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. 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. 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, 2004Stillwell, J., Mathematics and Its History, Springer, 2010O'Regan, G., A Brief History of Computing, Springer, 2008Cajori, F., A History of Mathematics, AMS Bookstore, 1991Smith, D. E., History of Mathematics, Courier Dover Publications, 1958 |