The History of Algebra

Introduction

Mathematics as a subject can be broadly divided into three significant branches Arithmetic, Algebra, and Geometry. Algebra is considered to be one of the oldest components in the history of mathematics. Algebra deals with the study of symbols, exponentials, known and unknown variables, and equations. The History of Algebra has been dealt with in detail here.

What Is Algebra?

The Number Theory, Geometry, and their analysis put together to make an extensive part of mathematics which is known as "Algebra". In other words, Algebra is a part of mathematics that deals with symbols and the rules to calculate those symbols.

Also read:

• Algebra in Real Life
• Algebra vs Calculus

History Of Algebra

Muhammad ibn Musa al-Khwarizmi was a Persian mathematician who wrote a book named Kitab Al Muhtasar fi Hisab Al Gabr Wa I Muqabala in the Arabic language, which was later translated into English as " The Compendious Book on Calculation by Completion and Balancing", from which the word ALGEBRA was derived. The book provides a systematic solution for linear and quadratic equations.

According to Al-Khwarizmi, the word algebra is described as 'reduction' and 'balancing' of subtracted terms that is a transposition to other sides of the equation (cancellation of like terms).

There are some renowned mathematicians from different countries who have made significant contributions in this subject, such as, the Babylonians, the ancient Egyptians, the Chinese, the Greek, and the Indians (Aryabhatta, Brahmagupta, Bhaskara)

Developmental Stages Of Algebra

There are three critical developmental stages in "Symbolic Algebra" which is as follows :

1. Rhetorical Algebra

It was developed by ancient Babylonians where the equation was written in the form of words that remained up to the 16th century.

Example: x + 5 = 8, is written as " The thing plus five equal to eight"

2. Syncopated Algebra

Its expression first appeared in Diophantus Arithmetica (3rd century ) Brahmagupta's "Brahmagupta's sputa Siddhanta" (9th century), where few symbols were used, and subtraction was used only once in the equation.

3. Symbolic Algebra

At this stage, all the symbols were used in Algebra. Many Islamic mathematicians like Ibn Al-Banna and Al Qalasadi wrote in their books about Symbolic Algebra. Francois Viete fully developed it in the 16th century. Rene Descartes introduced a modern notation that can solve geometrical problems in terms of algebra known as Cartesian Geometry.

\[\begin{align}&x^2 + px = q\\[6pt]&x^2 = px + q\\[6pt]&x^2 + q = px \end{align}\]

In early algebra, Quadratic equations played an important role, where it is said to belong one among the above three equations.

# The Greeks and Vedic Indian Mathematicians developed two more stages of algebra which lie between rhetorical and syncopated stages known as Geometric Constructive stages.

Contributions of different countries

I. Babylon

Ancient Babylonians developed a rhetorical stage of algebra where equations were written in the form of words. They used linear interpolation to approximate intermediate values as they were not interested more in exact solutions. Plimpton 322 tablet, one of the most famous tablets designed around 1900 - 1600 BC gives the tables of "Pythagorean Triplets".

Learn more about the .

Following are the significant contributions :

• They developed flexible algebraic operations to eliminate fractions and factors by adding equals to equals and multiplying like quantities on both sides of the equation.
• They also knew simple forms of factoring, three-term quadratic equations with the positive term, and cubic equations

II. Ancient Egypt

Ahmed, an Egyptian mathematician, wrote an Egyptian Papyrus in 1650 BC known as "The Rhind Papyrus" which is considered to be the most extensive ancient Egyptian Mathematical document in history. They mainly used linear equations.

The Rhind Papyrus contains problems of linear equation in the form of

x + xa = b and x + xa + bx = c where a, b and c are known terms and x is referred as " aha" or heap. The equations were solved by "method of false position" or "regular falsi" , in which a specific value is substituted to the left-hand side of the equation, and the obtained answer, after performing the required arithmetic operation is compared to the right-hand side of the equation.

III. China

• ZHOUBI SUANGJING is one of the oldest Chinese Mathematical documents.

The following are the five major books by Chinese mathematicians in algebra.

Nine Chapters on Mathematical Art	It is one of the most influential books that gives solutions for determining and indeterminate simultaneous linear equations using both positive and negative numbers. In one of the problems, it has a solution for five unknowns in four equations.
Sea-mirror of the Circle- measurement	LI ZHI wrote this book where he solved equations with the highest degree as six by using Horner's method.
Mathematical Treatise in nine section	Ch'in Chiu-Shao, a wealthy governor and minister, invented the Chinese Remainder Theorem to solve simultaneous congruences.
Magic Square	In this book, the author Yang Hui formed a magic square or matrix by placing coefficients and constants to solve simultaneous linear equations. He worked with column reduction methods to get the solution.
Precious mirror of the four elements	Chu Shih-Chieh wrote this book in 1303 where unknown quantities in algebraic equations were represented as heaven, man, earth, and matter. Horner's method is used to solve the simultaneous equation with the highest degree of fourteen.

 

Precious mirror of the four elements

IV Greece

The Greek mathematician represented the sides of geometric objects, lines, and letters associated with them, which is called Geometric Algebra.

They invented "The application of areas " to obtain the solutions for equations solved in geometric algebra.

Following are few Greek mathematicians whose contribution are the milestone in the history of Algebra :

1. Thymaridas (c 400 BCE - 350 BCE) created a famous rule called

 "Blooms Of Thymaridas" which states that

---

---

---

---