subject: Historical Algebra Facts & People [print this page] Historical Algebra Facts & People Historical Algebra Facts & People
By the time of Plato, Greek math had gone through an extreme change. Diophantus, often referred to as "the father of algebra", was an Alexandrian Greek mathematician and the writerof a numberof publications called Arithmetica. These texts deal with solving algebraic equations.
While the word algebra arises from the Arabic language and considerably of its strategies from Arabic/Islamic mathematics, its roots can be traced to earlier traditions, most notably ancient Indian mathematics, which in fact had a principal influence on Muhammad ibn Musa al-Khwarizmi who learned Indian math and introduced it to the Muslim world via his renowned arithmetic text, Book on Addition and Subtraction right after the Method of the Indians. Al-Khwarizmi later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is separate from geometry and arithmetic.
The roots of algebra may be traced to the ancient Babylonians, who developed a sophisticated arithmetical system with which they were able to do calculations in an algorithmic fashion. Like the Egyptians, their algebra was basically rhetorical.
The procedures used to solve problems had been taught by means of examples and no reasons or explanations had been given. Also like the Egyptians they recognized only positive rational numbers, despite the fact that they did uncover approximate solutions to difficulties which had no exact rational answer. By contrast, most Egyptians of this era, as well as Greek and Chinese mathematicians in the 1st millennium BC, typically solved such equations by geometric techniques, such as those described in the Rhind Mathematical Papyrus, Euclid's Elements, and The Nine Chapters on the Mathematical Art. Using letters instead of numbers allowed algebra to break free from the consideration of certain equations and thus allowed a wonderful boost in generality and opened the possibility for studying the relationship between the coefficients of an equation an the roots of the equation ("theory of equations"). Vietes algebra was still syncopated rather than entirely symbolic. The thought of a determinant was created by Japanese mathematician Kowa Seki in the 17th century, put into practice independently by Gottfried Leibniz 10 years afterwards, for the purpose of solving systems of simultaneous linear equations employing matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Paolo Ruffini was the first individual to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations.
Abstract algebra was developed in the 19th century, initially focusing on what is now known as Galois theory, and on constructibility problems. The "modern day algebra" has deep nineteenth-century roots in the work, for example, of Richard Dedekind and Leopold Kronecker and profound interconnections with other branches of mathematics such as algebraic number theory and algebraic geometry. George Peacock was the originator of axiomatic thinking in arithmetic and algebra. Augustus De Morgan discovered relation algebra in his Syllabus of a Proposed Program of Logic. Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices (this is a noncommutative algebra).
The idea of a group (a set of operations with a single operation which satisfies three axioms) grew out of the work of a number of mathematicians. Maybe the most essential actions had been by Galois (French, 1811-1832). By the use of this idea Galois could provide a conclusive response to the broad question of which polynomial equations are solvable by algebraic operations.
