Discoveries in Algebra

On algebra, we have an exhaustive list of discoveries, including algebra itself:

. Founded algebra as the science of Al-Jabr and Al-muqabala, or completion and balancing (Muhammad Ibn Musa Al-Khwarizmi).

. Generated a Pascal Triangle and almost gave a rigorous proof for the coefficients of a binomial expansion, and advancede the binomial theorem, arguably the most significant theorem in algebra save the fundamental theorem of algebra (Abu Bakr Al-Kharaji).

• Gave extensive and algorithmic solutions to ax² = bx, ax² = c, ax² = bx =c, ax² + c = bx, and bx+c = = ax², where a, b, and c are coefficients (Muhammad Ibn Musa AlKhwarizmi).

Solved quadratic equations by “completing the square” (Muhammad Ibn Musa AlKhwarizmi)

• Transitioned algebra as a science away from geometry and closer to modern arithmetic (Abu Bakr Al-Karaji).

. Almost gave the following property: x xn Bakr Al-Karaji) – xm+n, but did not define xº = 1 (Abu

An excerpt from Al-Khwarizmi’s algebra book, The Compendious Book on Calculation by Completion and Balancing which was used in Europe as the main text for algebra until the 16th century [10].

On Mathematical logic, we only have the use of premodern induction, and this is due to math’s only historically recent formulation of (and emphasis on) proof writing and logic.

**Conclusion***“Everything is Political” -Thomas Mann**“[Mathematics] finally secured a firm grip on life in the highly congenial soil of Greece and waxed stronglhy for a short period… With the decline of Greek civilisation, the plant reamined dormant for a thousand years… when the plant was transported to Europe proper and once more imbedded in fertile soil” **One cannot understate the impact of Islam in its contribution to mathematics. Indeed, almost all topics in mathematics, including but not limited to algebra, arithmetic, trigonometry, geometry, number theory, (informal) calculus, logic, and applied engineering, were all pushed to greater heights due to Islam’s mandate of seeking knowledge.**Now, as apolitical as it may seem, the discipline of mathematics is perhaps the most latently political. The vast majority of math historians, professors, and teachers know that the mathematical curriculum across the U.S. (and Europe) emphasize European Renaissance mathematics to the disadvantage of Babylonian, Chinese, Indian, and Islamic mathematics. However, just as the ancient Greeks acknowledged the triumphs in math of the ancient Egyptians and Babylonians, we too (The West) should acknowledge the debt we owe to Islamic empires [17]. Interestingly, we see that The European Renaissance relied heavily on**Plato and Plutarch acknowledged Egyptian advancements in math, astronomy, and other dicspilines. Thales and Pythagroas traveled to Egypt and Babylonia to learn about math. the mathematical, medical, and scientific discoveries of muslim scholars of the medieval age, discoveries which later became the building blocks of the current western world. so, how can we (the west), ensure mathematics veers towards a purely scientific science? this can occur through the teaching of multiculturism in math classrooms.**firstly, a multicultural approach allows students of all heritages to be proud of their heritages’ contributions to math. a multicultural approach paints math as a universal discipline, inconsistent with just european ambition, and consistent with babylonian, greek, egyptian, indian, chinese, islamic, and european ideas. a specific way to incorporate multiculturalism in mathematicians is through the naming and renaming of theorems, results, and ideas in the mathematical discipline.**for instance, though the pythagorean theorem is named after pythagoras, a brilliant mathematician in greek civilization, the theorem was used time and again by egyptians, ancient mesopotamians, and northern europeans centuries before the height of greek innovation. renaming of theorems and results leads to the exhibition of the inherent multiculturalism embedded in the study of mathematics.**math need be presented as a discipline interconnected between cultures, sought after by all, innovated incrementally by various civilizations, and discovered by indians, chinese, europeans, muslims, and others alike. math can be done, irrespective of creed, color, or origin, and different civilizations’ contributions should be emphasized in math classrooms from k-12 and beyond. this paper puts into perspective that one such creed and it’s followers, islam and muslims, have indeed contributed to mathematics, more so than meets the eye, and more so than what is taught.*