Arab Mathematics Bridges the Dark Ages. early fourth century and the European Giants in the seventeenth and eighteenth

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1 John Griffith Arab Mathematics Bridges the Dark Ages When most people think of Mathematics, they tend to think of people like Plato, Aristotle, Newton, Leibniz, and a plethora of Greek Mathematicians. Although there is no denying the everlasting impact these great thinkers had on the field of mathematics, what bridged the gap between the decline of Greek Mathematics in the early fourth century and the European Giants in the seventeenth and eighteenth centuries? Was there a period of 1300 plus years where no mathematical innovation occurred? Did Newton Leibniz, and others simply pick up were the Greeks left off? To put it simply, the answer is no. In fact, Newton and Leibniz were not standing directly on the shoulders of the great Greek philosophers, but rather they were standing on centuries of preservation and innovation set forth by Arab Mathematicians. Although the Arab Empire lasted from approximately the seventh century until the fourteenth century and were making advancements, particularly in mathematics, all along the way, we are going to focus on the influences in the preservation of Greek Mathematics and one man from the ninth century, the height of the Arab Empire. This man is Muḥammad ibn Mūsā al-khwārizmī. The reason we will focus specifically on al-khwārizmī is because he is the most remembered mathematician of the time, and he embodies much of what the region is remembered for. Out of all of his accomplishments, we will focus on his contributions to algebra and his efforts towards the Hindu-Arabic number system, which we still use today.

2 Long before al-khwārizmī began his work into algebra and numeric systems, the Arab Empire had been at work translating ancient Greek writings into Arabic. Although the translating of words may not seem worthy of mentioning when talking about the history of mathematics, it is important to note that these translators were not translating merely for the sake of translating. In J L Berggren s, Mathematics in Medieval Islam, he recalls some of the more important works: Of Euclid's works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes' works only two - Sphere and Cylinder and Measurement of the Circle - are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apollonius's works were translated, and of Diophantus and Menelaus one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of Ptolemy's Almagest furnished important astronomical material. The works just mentioned are all influential in the world of mathematics, even today. If not for the work of Arab research, many of them would have been lost during the rise of the Roman Empire when much Greek thought was suppressed by the rise of Christianity. Along with these straightforward translations, many of the Arabic manuscripts contain notes, corrections, and thoughts. The translation of these manuscripts paved the path for original thought by mathematicians such as al- Khwārizmī. One of the most significant contributions to mathematics by the Arab Empire was al-khwārizmī s influence on algebra. His book Al-jabr w al-muqubala is actually where we obtain the word algebra from, by using a Latin derivation of the word Aljabar. It is important to note the al-khwārizmī did not actually invent the field of algebra; many of the ideas that he brings forth were variations on thoughts from Greek philosophers. The important distinction to make between the two is that

Greek philosophers tended to look at everything geometrically, while al-khwārizmī created a way for rational numbers, irrational numbers, geometrical magnitudes, etc.

3 Greek philosophers tended to look at everything geometrically, while al-khwārizmī created a way for rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as algebraic objects. To better understand exactly what al- Khwārizmī did, let s look at his solution to x 2 +10x = 39: The method denoted above is a visual representation of what it means to complete the square, a method that we still use in algebra today. Along with his method for completing the square, he accomplished much more in the field of mathematics, like solving quadratic equations. What made al-khwārizmī s writings even more impressive is the fact that he did not use any mathematical notation. This means that everything he wrote about was written in enough detail for later generations to understand what he meant. In reality, al-khwārizmī s most significant contributions to mathematics are much more than teaching how to manipulate algebraic equations. His influence is more about his successors now thinking about

mathematics algebraically and not geometrically. One last thing to mention when talking about al-khwārizmī is his influence on the modern numeric system.

4 mathematics algebraically and not geometrically. One last thing to mention when talking about al-khwārizmī is his influence on the modern numeric system. There isn t nearly as much to say about how the numeric system came around as there is about the influence that it had on the future of mathematics. The number system is first described in Al-Khwarizmi's On the Calculation with Hindu Numerals. To understand the influence, it is most beneficial to see the evolution of the numbering systems: As we already know, the beginning of the modern numeric system that allowed us to move away from Roman numerals and towards what we see above was in India, but it is also clear that it did not jump directly from the Indian numbering system to the European numbering system. Al-Khwārizmī s book laid out his understanding of the Indian numbering system, and more famously laid out Al-Uqlidisi s method for writing decimal fractions. These small changes in the numeric system and how

5 numbers were written helped pave the way for the European mathematicians that we know. Today, much of the history that we look at is from the point of view of Western Europe. This means that when we think of the fifth to the fifteenth century, we tend to think of the Dark Ages. In reality, when Europe was in a time of cultural and intellectual stagnation, the Arab empire was thriving in both of those sectors and bearing the burden of preserving history. When Europe began to pull itself out of the Dark Ages, much of the credit should go to the Arab Empire. Although they had already been on the decline for a few centuries, it was their influence and diligence that allowed for intellectual thought to continue and allowed mathematicians such as Newton and Leibniz to thrive.

6 Bibliography 1. Robertson, E F. Forgotten brilliance? Arabic mathematics, wwwgroups.dcs.st-and.ac.uk/history/histtopics/arabic_mathematics.html. 2. Allen, Don. Arab Contributions, 6 Mar. 1997, 3. Mastin, Luke. Al-Khwarizmi - Islamic Mathematics - The Story of Mathematics, 2010, 4. Algebra and Trigonometry. PBS, Public Broadcasting Service, 5. The Editors of Encyclopædia Britannica. Hindu-Arabic numerals. Encyclopædia Britannica, Encyclopædia Britannica, inc., 8 Sept. 2017,

The Emergence of Medieval Mathematics. The Medieval time period, or the Middle Ages as it is also known, is a time period in

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