Mathematics in Islam: Contributions and Legacy

Dec 3


Yusha Sayyid

Yusha Sayyid

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Have you ever marveled at the intricate geometric patterns adorning ancient Islamic architecture or wondered about the origins of algebra? The fascinating history of mathematics in Islam not only spans centuries but also encompasses a unique blend of Hellenistic, Indian, and Persian knowledge. This wealth of wisdom laid the foundation for many mathematical concepts and techniques that we use today.

Join us as we embark on a journey through the world of mathematics in Islam and discover the brilliant minds and innovations that shaped modern mathematics.

Key Takeaways

  • Islamic mathematics was a result of the fusion of Hellenistic,Mathematics in Islam: Contributions and Legacy Articles Indian and Persian knowledge enriched by Muslim scholars in the 10th century.
  • Pioneers such as Al-Khwarizmi, Omar Khayyam and Thabit ibn Qurra made significant contributions to algebra, cubic equations and geometrical proofs.
  • The legacy of Islamic Mathematics has left a lasting impact on modern mathematical notation & techniques. Transmission to Europe profoundly impacted European mathematics.

The Birth of Islamic Mathematics

Illustration of ancient manuscripts and scrolls representing the birth of Islamic mathematics

Islamic mathematics, a prominent component of the Islamic exact sciences, emerged from the fusion of Hellenistic, Indian, and Persian knowledge, significantly enriched by the contributions of Muslim scholars. The synthesis of Greek and Indian mathematics played a pivotal role in the development of the medieval Islamic world. This amalgamation of cultures and ideas gave rise to a period of flourishing mathematical activity in the 10th century, when Arabic mathematics began to take shape.

Islamic scientists undertook three major mathematical projects during this period. These included the completion of arithmetic algorithms, the development of algebra and the expansion of geometry. Although Islamic mathematicians were already acquainted with negative numbers and negative or zero coefficients from Indian mathematicians, their recognition and use of negative numbers during this period were rather cautious.

The Translation Movement

The Translation Movement, spanning the eighth and ninth centuries, significantly influenced the development of Islamic mathematics. During this period, scholars undertook the monumental task of translating Greek, Persian, and Indian scientific and philosophical works into Arabic. This movement played a significant role in preserving and transmitting knowledge from these civilizations to the Islamic world, underscoring the significant Muslim contribution to mathematics.

Among the many translators of this era, Al-Kindī and Ḥunayn ibn Isḥāq stand out for their remarkable work in translating Greek texts into Arabic during the Abbasid Caliphate, providing the basis for the development of Arabic mathematics. Mathematical texts and theories from Greek mathematicians, such as Euclid, Archimedes, and Ptolemy, were translated, along with Persian, Hindu, and Hebrew mathematical texts. Al-Khwarizmi, a prominent Islamic mathematician, was one of the key figures in this movement. The Translation Movement provided Islamic scholars with access to these texts, fostering advancements in mathematics, including the emergence of algebra, known as “al-jabr” in Arabic, an important Arabic word in the field.

Key Mathematical Centers

Key mathematical centers, such as the House of Wisdom in Baghdad, played a significant role in the growth of Islamic mathematics. Established by the Abbasid caliphs, the House of Wisdom was a royal library that served as a research and educational center, housing a vast collection of books and manuscripts. Other important mathematical centers of the Islamic Golden Age included Khwarazm, Baghdad, and Kufa, all recognized for their substantial contributions to mathematics and scientific discoveries.

The House of Wisdom, in particular, made remarkable contributions to Islamic mathematics, including:

  • The invention of algebra by the mathematician Muhammad ibn Musa al-Khwarizmi, who worked at the House of Wisdom. He is credited as the founder of algebra.
  • The translation of the works of major Greek mathematicians by notable scholars such as Thabit ibn Qurra, a Sabian from Harran in northern Mesopotamia.
  • The discovery of a rule for determining amicable numbers by Thabit ibn Qurra. This rule established a lasting tradition in Islam and demonstrated the far-reaching impact of the work carried out in these mathematical centers.

Pioneers of Islamic Mathematics

Illustration of Al-Khwarizmi, Omar Khayyam, and Thabit ibn Qurra, pioneers of Islamic mathematics

Between the 9th and 12th centuries, several influential Islamic mathematicians left their mark on the world of mathematics. Among them were:

  • Al-Khwarizmi, who made significant contributions to algebra
  • Omar Khayyam, who worked on cubic equations
  • Thabit ibn Qurra, who focused on geometrical proofs

Their work resulted in Islamic mathematicians eradicating the differentiation between magnitude and number, permitting irrational quantities to be presented as coefficients in equations and to be answers to algebraic equations.

The treatise Algebra is attributed to Abū Kāmil Sjujū‘ ibn Aslam ibn Muhammad ibn Shujā, while Al-Kharaj (953 - 1029 CE) applied arithmetic to algebra and authored The Marvellous, in which he developed the algebra of expressions using high powers of the unknown. Al-Kharaj’s technique allowed him to treat equations such as x4 + 4x3 - 6 and 5x6 - (2x2 + 3). These pioneers of Islamic mathematics paved the way for future development and understanding of various mathematical concepts.

Al-Khwarizmi and the Invention of Algebra

Al-Khwarizmi, a Persian mathematician and astronomer, also known as Al Khwārizmī, laid the foundation for algebra as a separate discipline and introduced systematic methods for solving linear and quadratic equations. The word “algebra” itself is derived from the Arabic term for “restoring” found in the title of Al-Khwarizmi’s book, the Book of Restoring and Balancing.

Al-Khwarizmi’s work in algebra was groundbreaking, as he provided the first systematic solution of linear and quadratic equations. His methods for solving these types of equations, along with his contributions to the development of the decimal system, had a lasting impact on the field of mathematics and paved the way for future mathematicians to build upon his work.

Omar Khayyam and Cubic Equations

Omar Khayyam, a Persian mathematician, astronomer, and poet, developed methods for solving cubic equations using geometric techniques. His approach to solving cubic equations was a departure from the algebraic methods used by earlier mathematicians and marked a significant advancement in the field.

Khayyam’s contributions to cubic equations facilitated the understanding of higher-degree polynomials. He employed geometric methods, such as calculating conic sections, to find solutions to cubic equations. His work served as a catalyst for other mathematicians to further investigate and study higher-degree polynomials, paving the way for modern combinatorics.

Thabit ibn Qurra and Geometrical Proofs

Thabit ibn Qurra, a mathematician and astronomer, applied Euclid’s theorems in his algebraic proofs and followed the definition-theorem-proof model. He composed a treatise on geometrical proofs, which showcased his ability to provide flawless proofs of mathematical theorems, such as Menelaus’ theorem.

Ibn Qurra’s contributions to geometrical proofs emphasized the importance of rigorous proof in mathematical reasoning. His work in geometry laid the groundwork for future mathematicians to explore and develop new theorems and methods in the field.

Innovations in Number Systems and Arithmetic

Illustration of ancient numerals and mathematical calculations, representing innovations in number systems and arithmetic in Islamic mathematics

Islamic mathematicians introduced decimal fractions, the decimal system, and the Hindu-Arabic numeral system, revolutionizing arithmetic and calculations. Decimal fractions constituted a substantial development in Islamic mathematics, as Islamic mathematicians were the first to extend the Hindu-Arabic numeral system to denote portions of the unit through decimal fractions.

The introduction of the decimal system by Al-Khwarizmi was a significant turning point in Islamic Mathematics. The application of the decimal system enabled more precise and accurate calculations, making it simpler to carry out complex mathematical operations. This innovation in decimal arithmetic was instrumental in numerous mathematical and scientific advances in the Islamic world.

Decimal Fractions and the Decimal System

Decimal fractions and the decimal system allowed for more efficient and accurate calculations in various fields. Al-Kashi is credited with the introduction of decimal fractions in the Islamic world. The introduction of decimal fractions and the decimal system in Islamic mathematics was a major development, as it marked their first appearance in Arab mathematics.

The use of decimal fractions and the decimal system facilitated more effective and accurate calculations due to the fact that decimals are easier to comprehend, quicker to calculate, and typically more precise than fractions. This development had a profound impact on the field of mathematics and created a pathway for further developments in arithmetic.

Hindu-Arabic Numerals

The Hindu-Arabic numeral system is a set of 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) employed to represent numbers in a decimal number system, which is believed to have originated in India during the 6th or 7th century. The system was subsequently adopted by the Arabs and disseminated to other parts of the world during the eighth century when Islamic incursions occurred in the northern region of India.

The adoption of the Hindu-Arabic numerals brought about a revolution in mathematics, astronomy, engineering, and science within the Islamic world. The system’s positional notation and the inclusion of zero enabled simpler addition, subtraction, multiplication, and division. This system was a noteworthy progression in mathematics and was introduced to the Muslim world by mathematicians such as Al-Khwarizmi.

Advances in Geometry and Trigonometry

Illustration of geometric shapes and trigonometric functions, representing advances in geometry and trigonometry in Islamic mathematics

Islamic mathematicians made notable advances in geometry and trigonometry, including the development of trigonometric functions and spherical trigonometry. These advancements had a lasting impact on various disciplines, such as astronomy, navigation, and engineering, and paved the way for future developments in mathematics.

In the field of plane geometry, Islamic mathematicians achieved remarkable progress, particularly in the area of geometric patterns and designs. They created intricate and sophisticated geometric patterns, such as tessellations and star polygons, which were utilized in architecture, art, and design. These patterns reflected their understanding of symmetry, proportion, and geometric transformations.

Plane and Spherical Geometry

Plane and spherical geometries were expanded upon by Islamic mathematicians, with new theorems and methods being introduced. Islamic mathematicians made considerable contributions to the study of conic sections, including the classification and properties of ellipses, parabolas, and hyperbolas.

Notable Islamic mathematicians, such as:

  • al-Banna
  • Muhammad bin Musa al-Khwarizmi
  • Ibn Yunus
  • Ibn al-Haytham

made important contributions to spherical geometry, including the development of spherical trigonometry, which is essential for precise calculations involving the sphere. These contributions laid the foundation for further advancements in astronomy and navigation.

Trigonometric Functions and Spherical Trigonometry

Trigonometric functions and spherical trigonometry were developed by Islamic mathematicians, leading to the discovery of the law of sines and other important trigonometric relationships. Islamic mathematicians introduced the concept of the sine function, constructed precise trigonometric tables, and made advances in spherical trigonometry, which formed the basis for the trigonometric functions that are still used today.

Abu-Mahmud Khojandi, Nasir al-Din al-Tusi and Abu Nasr Mansur jointly discovered the spherical law of sines. Abu al-Wafa’ Buzjani also contributed to it. This significant mathematical discovery contributed to the development of spherical trigonometry and its applications in various fields, including astronomy, navigation, and engineering.

Mathematical Induction and Combinatorial Methods

Illustration of mathematical induction and combinatorial methods, essential tools in modern mathematics

Islamic mathematicians introduced the concepts of mathematical induction and combinatorial methods, which are key tools in modern mathematics. Mathematical induction is a proof technique employed to establish a statement for all natural numbers and was first used by Islamic mathematicians such as Al-Karaji and al-Samaw’al.

Combinatorial methods were developed and applied to various mathematical problems, paving the way for modern combinatorics. These methods were employed in various disciplines, including algebra, astronomy, and trigonometry, and were instrumental in the development and application of spherical trigonometry in astronomy.

Mathematical Induction

Mathematical induction was first hinted at by Euclid and later explicitly formulated by al-Karaji and al-Samaw’al. Al-Karaji, a renowned mathematician and engineer, made remarkable contributions to mathematics and engineering and employed mathematical induction as a proof technique in his work.

Al-Samaw’al, another significant Islamic mathematician, outlined five propositions related to mathematical induction in his work. He utilized mathematical induction to broaden the scope of arithmetic operations so as to accommodate polynomials and supplied a mathematical proof of both the binomial theorem and Pascal’s triangle.

Combinatorial Methods

Combinatorial methods in mathematics refer to the techniques and principles employed in combinatorics, which is the study of counting and arranging objects. Mathematicians such as Al-Farisi made significant contributions to the development of combinatorial methods by introducing new ideas concerning factorization. These methods were applied in various disciplines, including algebra, astronomy, and trigonometry.

Islamic mathematics was a fusion of Greek and Indian mathematical developments, which led to the creation of polynomial algebra and other advancements. Combinatorial methods were also employed to address various mathematical problems, such as permutations, combinations, graphs, and other combinatorial structures, providing the foundation for modern combinatorics.

The Philosophy of Mathematics in Islam

The philosophy of mathematics in Islam explored the nature of mathematical objects, infinity, and the epistemology of mathematical principles. Muslim philosophers debated the existence of mathematical objects and the concept of infinity, with various arguments and viewpoints being presented.

Islamic philosophers also explored the epistemology of mathematical principles, with some advocating for foundationalist/axiomatic accounts and others emphasizing the role of imagination in understanding mathematics. This rich philosophical exploration of mathematics in Islam provided a deeper understanding of the nature of mathematical knowledge and its relationship to the world.

Mathematical Objects and Infinity

Islamic philosophers debated the existence of mathematical objects and the concept of infinity. Some scholars, such as Ibn Sina, viewed mathematical objects as mental objects, emphasizing intuition and thinking. Others, for example, Avicenna, subscribed to mathematical finitism, suggesting that certain mathematical concepts cannot exist in actuality.

The concept of mathematical objects in Islamic philosophy varies among different scholars and schools of thought. However, the exploration of these concepts has contributed significantly to the understanding of mathematics and its relationship with the physical world.

Epistemology of Mathematical Principles

The epistemology of mathematical principles was explored by Muslim philosophers, who presented various perspectives on how mathematical knowledge is acquired and justified. Most Muslim thinkers have discussed the epistemology of Islam, wherein mathematical concepts are believed to be formed through mathematical concepts.

Islamic mathematicians and philosophers also investigated the role of imagination in mathematical comprehension, viewing it as an instrument for creating idealized objects and concepts. Imagination was perceived as a way to visualize and conceptualize mathematical principles and notions, allowing scholars to better understand the intricacies of mathematical objects and relationships.

The Legacy of Islamic Mathematics

The legacy of Islamic mathematics encompasses its transmission to Europe and the development of modern notation and techniques. Islamic mathematics reached Europe through translations and interactions between scholars, exerting a strong influence on the development of European mathematics.

Islamic mathematicians contributed significantly to modern mathematical notation and techniques. Their key contributions include:

  • The development of algebra
  • The introduction of Arabic numerals
  • Advancements in trigonometry
  • The systematization of mathematical knowledge

These contributions have had a lasting and profound impact on modern mathematical notation and techniques.

Transmission to Europe

Islamic mathematics was transmitted to Europe through translations and interactions between scholars during the 10th to 12th centuries. European scholars such as Gerard of Cremona, Adelard of Bath, and Fibonacci translated Islamic mathematical works, making them accessible to the European intellectual community.

As a result, Europe adopted several mathematical concepts from Islamic mathematics, including:

  • Arabic numerals
  • Algebra
  • Trigonometry
  • Algorithms

The transmission of Islamic mathematics to Europe significantly influenced the development of European mathematics and laid the groundwork for the Scientific Revolution.

Modern Notation and Techniques

Modern notation and techniques in mathematics can be traced back to the contributions and innovations of Islamic mathematicians. The use of Arabic numerals and algebraic notation, as well as significant contributions to trigonometry and geometry, provided the basis for the symbolic representation and manipulation of mathematical equations.

From the development of algebra by Al-Khwarizmi to the geometric methods employed by Omar Khayyam for solving cubic equations, Islamic mathematicians laid the foundation for modern mathematical notation and techniques. Their work has had a lasting impact on the field of mathematics and continues to inspire mathematicians to this day.


Throughout history, Islamic mathematicians have made remarkable contributions to the world of mathematics, from the development of algebra to advances in geometry and trigonometry. Their innovative methods and techniques laid the groundwork for modern mathematics, influencing the development of European mathematics and paving the way for future generations of mathematicians. As we continue to explore the fascinating world of mathematics, let us remember the rich legacy of Islamic mathematics and the brilliant minds that shaped it.

Frequently Asked Questions

What are the facts about math in Islam?

Muslim mathematicians played a pivotal role in developing the mathematical systems we use today, introducing zero to the Arab and European worlds and creating the present arithmetical decimal system with the fundamental operations connected to it. They also adopted Indian numerals, developed algebra, used decimals, practiced mathematical induction, and created trigonometry.

Who is the most famous Muslim mathematician?

Muhammad ibn Musa al-Khwarizmi, a Persian Shi'a Muslim mathematician, astronomer, astrologer and geographer of the Islamic Golden Age, is the most famous Muslim mathematician. His many contributions include several influential treatises and the terms algorithm and algebra.

What were the main influences on Islamic mathematics?

Islamic mathematics was significantly influenced by both Greek and Indian mathematics, playing an integral role in the development of the medieval Islamic world.

What was the Islamic Translation Movement and its importance to Islamic mathematics?

The Islamic Translation Movement of the 8th and 9th centuries was pivotal for the preservation and transmission of knowledge from other civilizations to the Islamic world, providing the basis for the development of Islamic mathematics. This movement allowed for significant Muslim contributions to the field.