Mathematics has evolved over the centuries in The House of Wisdom in Baghdad. Famous scholars such as Muhammad al Khwārizmī, Muhammad al Karaji, Omar Khayyam, and Nasir al Din al Tusi studied at the House of Wisdom and made many important discoveries concerning mathematics.1 Many other important scholars, astronomers, geographers, and mathematicians have studied here. Ever since the 8th century, in this Golden Age, the attitude of these scholars is, "the ink of a scholar is more holy than the blood of a martyr."2
Muhammad al Khwārizmī was a 9th century Persian astronomer, geographer, and mathematician.3 He was famously the director of the house of wisdom. He is famous for revolutionizing the Hindu numbering system (1-9 and 0) and is famous for inventing Algebra. He introduced the methods of reducing and balancing in algebraic expressions. He is the creator of the mathematical language used today.4 As one of the original scholars of the House of Wisdom, he is considered to be an extremely important figure in Islamic Mathematics.
Muhammad al Karaji was a 10th century Persian mathematician and engineer. 5 He studied the algebra of exponents, and 'freed algebra from geometry.'6 He extended algebra into algebraic calculus, and introduced the method of proof by mathematical induction. He is also famous for his binomial theorem and inventing Pascal's Triangle.7
Two centuries later, a poet/astronomer/writer/mathematician named Omar Khayyam revolutionized mathematics again. He came up with methods for finding square, cube, fourth, and beyond roots of numbers. He also developed the idea that there were several types of cubic equations.8 He wrote a very important treatise named the Treatise on Demonstration of Problems of Algebra. It explains a theory for solving cubic equations by intersecting a hyperbole with a circle. 9 A treatise is a paper generally longer than an essay concerning one specific subject. 10 He did not study at the House of Wisdom, but was and still is very influential with his work in mathematics, but his writing and poetry as well. Another work of his is the book On the Difficulties of Euclid's Definitions, the ideas of which led to the development of non-Euclidean geometry11, which is geometry based on the science of absolute statements that cannot be argued. 12
A century later, Nasir al-Din al-Tusi, a Persian astronomer, introduced trigonometry as a separate mathematical discipline. He developed and studied spherical trigonometry and formed the law of sines for plane triangles. 13 He has about 150 works including, but not limited to, Kitāb al-Shakl al-qattāʴ a book on the complete quadrilateral, Al-Tadhkirah fi'ilm al-hay'ah a memoir on the science of astronomy, and Zij-i ilkhani (Ilkhanic Tables) a major astronomical treatise. 14
Unfortunately, the House of Wisdom no longer holds the world's greatest minds or the works of geniuses. It was destroyed by the Mongols around 1258. However, not all was lost. When he fled to Maragheh, Nasir al-Din al-Tusi rescued around 400,000 works and manuscripts.15 Without those, we would not have the mathematical advancement or be at the same level of thinking as we are today. We owe our knowledge to the great minds who studied at the House of Wisdom.
1 (Islamic Mathematics)
2 (Gregorian, 26–38)
4 (Islamic Mathematics) In the time period al Khwārizmī was considered the inventor of Algebra, but it is later revealed that he took most of his work from Greek scholars. In fact, most mathematical advancements of the time are taken from the work of the Greeks.
5 (Christianidis, 260)
6 (Kats, 237)
7(Islamic Mathematics) al Karaji used the triangle long before Blaise Pascal 'invented' it. In fact many Persian, Indians, Chinese, and Italian mathematicians used this triangle before Pascal lived.
9 (Connor, Robertson)
12 (Simpson, Weiner)
13(Islamic Mathematics) He also studied Pascal's Triangle, but that was created long before his lifetime.