The development of algebra is a fascinating story of mathematical innovation that spans several ancient civilizations and continued to evolve through the medieval period and into modern times. 

Here is an overview of its development:

1. Ancient Beginnings:
   • Babylonian Mathematics: Around 1800 BCE, Babylonian mathematicians developed advanced arithmetic techniques to solve quadratic equations. They used tables to find squares and inverted factors, which are early instances of algebraic thinking.
   • Greek Contributions: Although Greek mathematicians like Diophantus of Alexandria (circa 250 CE) made significant contributions to algebra, focusing on solving linear and quadratic equations, their approach was more arithmetical and geometric rather than symbolic, which is central to contemporary algebra.
2. Indian Contributions:
   • Indian mathematicians made significant strides in the field of algebra. Aryabhata (5th century CE) and Brahmagupta (7th century CE) presented methods for solving algebraic problems and the general solution for quadratic equations, including negative and zero values.
3. Islamic Golden Age:
   • Al-Khwarizmi: Often referred to as the “father of algebra,” the Persian mathematician Al-Khwarizmi wrote “Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala” in the early 9th century. This work, the title of which contains the word “al-jabr,” meaning “completion” or “restoration,” is where the term “algebra” originates. The text laid groundwork for a systematic approach to solving linear and quadratic equations using an algebraic method.
   • Al-Khwarizmi’s Approach: He established methods for transforming equations to simpler forms, which involved balancing (muqabala) and restoration (al-jabr). This systematic approach was later expanded upon by other Islamic scholars.
4. Medieval and Renaissance Europe:
   • Translation Movement: Arab mathematical works, including those of Al-Khwarizmi, were translated into Latin in the 12th century, making their way to Europe and boosting the development of mathematics there.
   • Development of Symbolic Algebra: Mathematicians such as Leonardo of Pisa (Fibonacci) and later René Descartes and François Viète in the 16th and 17th centuries contributed to the development of symbolic notation, which brought about the modern notion of algebra as an abstract subject.
5. Modern Algebra:
   • Abstract Algebra: In the 19th and 20th centuries, algebra evolved to include structures like groups, rings, and fields, forming the branch of mathematics known as abstract algebra. This was advanced by mathematicians such as Évariste Galois and Emmy Noether.
   • Linear Algebra and Beyond: Linear algebra, dealing with vector spaces and linear mappings between these spaces, became formalized and pivotal in the context of multi-dimensional spaces, finding applications across numerous scientific disciplines.

The development of algebra reflects a cumulative tradition of mathematical thought. It has transformed from practical arithmetic procedures into an abstract and highly symbolic discipline, crucial for various branches of mathematics and countless applications in science and engineering.

Written by AI. A more correct, God given, explanation can be found here.