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

Transcription

1 The Emergence of Medieval Mathematics The Medieval time period, or the Middle Ages as it is also known, is a time period in history marked by the fall of the Roman civilization in the 5 th century to the Renaissance which began around the 15 th century. This time period is usually associated with the medieval knights, wars, and crusades of the European perspective. While all this conflict filled Europe, the Christian religion replaced efforts into mathematics for some time. However, this time period was also marked with the birth or rather blooming of mathematics in other parts of the world. The secluded China was busy developing their own mathematics to solve their own practical problems. The Hindu were making breakthroughs in concepts such as zero being a number, and the Arabians were also busy as the argued Father of Algebra 1 emerged. Despite some countries being in the dark of the mathematical world, others began to flourish and contribute to its history. As religion began to sweep across Europe during the Middle ages, the region began to see a decline in learning mathematics for nearly 700 years 2. This period of religion, as stated by Morris Kline 3, was due to Christianity leading the people of the time to seek spiritual knowledge and ready themselves for the afterlife which caused other teachings especially mathematics to decline or be abandoned. However, despite the decline over the extensive amount of time learning did not completely disappear. The rise of mathematics in Medieval Europe began in the High Middle Age and continued to grow into the Late Middle Age. This new movement was led by the church, as it began pushing to preserve knowledge and to increase literacy among the 1 Ayyubi, N Akmal. Contribution of Al-Khwarizmi to Mathematics and Geography. Contribution of Al- Khwarizmi to Mathematics and Geography Muslim Heritage, 2 Ji, Shanyu. History of Mathematics. Lecture Oct Page Morris Kline, Mathematical Thought from Ancient to Modern Times, volume 1, New York Oxford, Oxford University Press, 1972, p.204

2 people of the church 4. With the new movement to preserve knowledge came the introduction of universities such as Bologna and Oxford. The rise in intellectual thought and drive to learn brought about a new wave of efforts that influenced mathematics. Leonardo Pisano of Italy ( ), also known as Fibonacci, made a lasting influence in number theory with his widely known Fibonacci sequence. The sequence was derived from a problem in his book Liber abaci of when he studied the rate of which rabbits multiplied 5. It became the first recursive sequence in Europe 6 and is still used today. Another contributor is Nicole Oresme ( ) who made contributions in convergent series, kinematics, and in the theories of infinites. Oresme s contributions also led to him proving that the Harmonic series diverges to infinity by using the sum of a group of terms to be at least ½. He also concluded that infinites are not comparable in and inequality view point 7. However despite the reemergence of mathematics, Europe was still struggling as conflicts such as the Hundred Year War, the War of the Roses, and also The Black Plague made European contributions to slow down. In another part of the world was a secluded Chinese empire. Chinese mathematics during the thirteenth century made a huge mathematical contribution with Qin Jiushao. Qin Jiushao ( ) wrote the book Mathematical Treatise in Nine Sections in 1247 and included the Chinese remainder theorem and also work on how to solve quadratic equations up to a tenth 4 Christianity in the Middle Ages. Wikipedia, Wikimedia Foundation, 6 Oct. 2018, en.wikipedia.org/wiki/christianity_in_the_middle_ages. 5 Ji, Shanyu. History of Mathematics. Appendix Oct Page 1 6 Gies, Frances Carney. Fibonacci. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 11 June 2018, 7 Kirschner, Stefan. Nicole Oresme. Stanford Encyclopedia of Philosophy, Stanford University, 28 Aug. 2017, plato.stanford.edu/entries/nicole-oresme/#mat.

3 degree 8. His work also introduces the use of zero as a number and symbol, which added a new concept from India to be used more in the world of mathematics. Zhu Shijie (1250 early 1300s) was another important contributor of mathematics during the medieval time period. Zhu Shijie was most know for Introduction to Mathematical Science written in 1299 and Jade Mirror of the Four Elements written in While the Introduction of Mathematical Science influenced the math world in other countries. Zhu Shijie s other book Jade mirror of the Four Elements was his most famous and likely influenced the whole world. This book covered elements that predated methods well before their time, such Horner s synthetic division and modern matrix methods to solve polynomial equations with more than three variables 10. These created a strong foundation of Chinese mathematics and solidified its developments in the history of mathematics for all time. Unlike China, India was not as secluded and could see influences from places such as Alexandria 11. From the influences and practical representations, India introduced negative numbers, accepted the concept of irrational numbers, and also introduced the use of sine, cosine, and tangent 12. One of the most notable contributions was the addition of zero into the counting system as an empty circle, Brahmagupta ( ) was one of the main Indian mathematicians that used zero and introduced methods such as A positive number multiplied by 8 Carr, K.E. Math and Numbers in Ancient China. Quatr.us Study Guides, June 7, Web. October 14, Horiuchi, Annick. Zhu Shijie. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 16 Jan. 2017, 10 Jade Mirror of the Four Unknowns. Wikipedia, Wikimedia Foundation, 31 Aug. 2018, en.wikipedia.org/wiki/jade_mirror_of_the_four_unknowns. 11 Ji, Shanyu. History of Mathematics. Lecture Oct Page Mastin, Luke. Indian Mathematics. Indian Mathematics - The Story of Mathematics, 2010, 13 Carr, K.E. Invention of Zero Indian Numbers History of Mathematics. Quatr.us Study Guides, July 22, Web. October 14, 2018

4 a negative number is negative 14. Brahmagupta also had found a formula for the area of a cyclic quadrilateral however lacked a geometric proof. With Hindu mathematics on the rise, just across the Arabian Sea other mathematicians were at work. Along with India, the Arabs were also active during the Middle ages. A contribution and combined effort of Arabic and Hindu math, was the inclusion of zero as a place value in a numerical system 15. The main contribution comes from the fact that the Arabs had obtained manuscripts and books of Greek origin and had all the essential works from the famous Greek mathematicians, as well as works from Indian mathematicians. With these manuscripts, the Arabs studied, translated 16, and copied the material ultimately preserving them, as this made the ancient works available to the world. Another contribution from the Arabs was from the Arabic mathematician Muḥammad ibn Mūsā al-khwārizmī ( ) who is also known as the Father of Algebra 1. His contributions to the math are from his book Al-jabr w al-muqubala which include the foundation of modern day algebra and led to a uniformity of abstract Greek mathematics with concrete visualizations and equations. Although the Middle Ages were filled with the spread of religion, wars, and plague in Europe, it did not stop the rest of the world to continue its progress and contribute to the world of mathematics. Math as an idea drove some countries to achieve scientific heights, introduce new concepts, and even preserve ancient history. With gaps of no progress, Europe made efforts and progressed in education and mathematics towards the middle and end of the time period. China worked on its own methods that would later influence modern math. All while, Indian and 14 Home. Famous Mathematicians, 2018, famous-mathematicians.com/brahmagupta/. 15 Ji, Shanyu. History of Mathematics. Lecture Oct Page Ji, Shanyu. History of Mathematics. Lecture Oct Page Ayyubi, N Akmal. Contribution of Al-Khwarizmi to Mathematics and Geography. Contribution of Al- Khwarizmi to Mathematics and Geography Muslim Heritage

5 Arabic mathematics took new concepts and began to preserve and influence the rest of the world through math.

6 Sources 1. Ayyubi, N Akmal. Contribution of Al-Khwarizmi to Mathematics and Geography. Contribution of Al-Khwarizmi to Mathematics and Geography Muslim Heritage, 2. Ji, Shanyu. History of Mathematics. Lecture Oct Page Morris Kline, Mathematical Thought from Ancient to Modern Times, volume 1, New York Oxford, Oxford University Press, 1972, p Christianity in the Middle Ages. Wikipedia, Wikimedia Foundation, 6 Oct. 2018, en.wikipedia.org/wiki/christianity_in_the_middle_ages. 5. Ji, Shanyu. History of Mathematics. Appendix Oct Page 1 6. Gies, Frances Carney. Fibonacci. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 11 June 2018, 7. Kirschner, Stefan. Nicole Oresme. Stanford Encyclopedia of Philosophy, Stanford University, 28 Aug. 2017, plato.stanford.edu/entries/nicole-oresme/#mat. 8. Carr, K.E. Math and Numbers in Ancient China. Quatr.us Study Guides, June 7, Web. October 14, Horiuchi, Annick. Zhu Shijie. Encyclopædia Britannica, Encyclopædia Britannica, Inc., 16 Jan. 2017, Jade Mirror of the Four Unknowns. Wikipedia, Wikimedia Foundation, 31 Aug. 2018, en.wikipedia.org/wiki/jade_mirror_of_the_four_unknowns. 11. Ji, Shanyu. History of Mathematics. Lecture Oct Page Mastin, Luke. Indian Mathematics. Indian Mathematics - The Story of Mathematics, 2010, Carr, K.E. Invention of Zero Indian Numbers History of Mathematics. Quatr.us Study Guides, July 22, Web. October 14, Home. Famous Mathematicians, 2018, famous-mathematicians.com/brahmagupta/. 15. Ji, Shanyu. History of Mathematics. Lecture Oct Page Ji, Shanyu. History of Mathematics. Lecture Oct Page