Mathematics in Islamic Civilization

Definition and Etymology

Mathematics (Arabic: علم الحساب or ʿilm al-ḥisāb, Turkish: matematik) refers to the study of numbers, quantities, and shapes, as well as the relationships between them. In medieval Islamic civilization, scholars made significant contributions to mathematics by building upon Indian and Greek sources.

Key Contributions and Developments

Arabic Numerals

One of the most notable contributions is the place-value system of decimal numbers. These numerals, often known as Arabic numerals, became the foundation for modern numerical systems. Islamic mathematicians adopted the use of zero (sifr), which was a revolutionary concept allowing more advanced calculations.

Decimal Fractions and Irrational Numbers

Islamic scholars made strides in the study of decimal fractions and irrational numbers. They expanded upon Indian decimal techniques and translated and commented on Greek works, incorporating them into a more systematic framework.

Algebra

The term “algebra” derives from the Arabic word الجبر (al-jabr), which appears in the title of Al-Khwarizmi’s key work, “Kitab al-Jabr wa-l-Muqabala” (The Book of Completion and Balancing). This text laid the groundwork for algebra as a distinct mathematical discipline.

Trigonometry and Geometry

In trigonometry, Islamic scholars calculated trigonometric functions such as sine, cosine, and tangent with remarkable precision. Their work in geometry extended Greek traditions and integrated them with new, innovative methods.

Prominent Islamic Mathematicians

Al-Khwarizmi

Often called the “father of algebra,” Muhammad ibn Musa al-Khwarizmi’s works were foundational in establishing the fields of algebra and algorithms. His texts were translated into Latin, significantly influencing European mathematics.

Al-Biruni

A polymath whose works covered various scientific disciplines, Al-Biruni made essential contributions to geometry and trigonometry, as well as geographic measurements and mapping.

Omar Khayyam

Known for his poetry as well as his scholarly endeavors, Omar Khayyam made key contributions to the cubic equations and developed geometrical solutions.

Books for Further Reading

• “A History of Mathematics” by Carl B. Boyer - This book provides an in-depth look at the development of mathematics, including substantial material on the contributions from Islamic civilizations.
• “Mathematics in the Medieval Islamic World: A Volume of Studies” by J. L. Berggren - Offers comprehensive studies on various aspects of Islamic mathematical sciences.
• “Islamic Science and the Making of the European Renaissance” by George Saliba - Investigates the role that Islamic science played in shaping the European Renaissance, with an emphasis on mathematics.

Takeaways and Conclusion

The mathematical advancements developed in the medieval Islamic world laid the foundation for numerous areas of modern mathematics. Scholars harnessed the knowledge from Indian and Greek traditions to introduce innovations such as Arabic numerals, the concept of zero, algebra, and sophisticated geometric and trigonometric analyses. Their works had a lasting influence, extending their impact into the modern age.

Islamic mathematicians, through intercultural scholarly dialogue, substantially enriched mathematical sciences, emphasizing the global and timeless nature of scientific development.

By expanding our knowledge of mathematical developments in Islamic civilization, we gain insight into the rich, interconnected history of scientific progress that continues to shape the world today.