Islamic Mathematics



Abstract


This project will provide a summery of the transmission of Greek mathematics through the Islamic world, the resulting development of algebra by Muhammad ibn Mūsā al-Khwārizmī, and the applications of Islamic algebra in modern mathematics through the formulation of the Fundamental Theorem of Algebra. In addition to this, I will attempt to address several cultural issues surrounding the development of algebra by Persian mathematicians and the transmission of Greek mathematics through Islamic mathematicians. These cultural issues include the following questions:


  • Why was the geometry of Euclid transmitted verbatim while algebra was created and innovated by Muslim mathematicians?
  • Why didn’t the Persian mathematicians expand or invent new theorems or proofs, though they preserved the definition-theorem-proof model for geometry? In addition, why did the definition-theorem-proof model not carry over from Greek mathematics (such as geometry) to algebra?
  • Why were most of the leading mathematicians, in this time period, Muslim? In addition, why were there no Jewish mathematicians until recently? Why were there no Orthodox or Arab Christian mathematicians?


Sources


Al-Daffa, Ali Abdullah. The Muslim Contribution to Mathematics. London: Croom Helm Ltd, 1977.


Bashmakova, Isabella, and Galina Smirnova. The Beginnings and Evolution of Algebra. transl. Abe Shenitzer, ed. David Cox. Washington, DC: The Mathematical Association of America, 2000.


Berggren, J. Lennart. Episodes in the Mathematics of Medieval Islam. New York, NY: Springer-Verlag, 1986.


Berggren, J. Lennart. “Mathematics in Medieval Islam,” in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. ed. Victor J. Katz. Princeton, NJ: Princeton University Press, 2007.


Boyer, Carl. “The Arabic Hegemony,” in A History of Mathematics. Revised by Uta Merzbach. New York, NY: John Wiley & Sons Inc, 1991.


Mohamed, Mohini. The Lives and Contributions of Selected Non-Western Mathematicians During the Islamic Medieval Civilization. Temple University. Ann Arbor, MI: University Microfilms International, 1990.


Papantonopoulou, Aigli. Algebra, Pure & Applied. Upper Saddle River, NJ: Prentice Hall, 2002.


Turner, Howard. “Forces and Bonds: Faith, Language, and Thought,” and “Mathematics: Native Tongue of Science,” in Science in Medieval Islam. Austin, TX: University of Texas Press, 1995.


van der Waerden, B. L. A History of Algebra: From al-Khwārizmī to Emmy Noether. New York, NY: Springer-Verlag, 1980.