The invention of Algebra.
Algebraic problems have been used ever since the mathematical writings of the Egyptians and Babylonians which used clay tablets that we have preserved and gained knowledge that we know today. As found in research, Algebra started over 4000 years ago by the Babylonians, who were discovering how to use mathematics to perform ways of daily life, and to evolve as a dominant civilization. For both civilizations (Babylonian and the Muslim), Algebra was used for finance, engineering, calculation of land, and several more. Greatly used for separating land, and constructing buildings correctly.
[13] Scholars in library of the ‘House of Wisdom’, Baghdad 1237 AD
The House of Wisdom was established by the 9th Century by caliph al-Rashid. It was mainly a library, a place for translation, and researching.
Algebra has been used the same ever since the Babylonians. It was even used in calculating the longitude of the sun and moon, and helped in the making of jewish calendar. Mathematics from the medievel Middle East is still important in modern days, as we still use it today.
For todays use of Algebra which still impacts civilization and is used everyday. It is used for measuring and calculating ingredients for food, finding out the distance of time, estimate time arrivals, and cost of loans or finance in general just like how the Babylonians would use algebra! High school mathematics in algebra were fully finisished by 1750.
[3] Tracing the algorithm: Al-Khwarizmi, the 9th century muslim mastermind behind the algebraic function.
The father of algebra is “Al-Khwarizmi” who is credited with Islamic algebra and was most likely born in Khwārizm south of the Aral Sea. Al-Khwarizmi had great impacts in the states six basic types of equations, and explains how no non-negative coefficients were used for the introduction of "0" (zero).
Zero is neither a positive number, nor a negative. One of algebra's most important innovations was in the 9th century when Al-Khwarizmi wrote the book "Al-Jabr" which possibly meant "restoration" or "completion" which introduced systematic methods for for solving equations. Al-Khwarizmi also discussed methods of extracting the square root, which was adapted by the Hindu sources.
[21] The earliest extant map of the Nile by Muhammad ibn Musa al-Khwarizmi