the middle east, Turkey, north Africa, the Chinese border area, and part of Spain, according to the territory of the Islamic caliphate at the time.

Caliph Harun Al-Rashid, the fifth caliph during the Abassid dynasty, during his caliphate, which began around 786, undertranslated large mathematical texts (as well as other sciences) of the ancient Greeks into Arabic. The next caliph, caliph Al-Ma’mun during his caliphate in Baghdad was founded by the Council of Wisdom,
which became the center of research and translation of Greek manuscripts.

Scholarships are provided to translators and generally they are not only language experts, but also scientists who are experts in mathematics. For example, Al-Hajjaj translated the manuscript elements (containing a collection of mathematical knowledge) written by Euclid. Some other translators include Al-Kindi, Banu Musa brothers, and Hunayn Ibn Ishaq.

As many mathematical historians have pointed out, especially those written by Westerners, Muslim contributions to mathematical development are limited to the translation of ancient Greek manuscripts into Arabic. Many mathematicians do not feature about the muslim’s large contribution to the development of mathematics, either by willfulness or ignorance.

But not a few mathematician historians from the West are more objective in presenting the actual facts
Happen. In one source written by J. J. O’Connor and E. F. Robertson it is said that the western world has in fact
owe it to scientists/mathematicians and Muslims. Furthermore, the rapid development in mathematics in the 16th to 18th centuries in the western world, had actually been started by Muslim mathematicians centuries earlier.

Contributions of Muslim mathematicians

One of the brilliant mathematicians of the early days was Al-Khawarizmi. In addition to his contributions as stated, Al-Khawarizmi is also known as a pioneer in the field of algebra. The researchers of an Al-Khawarizmi were a major revolution in the world of mathematics, connecting the geometric concepts of ancient Greek mathematics into new concepts. The researchers an Al-Khawarizmi produced a joint theory that allows rational/irrational numbers, the magnitude of geometry to be treated as “algebraic objects”.

The next generation of Al-Khawarizmi, such as Al-Mahani (born 820), Abu Kamil (born 850) focuses research on the systematic applications of algebra. For example the application of arithmetic to algebra and vice versa, algebra against trigonometry and vice versa, algebra against the theory of numbers, algebra against geometry and vice versa. These studies underlie the creation of polynomic algebra, commurtory analysis, numerical analysis, numerical solutions of equations, number theory, and geometry construction of equations.

Al-Karaji (born 953) is believed to be the first to completely separate the influence of geometry operations in algebra. Al-Karaji defines monomial x, x2, x3,… and 1/x, 1/x2, 1/x3,… and give the rules for the multiplication of the two tribes thereby. In addition, he also managed to find a binomial theorem for the rank of integers. Further to advance mathematics, he founded an algebra school. His next generation (200 years later), Al-Samawal was the first to discuss new topics in algebra. According to him that operating something unknown (variable) is the same as operating something known.

Another Muslim mathematician was Omar Khayyam who was born around 1048. He contributed greatly through his research, providing a complete classification of the third-rank equation through the completion of geometry using the concept of cone cutting. He also gave a conjecture (allegedly) about the full description of the algebraic settlement of the three-rank equations.

The next mathematician was Sharaf al-Din al-Tusi who was born in 1135. He followed Omar Khayyam in applying algebra to geometry, which eventually became the beginning for the algebraic geometry branch.

Outside the field of algebra, Muslim mathematicians also have a reliable. One of the Banu Musa brothers, Thabit Ibn Qurra (born 836), had a great contribution to mathematics. One of them is in the theory of numbers, namely the discovery of pairs of numbers that have unique properties; two numbers each are the sum of the true divider of another number and are called amicable numbers. Ibn Qura’s Thabit theorem was later developed by Al-Baghdadi (b. 980).

Next up was Abu Ali Hasan Ibn Al-Haytam (born 965 in Basrah Irak), known by Westerners as Alhazen. Al-Haytam was the first to classify all perfectly even numbers, i.e. numbers that are the sum of the true divider, such as the 2k-1(2k-1) in which 2k-1 is the prime number. Furthermore Al-Haytam proves that when p is a prime number, 1+(p-1)! depleted divided by p.

Unfortunately, much later, these results are known as the Wilson Theorem, not the Al-Haytam Theorem. This theorem was called the Wilson Theorem after Warring in 1770 stating that John Wilson had announced these results. In addition to mathematics, Al-Haytam is also well known in the world of physics, studying the mechanics of movement of an object. He is the first to state that if an object moves, it will move continuously unless there is an outer force affecting it. This is none other than the law of the first motion, commonly known as newton’s first law. In addition, Al-
Haytam provides a huge role for the development of optical theory and practice. Al-Pharisees (born 1260) provided a new method of proof for Theorem of Thabit Ibn Qurra. He introduced new ideas regarding factoring and commutorial methods.

Another mathematician was Al-Kashi (born 1380) who contributed greatly to the development of decimal fraction theory. This theory is very closely related to the theory of real numbers and the history of the discovery of numbers (pi). Next he developed an algorithm of calculating the root rank n. This method a few centuries later was developed by western mathematicians Ruffini and Horner.

Field of astronomy

Astronomical problems, timing, and geography problems are other motivations for Muslim mathematicians to conduct research. For example Ibrahim Ibn Sinan (born around the 910s) and his grandfather Thabit Ibn Qurra, studied the curves required in constructing the sun clock. Abul-Wafa (born 940s) and Abu Nasr Mansur (born 970s) apply ball geometry to astronomy and use formulas involving sinuses and tangents. Then Al-Biruni (born 973) used the sinus formula both in astronomy and in the calculation of the longitude and latitude of the cities. In this case, Al-Biruni conducted a very vigorous study in the projection of the ball on the
Field.

Thabit Ibn Qurra also contributed to the theory and observation in astronomy. Al-Batanni (born 850) made accurate observations that allowed him to correct ptolemy’s data on the moon and sun. Nadir al-Din al-Tusi (born 1201), based on his theoretical astronomy in Ptolemy’s work, made a very significant development in planetary system models.

The creation of trigonometric function tables is part of the work of Muslim mathematicians in astronomical research, as did Ulugh Beg (born 1393) and Al-Kashi. The construction of astronomical tools is also inessiable from the influence of Muslim mathematicians.

The above description is not enough to thoroughly review the works of Muslim mathematicians. Many are still not covered, and have not been revealed. It has not been covered and has not been revealed solely due to the lack of sources telling them. Thus, it is appropriate for us to say that Muslim mathematicians are forgotten mathematical heroes. Or, it’s deliberately forgotten.
Wallahu a’lam.***

It was first published in People’s Minds in 2006.

Dr. Saeed Saeed
Alumni of S-3 Bandung Institute of Technology (ITB), Doctorate in
mathematics (Field of Algebraic Analysis study), Teaching staff
University of Education Indonesia (UPI) Bandung.

Al Jupri
Alumni of Universitas Pendidikan Indonesia (UPI), 3rd Place
International Mathematics Olympiad
Students, together with the Republic of Indonesia team) in Isfahan, Iran
2003, Faculty of Indonesian University of Education (UPI) Bandung