1. history of algebra

7/27/2019 1. History of Algebra

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Prepared by:Mr. Christopher N. Satiada

Math IV Teacher


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The history of algebra began inancientEgypt and Babylon,where people learned to solve

linear(ax = b) and quadratic (ax2+ bx = c) equations, as well asindeterminate equations suchas x2 + y2 = z2, whereby several

unknowns are involved.


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The ancient Babylonianssolved arbitrary quadratic

equations by essentially thesame procedures taught

today. They also could solveindeterminate equations.


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The AlexandrianmathematiciansHero andDiophantus continued the

traditions of Egypt andBabylon, but Diophantus' book

Arithmetica is on a muchhigher level and gives many

surprising solutions to difficult


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In the Islamic world, where itwas known as the science ofrestoration and balancing.

(The Arabic word for restoration,

al-jabru, is the root of the word

algebra, and algebra as ascience is an Arabic

contribution.)


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In the 9th century, al-Khwarizmiwrote one of the

first Arabic algebras, asystematic expos of the basic

theory of equations, with bothexamples and proofs.


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By the end of the 9th century theEgyptian Abu Kamil (850-930)stated and proved the basic laws

and identities of algebra andsolved such complicated

problems as finding x, y,and z such that x + y + z = 10,

x2 + y2 = z2, and xz = y2.


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Ancient civilizations wrote out

algebraic expressions, using only

occasional abbreviations, but by

medieval times Islamicmathematicians were able to talk

about arbitrarily high powers of the

unknown x, and work out the basicalgebra of polynomials (without yet

using modern symbolism).


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In the 12

th

century , a Latin translation ofal-Khwarizmi's Algebra, and in the early13th century appeared the writings of the

great Italian mathematicianLeonardoFibonacci (1170-1230), among whoseachievements was a close approximation

to the solution of the cubic equationx3 + 2x2 + cx = d.


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Early in the 16th century, the Italianmathematicians Scipione del Ferro (1465-

1526), Niccol Tartaglia (1500-57), andGerolamo Cardano (1501-76) solved the

general cubic equation in terms of the

constants appearing in the equation.Cardano's pupil, Ludovico Ferrari (1522-65), soon found an exact solution to

equations of the fourth degree, and as a

result, mathematicians for the next several

centuries tried to find a formula for the roots

of equations of degree five, or higher.

Early in the 19th century, however, the


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An important development in algebra in the

16th century was the introduction ofsymbols for the unknown and for algebraicpowers and operations. Thus Book III of the

French philosopherand mathematicianRen Descartes'Lagometrie (1637) looksmuch like a modern algebra text.

Descartes is most significant in mathematics,however, for his discovery of analytic

geometry, which reduces the solution of

geometric problems to the solution of

algebraic ones.


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Until 1799 was the proof published, by the

German mathematician Carl FriedrichGauss, that every polynomial equation has atleast one root.


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Groups began as systems of permutations andcombinations of roots of polynomials, but they

became one of the chief unifying concepts of19th-century mathematics.

Important contributions to their study were

made by the French mathematicians Galoisand Augustin Cauchy, the Britishmathematician Arthur Cayley, and the

Norwegian mathematicians Niels Abel andSophus Lie (1842-99).Quaternions were

the discovery of the British mathematicianWilliam Rowan Hamilton,who extended the

arithmetic of complex numbers to quaternions


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Immediately after Hamilton's discovery, the German

mathematician Hermann Grassmann (1809-77) began

investigating vectors . Despite its abstract character,American physicist J. W. Gibbsrecognized in vector

algebra a system of great utility for physicists, just as

Hamilton had recognized the usefulness of quaternions.

The widespread influence of this abstract approach led tothe publication in 1854 of George Boole's The Laws of

Thought, an algebraic treatment of basic logic. Since that

time, modern algebraalso called abstract algebrahas

continued to develop. Important new results have been

discovered, and the subject has found applications in all

branches of mathematics and in many of the sciences, as

well.

1. history of algebra

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