Al-Khwarizmi wrote a book called “The Compendious Book on Calculation by Completion and Balancing.” He systemized the book and integrated notions from Greek theoretical mathematics. He solved quadratic calculations and formulas were written using words, with no symbols or numbers. This is known as rhetoric algebra.
Al-Khwarizmi classified three terms; the square root, the root multiplied by a numerical coefficient, and known numbers. Which were then further divided into six definitive types that have their own solving algorithms. He created geometric figures to illustrate algebraic quantities and established algorithms by the “cut-and-paste” method. Which was created by Babylonian mathematicians.
Algebra from Islam was spread by the abacus school. The abacists spread the knowledge of numeracy, abbreviations and symbolism. Examples of the terms they used were: cosa, censo, and cubo. Powers were emerged into these terms. Also, mathematical figures like +, -, =, √ were born. As these methods spread to northern countries, algebra became known as the cossic art.
A new concept of numbers was established where theory and practice were combined. This was constructed by Simon Stevin at the end of the 16th century. He claimed that, “numbers must include continuous quantities, one, fractions, surds and other irrational quantities.”
Francois Viète, a French mathematician regarded algebra as a “corrupt remnants of the ancient Greeks.” He suggested better symbolism. Where vowels were used to express unknowns, consonants for given quantities and cossist signs for operations. He used these to study the structure of equations and solutions. And favoured the principle of homogeneity.
Thereafter, Rene Descartes published his work called, “La Geometrie” in 1637. He established a “new interpretation of multiplication and powers based on the theory of proportions.” He also included Stevin’s definition of numbers and Viète’s mathematical symbols, which therefore created symbolic algebra.
To conclude, the evolution of algebra and numbers didn’t develop from nothing. It also did not stay the same but altered over time as new discoveries emerged.