WHAT IS ALGEBRA?
Algebra is a branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. The notion that there exists such a distinct subdiscipline of mathematics, as well as the term algebra to denote it, resulted from a slow historical development.
This article presents that history, tracing the evolution over time of the concept of the equation, number systems, symbols for conveying and manipulating mathematical statements, and the modern abstract structural view of algebra. For information on specific branches of algebra, see elementary algebra, linear algebra, and modern algebra.
WHO IS THE FATHER OF ALGEBRA?
- Al-Khwarizmi: The Father of Algebra. We explore the origins of algebra and mathematics that underpin the science of flight and future transport.
A BRIEF HISTORY OF ALGEBRA:-
“Algebra” comes from the Arabic word “al-jabr,” which has been translated to be “reunion” or “restoration.” Algebra as a proper field of mathematics can be traced to the end of the 16th century, but the true theory of algebra started much earlier. Algebra began with computations similar to that of basic arithmetic but with letters standing in for numbers.
∼Their methods for solving linear equations, quadratic equations, and indeterminant linear equations are still in use today! 2000-1600 BCE: Babylonians developed advanced arithmetical systems allowing them to do calculations via algorithms. Compare this to the premier works of the Egyptians (Mathematical Papyrus), the Greeks (Euclid’s Elements), and the Chinese (Nine Chapters in Mathematical Art), which all used geometric methods to solve similar problems.
∼780-850 CE: Persian mathematician al-Khwarizmi (earlier transliterated as Algoritmi—and from where we get “algorithm”!) was directly influenced by more ancient Greek and Indian mathematician's work The Compendious Book on Calculation by Completion and Balancing. This helped established algebra as a field separate from arithmetic and geometry. His work was done without the use of negatives or zero. His work was eventually translated in the 12th century and brought to Europe, introducing Europe to Arabic numerals, which we still use today.
∼628 CE: Indian mathematician Brahmagupta’s work gave the first complete arithmetical solution to the quadratic equation, including zero and negatives, and gave a generalized solution to linear equations.
∼1070 CE: Omar Khayy´am’s influential Treatise on Demonstration of Problems of Algebra derived general methods of solutions to cubics (and some higher-order) and discussed the triangular array of binomial coefficients, what we know as Pascal’s triangle. This became part of the body of Persian mathematics and would eventually be translated to Europe.
The algebra we will be doing is known as “elementary algebra” and is not the algebra studied by mathematicians now. Abstract, or modern, algebra is a field of mathematics concerned with the properties of algebraic structures—sets (not necessarily of numbers) which have some behavior under an operation, usually denoted as +. One useful example is the area of group theory. Groups can be thought of as symmetry operations.
Different shapes have different amounts of symmetry (consider the square versus the hexagon). Group theory is actually used in physical chemistry to reduce unnecessary computations and predict molecules' behavior or existence.
This is a very, very brief outline of just one area of mathematics—there’s much, much more! If you’re interested in learning more about the history of mathematics, you can check out the (brief) reading list and view them on Amazon by clicking. Further, the S&T call number is listed and will link to the book’s page on the library website. While there are only three books listed, I am confident these three alone will give a great view of the history of mathematics. However, keep in mind that mathematics is constantly developing, so that any published book will be out of date for the most recent advancements!
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