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A Short History Notes About Algebra

Algebra is a mathematical system that is a generalization of arithmetic in symbolic form; it uses letters or symbols to represents numbers. It includes advanced topics such as groups, rings, and invariant theory. The word “algebra” comes from the Arabic word al-jabr which is a part of the title of al-Khwārizmī’s treatise on algebraic methods which means “restoring,” that is, the operation of adding a term to both sides of the equation.

Early works of algebra of ancient Babylonians and Egyptians lack the abstract notation that algebra has today. The Babylonians had methods of solving quadratic equations, while the Egyptians used the symbol heap for the unknown.

In China, a treatise called Nine Chapters was compiled in the first century CE composed of 246 problems. The text shows methods of solving determinate and indeterminate equations. More sophisticated than the works of the Babylonians and Egyptians, the treatise is mostly what is known today as rhetorical algebra—problems and solutions are expressed in words rather than in algebraic notations.

Algebra to the ancient Greeks is an unknown science except for the Greek mathematician Diophantus of Alexandria (3rd century BCE). His work Arithmetica contains the first suggestions of algebraic notations and is probably the earliest treatise on algebra. He used algebraic equations and notations in presenting problems and solutions in Arithmetica.

      
image of Diophantus
   Diophantus of Alexandria

In the 6th century CE in India, Aryabhata’s works show knowledge in summing an arithmetic series, and solving quadratic equations and indeterminate linear equations. Shortly after, in the 7th century, Brahmagupta applied algebra to astronomy; his works gives the rules for using negative numbers, and solving quadratic equations.

image of al-Khwarizmi
  A stamp issued Sept. 6, 1983
        in the Soviet Union,
          commemorating
  al-Khwārizmī's 1200th birthday.

The Islamic scholars made several contributions to algebra as well—most notable of them is al-Khwārizmī. His treatise A short book on the calculus al-jabr and al-muqabalah, deals with the solution of quadratic equations. He did not use algebraic notations in his treatise but employed rhetorical algebra. This is one reason why some consider Diophantus as the “Father of Algebra” rather than Al-Khwārizmī.





References:

John, T., Algebra: Sets, Symbols, and the Language of Thought, Infobase Publishing, 2004

Stillwell, J., Mathematics and Its History, Springer, 2010

O'Regan, G., A Brief History of Computing, Springer, 2008

Cajori, F., A History of Mathematics, AMS Bookstore, 1991

Smith, D. E., History of Mathematics, Courier Dover Publications, 1958


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