Abstract

Mathematics is a universal language that exceeds cultural and religious boundaries. Throughout history, various civilizations have made significant contributions to the field of mathematics. One such civilization is the Islamic civilization, which flourished from the 8th to the 15th century. Muslim contributions to mathematics have played a significant role in shaping the field and its evolution throughout history. From the 8th to the 15th century, Islamic scholars made substantial advancements in various branches of mathematics, including algebra, geometry, trigonometry, and arithmetic. These contributions had a profound influence on the development of mathematics and continue to shape modern mathematical theories, techniques, and applications. Their works were translated into Latin and other European languages, preserving and distributing their knowledge throughout the world. The reintroduction of these works during the European Renaissance prompted further advancements in mathematics and science.

This study explores the noteworthy contributions of Muslim mathematicians, highlighting their advanced ideas, influential works, and lasting impact on the development of mathematical knowledge. For completion of this paper, I will use several bibliographic resources as my library research and data collecting like books, internet sources, journals, articles, newspapers etc. I have particularly focused on the book of Edward Gratten Companion Encyclopaedia of History and Philosophy of Mathematics, Vol.1. Also, I focused on the book of Ali Abdullah Al-Daffa: The Muslim contribution to Mathematics. In conclusion, this paper will show the importance of mathematics in Islam and elaborate the contribution of Muslim in Mathematics and how these have a lasting impact on this contemporary world.

Introduction:

The root and one of the fundamental branches of science is mathematics. Mathematics has been a fundamental discipline in human development, providing a framework for understanding the world and solving complex problems Muslim mathematicians have made an unforgettable contribution to the origin, development and excellence of this discipline. The Muslim world has a rich history of mathematical achievements, which span several centuries, from the 8th to the 15th century. They were able to solve the complex problems of Greek geometry through basic research. The concept of Indian zero (0) was introduced in Europe through the efforts of Muslim mathematicians. The decimal system, algebra, introduction of rounded trigonometry, etc. have immortalized the contribution of Muslims in mathematics. According to many researchers in mathematics such as Afzalur Rahman (1994), Dr. Maurice Bucaille (1979), Prof Dr Carra de Paux, the Qur’an itself encouraged the accumulation of knowledge. Mathematics or ‘Al hisab’ has been used for 48 times in the Holy Quran. Sheikh Tantawin Jauhari wrote Al Jawahir fi Tafsir al-Quran where in this book there are about 750 verses related to science and mathematics. Al- Quran has already mentioned the important digits used in mathematical knowledge such as number 1 to 10. There are some main aspects of religious rituals in which mathematics is applied compulsorily such as Muwaqeet, regulation of lunar colander for Hajj and Ramadan, determination of direction of Qibla for Salat and hajj routs, Ilm-ul-Faraid (Inheritance), Islamic decorative art, calculation of Zakat, Ushr, and Kharaj, weight and measured so on. These Quranic commands and religious necessities compelled and led the Muslim scientists to mathematical research which resulted in the journey of discovery and advancement of Muslim mathematicians.

Background and Historical Context

According to Galileo Galilei, "Mathematics is the key and door to the sciences." It is used throughout the world as an essential tool in many fields. The earliest used of mathematics were in trading, land measurement, painting, weaving patterns, recording of time, values of ancestors’ properties, architecture and also war. More complex mathematics did not appear until 3000BC where Babylonians and Egyptians began to use mathematics for taxation and other financial calculations for building, construction and for astronomy. In modern world, mathematics is being used in natural science, engineering, medical and social science. Even according to Rene Descartes, “all things in nature occur mathematically”.

The study of Mathematics begins in the 6th century B.C with the Pythagoreans who coined the term ‘Mathematics’ from the ancient Greek meaning ‘subject of instruction’. Chinese Mathematics made early contribution including a place value system. By 700 the Islamic empire included Persia and Syria, where remnants of ancient scientific traditions were still to be found. The history of Arabic science begins after the creation of the Abbasid Empire (in 760) and the foundation of the new capital, Baghdad. The House of Wisdom (Daru-Ul-Hikmat), a kind of academy of science was set up in Baghdad around 810, and work started almost immediately on translating the major Greek and Indian mathematical and astronomy works into Arabic. This led to the development of new mathematical concepts and methods, which were further refined and expanded by Muslim mathematicians.

Discovery and Advancement

Islamic scholars made substantial advancements in various branches of mathematics, including algebra, geometry, trigonometry, and arithmetic. According to Hittti, 'the sciences of trigonometry, such as algebra and geometry, were mainly established by the Arabs. Also, the famous Western mathematician Leonardo Fibonacci (1180-1250) said, "The algebra of Muslim scientists is much more advanced, orderly and discussed in detail than the algebra of Greek or Indian scientists."

Algebra:

One of the most significant contributions of Muslim mathematicians was the development of algebra. The term "algebra" comes from the Arabic word "al-jabr," which means "reunion of broken parts." This seminal work not only introduced algebra to the world but also gave rise to the term "algorithm." The works of mathematicians like Al-Khwarizmi, Omar Khayyam, and Abu al-Wafa laid the foundation for algebraic notation, quadratic equations, and the study of polynomial equations.

Trigonometry:

Muslim mathematicians also played a crucial role in the development of trigonometry. They developed trigonometric functions, such as sine, cosine, and tangent and derived formulas for calculating the values of these functions. The work of mathematicians like Al-Battani and Nasir al-Din al-Tusi led to the development of trigonometric tables and the use of trigonometry in astronomy and navigation. Also, the works of Al-Battani, Ibn Haytham and Al-Biruni led to advancements in spherical trigonometry and the development of accurate astronomical instruments. Muslim astronomers also made substantial progress in understanding celestial mechanics, contributing to the development of the astrolabe and celestial globes.

Decimal System and Arithmetic Operations:

Muslim mathematicians invented the arithmetical decimal system, which is the foundation of modern mathematics. They introduced the concept of zero and the decimal point, revolutionizing numerical representation. Additionally, they developed the fundamental operations of addition, subtraction, multiplication, division, raising to a power, and extracting square and cubic roots. They developed new methods for finding prime numbers, solving Diophantine equations, and understanding the properties of integers. The work of mathematicians like Al-Karaji and Ibn al-Haytham led to the development of new number-theoretic concepts and techniques, which have applications in cryptography, computer science, and other fields. However, the Roman numerals were represented by special symbols but these were not fit for arithmetical operation particularly, for multiplication and division. The calculations were laborious and clumsy, like: DCCCVIII=808 DCCCLXXXVIII= 888

It is quite obvious that for simplest arithmetical problem, roman numerals called for enormous time and labour. Moreover, the Roman numerals have many deficiencies as discussed for Greek numerals, due to which no proper scientific number system could be evolved by the Romans. Fortunately, by the 9th century the Muslim world was using the Arabic system of numerals with the essential addition of the zero. Without the latter, it was impossible to know what power of ten accompanied each digit. Hence 8 8 might mean 88, 880 or 808.

Calculus:

Although the development of calculus is often attributed to Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, Muslim mathematicians had already made significant contributions to the field centuries earlier. Hasan Ibn al-Haytham, in the 11th century, developed a method for finding the area of a parabola using a technique similar to modern integral calculus. Later, Sharaf al-Din al-Tusi, in the 13th century, developed a method for finding the derivative of a function, which is a fundamental concept in calculus. In addition, Scholars like Al-Karaji and Alhazen worked on problems related to finding areas and volumes, laying the groundwork for integral calculus.

Geometry:

Muslim mathematicians also made significant contributions to geometry. They developed new methods for constructing geometric figures, measuring angles and distances, and calculating the areas and volumes of various shapes. The work of mathematicians like Ibn al-Haytham and Omar Khayyam led to the development of new geometric theorems and proofs, as well as the discovery of new properties of geometric figures. Muslim scholars also made advancements in Euclidean geometry, such as the Persian mathematician Omar Khayyam's study of conic sections.

Overview of Muslim Mathematicians

The historian Gibbon rightly said in his book 'Decline and Fall of the Roman Empire', "When the streets of London were immersed in darkness, the streets of Cordova were illuminated with lights." Had it not been for the Muslim defeat at the Battle of Tours, Arabic would probably have been practiced at Oxford. Not only Gibbon, Western Christian historians like Draper, Church, Davenport, Lenpool, Merton, Hittite etc. have unanimously acknowledged the immense contribution of Muslims to world civilization.

In fact, history shows that from the eighth century to the fifteenth century, more than 500 Muslim scientists have indebted the world with their important contributions. Professor George Sarton, a scholar of mathematics, has rightly said in his book 'Intuition to the History of Science', "The number of scientists who have left their mark in knowledge and science in the age of Muslim dominance is probably not much less than the number of scholars of the present age."Among the Muslim scholars who made significant contributions to the development and development of mathematics are al-Khawarizmi, al-Biruni, al-Battani, Nasir al-Din Tusi, Omar Khayyam, Al-Bujzani, Al-Karaji etc. The details are discussed below-

Al-Khawarzimi (780-850 AD):

He was born in Khawarizm, Khorasan in Central Asia. He is an astronomer and inventor of mathematics and algebra on the other. His greatest contribution to mathematics is that thanks to him the zero symbol and the designation of an unknown quantity as “x” appeared. The root which is the unknown quantity ‘shay’ in Arabic meaning “a thing” However, in translations made in Toledo, (the centre for translation of Arabic books), the absence of a “sh” sound in the Spanish language meant that a suitable letter had to be chosen. The choice fell upon “x”, which may well explain why Don Quixote is often pronounced as “Don Quishote”.His unforgettable book on algebra is titled "Al-Kitab al-Mukhtasar fi Hisab al-Jabrwal-Muqabala"(The Compendious Book on Calculation by Completion and Balancing) which was translated into Latin during the 12th century, algebra (al-jabr) derived its name.By any measure, 'Hisab al-Jabr' is the first and best book in algebra. It analyses the solution of the quadratic equation, algebraic multiplication and division, and al-Khwarizmi’s own laws and solution of problems. In the book, he presented more than eight hundred examples of different types of 2/3 mathematics.It was the best textbook of mathematics in many European universities and has taught in High School until the end of 16th century. Following the Indian method of calculation, al-Khawarizmi wrote a treatise on arithmetic called Kitabul Hind. His famous book on the origin of numbers is 'Al-Jam wat Tafriq'. Al-Khawarizmi discussed in detail the method of calculating the size and circumference of triangles, quadrilaterals, circles, pyramids, etc. as a perimeter.He was the first to introduce the Arab numeral system into algebra. His another book is Kitab-ul-Wasaya, which is also related with the mathematics. It is attributed to him the eponymous word 'algorithm' as well as 'algebra’. In this contemporary world, he is known as the Father of Algebra for his unforgettable contribution in Algebra. His discovered algebra is often called the lifeblood of modern science. Because almost everything in the modern era has been discovered based on this algebra.

Al-Battani (858-929 AD):

The Muslim researcher and scientist Abu Abdullah ibn Jabir ibn Sinan al-Battani being the first to use the expressions "sine" and "cosine" and was very much aware of the superiority of his 'sines' over the Greek chords. His methods were copied in Western Europe in the fifteenth century by the astronomer Regiomontanus. In the West, he was known under the name Albatenius. The expression of the ratios of trigonometry is al-Battani's fundamental contribution. He made a special contribution to the improvement of trigonometry and first table of cotangents. He discovered various relationships between these signals. If you know the sign of an angle, then find its tangent and if you know the tangent, then he invents the rule of finding its sign. He tended rather to correct Ptolemy in a tacit way, without referring to Ptolemy’s errors. In general, al-Battani’s place in history is that of a refiner of Ptolemy’s investigations. So, sometimes referred to as the “Ptolemy of the Arabs”.

Al-Karji:

The Persian mathematician Muhammad ibn Ahmad al-Karaji (953-1029 CE) introduced the concept of algebraic calculus and developed methods for calculating powers and roots of numbers. He also introduced the binomial theorem for positive integral indices. He extended al-Khawarizmi's ideas of algebra. He was the first person to completely separate algebra from geometric operations and formulate and explain the algebraic links with arithmetic, one of the most important foundations of modern algebra. He was the first to discover the exponent of algebra. His book ‘Al-Kafi fi Al-Hisab’ (Essentials of Arithmetic) covers the rules of computation. Sometimes referred to as "the father of algebraic geometry,"

Abul Wafa Buzjani:

Abul Wafa (840-918), the greatest Muslim scientist of the tenth century, compiled the list of trigonometry. He was the first to establish the generality of spherical triangles with the sine theorem. He was the first to prove some trigonometric theorems and introduced the trigonometric functions tangent and cotangent. In addition, the scientist found with high accuracy the value of the sine of one degree and derived a formula for the sine of the sum of two angles.

Omar Khayyam:

Omar Khayyam (1021-1123) was one of the most distinguished mathematicians. His most fundamental contribution to mathematics was the solution of the cubic equation by geometric method. His “Maqalatu fi al-Jabrwal Muqabila”(Treatise on Demonstrations of Problems of Algebra) is considered an important book in mathematics. In this book, he classified equations as powers and wrote down the rules for solving quadratic equations. He played a significant role in improving algebra by analysing cubic equations and other advanced equations and classifying them by definition. He also did important work on arithmetic and geometry. He formulated the universal definition of mathematics and demonstrated extraordinary skill in classifying and analysing binomial, cryptic and quadrupedal equations. One of his treatises that have not come down to us described the method he developed on the basis of the works of Chinese and Indian mathematicians for finding the roots of natural numbers of the second, third and fourth degrees. His “Mushkili-Hisab” is another famous book. As an astronomer, he designed a solar calendar known as the Jalali Calendar.

Al-Biruni:

Al-Biruni (973-1048) was another Muslim scientist. Born in Khawarizm, the contribution of this great scientist to mathematics is widely recognized. He was the best scientist in mathematics and physics, worked out that the earth rotates on its own axis and succeeded in calculating its circumference. His work al-Qanun al-Mas'udi is considered his greatest contribution to mathematics. Some call the book an encyclopaedia of mathematics. Al-Biruni in his book has presented the solution of subtle, complex and mathematical problems in geometry, trigonometry, calculus etc. In addition, he discussed the measurement system, which is still recognized and followed today.

Nasiruddin al-Tusi:

Muhammad Nasiruddin Tusi (1201-1274) is a brilliant name in the study of Muslim mathematics. He is the Muslim mathematician of Khorasan who made fundamental contributions to all subjects such as mathematics, algebra, geometry, trigonometry, etc. He distinguished trigonometry from astronomy and discussed plane and spherical trigonometry.

Other notable mathematicians are Abu Kamil (Egyptian Calculator), Al-Haytham, Al-Kindi, Thabith bin Qurrah, Al-Kashi, Al-Farabi, Banu Musa, Uqlidshi and so on.

Arabic Mathematics in Europe

Muslim scholars played a crucial role in preserving and translating ancient mathematical texts from various civilizations, including Greek, Babylonian, and Indian. Their translations and commentaries ensured the survival of these mathematical works, which later influenced European mathematicians during the Renaissance. Muslim Mathematicians’ noteworthy work paved the way for the scientific revolution in Europe and had a profound influence on the development of modern science and technology. There was the period of the Dark Ages that may be called the Muslim Age in the history of mathematics. Muslim Scientific knowledge was transferred to Europe during the Dark Ages. In the 12th and 13th centuries many Arabic mathematical texts were translated into Latin in Spain and, to a lesser extent, in Sicily. These were Arabic translations of Greek mathematical works, but also works by Arabic authors, such as treatises on Indian numbers and algebra by al-khawarzimi and the Optics of Ibn al-Haytham.

Another type of transmission is exemplified by Leonardo of Pisa (Fibonacci), who travelled and studied in the Western Arabic world and wrote various books on mathematics was much higher in the Eastern Islamic world (Iraq and Persia) than in the Western world, and that most of the mathematical discoveries were unknown in areas west of Egypt. Latin and Hebrew translations of Arabic mathematical treaties that are now lost. It was through them that modern science began and progressed. The decimal numeral system, introduced by Muslim mathematicians and popularized by Fibonacci, revolutionized arithmetic and facilitated the growth of commerce and science.

Impact in Contemporary world:

Indeed, the discoveries and advancements of Muslim Mathematicians have been immense and have had a lasting impact on the contemporary world on the field, with many concepts still in use today. Such as, the Muslim contribution in mathematics laid the foundation for modern scientific and technological advancements in the contemporary world. The decimal system and arithmetic operations are fundamental to fields such as engineering, computer science, cryptography, commerce, finance and economics. The Indian numeral system, transmitted through Muslim scholars, revolutionized mathematics and became the basis for modern number representation and computation worldwide. Algebra, trigonometry, geometry and calculus are essential in physics, astronomy, navigation, geodesy, architecture and computer graphics. For example, the astrolabe, a device used for measuring angles and determining the positions of celestial bodies, was developed by Muslim mathematicians and was used for centuries in astronomy and navigation. The use of algebraic equations, geometric principles, and trigonometric functions are essential in modern technologies such as computers and GPS systems. Also the mathematical techniques developed by Muslim scholars have influenced modern statistics, optics, and even art and music.

In addition, the Muslim contribution in mathematics facilitated cultural exchange and globalization. The spread of Islamic civilization allowed for the exchange of mathematical knowledge between different regions, leading to the dissemination of mathematical concepts and techniques. This exchange of knowledge contributed to the development of mathematics as a global discipline. In the end, it can be said that the development of modern mathematics, Science and technology has been achieved by the hands of Muslim scholar.

Conclusion:

The journey of discovery and advancement undertaken by Muslim mathematicians over the centuries has left an indelible mark on the contemporary world. Through their preservation and translation efforts, development of algebra and algorithms, exploration of trigonometry, and influence on modern science and technology, these scholars have shaped the course of mathematics and its applications. The contributions of Muslim mathematicians remind us of the richness and diversity of human intellectual achievements and emphasize the importance of recognizing and appreciating the scientific endeavours of cultures throughout history. Also, the legacy of Muslim mathematicians continues to inspire and influence mathematicians and scientists around the world, serving as a reminder of the rich history of mathematical thought and the importance of cultural diversity in scientific progress.

In conclusion, their work not only laid the foundation for modern mathematics, but also influenced other fields and continues to be used in various aspects of our daily lives. As a quotation of “Human Computer” Shakuntala Devi, "Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers." As such, the contributions of Muslim mathematicians should be recognized and celebrated as an essential part of the global history of mathematics.

.    .    .

Reference:

• Gratten (ed): Companion Encyclopedia of History and Philosphy of Mathematics, vol.I
• Rushdi Rashed: The Development of Arabic Mathematics: Between Arithmetic and Algebra,Translated by Angela Armstrong.
• Ali Abdullah Al-Daffa: The Muslim contribution to Mathematics
• Rushdi Rashed: Encyclopedia of History of Araic Sciences
• Wan Norliza Wan Bakar: Mathematicsin the Holy Quran (Journal of Academic Minds Vol.5 No. 53-64, 2011
• Noor Muhammad Awan: Quran and Mathematics-I (Jihat al-Islam Vol.3 {July-December 2009} No.1)
• Dr Noor Muhammad Awan: Qur’an and Numeral System (Al-Qalam June 2011)
• J L Berggren, Episodes in the Mathematics of Medieval Islam (1986).
• Adrienne Bernhard: How modern mathematics emerged from a lost Islamic library (bbc.com)
• Dr.Zohor Shanan Idrisi ;A Brief Look At Islam’s Contribution to Mathematics (islamreligion.com)
• Zin Eddine Dadach: Muslim Mathematician (Journal: researchgate.net)
• Mufti Fahad Ahmed Qureshi: Contribution of Muslim Scholars: In the Field of Mathematics (Liked.in Jun 5, 2016)
• Dr. Khaled Mahmoud Salim Al-Faqih: A Mathematical Phenomenon in the Quran of Earth-Shattering Proportions: A Quranic Theory Based on Gematria Determining Quran Primary Statistics (words, verses, chapters) and Revealing its Fascinating Connection with the Golden Ratio (Journal of Arts and Humanities, June 2017)
• Encyclopaedia Britannica: Mathematics in the Islamic world (8th–15th century)
• Encyclopaedia Britannica: Islamic contributions
• Encyclopaedia Britannica: Algebra - Islamic Contributions
• Muslim Founders of Mathematics (Muslim heritage)
• Arabic mathematics: forgotten brilliance (Mac Tutor)
• Ten Muslim scientists who contributed to the development of mathematics (Islamic bridge)