**By: Lauren Krause**

**Timeline: The History of Algebra**

**European Algebra After 1,500**

In the beginning of this period they had accepted zero and irrational numbers were often used but were still questioned if they were actually numbers.

Europeans during this time were aware of negative numbers but they were not used or fully accepted yet.

The concept of todays number system was not fully accepted until the 19th century.

Much effort was put into solving polynomial, quadratic, cubic. and quartic equations. This used great mathematics but came back with various negative outcomes.

Symbolic algebra came to Europe in 1639 with the publication of Descartes' La Géométrie.

**How algebra was used in the European culture**

**European Contributions to Algebra**

During the 16th century many Europeans made great advances in mathematical techniques and found solutions to various types of equations.

Many of the European achievements would often be described by mathematician, Boyer as "Perhaps the greatest contribution to algebra since the Babylonians learned to solve quadratic equations almost four millennia earlier."

Cultural, Architectural, Agricultural or Other Cultural Developments That Came About as a Result of the Use of Algebra,

1200

1202:

**Timeline of the History of Algebra**

Europeans are introduced to Algebra through Leonardo Fibonacci who created "Liber Abaci".

1300

1400

1500

1600

1700

1800

1900

2000

c. 1300

Chinese Mathematician Zhu Shijie begins to discover more about polynomial algebra, quadratic equations, some quartic equations, equations with up to four unknowns, and simultaneous equations.

1412

Arab Mathematician Abū al-asan ibn Alī al-Qalaādī introduces algebraic symbolism by using short arabic words or letters for mathematical symbols.

1535

Italian Mathematicians such as Niccolò Fontana Tartaglia were able to solve general cubic equations independently.

1545

Italian Mathematician Girolamo Cardano publishes Ars magna -The Great Art which is able to help us to solve a general quartic equation.

1572

Complex roots of cubic equations and modern day notation are discovered and improved upon by Italian Mathematician, Rafael Bombelli.

1631

The symbols ">" and "<" are first used for "greater than" and "less than" by Thomas Harriot.

1637

René Descartes first uses the term "imaginary number"

1637

Pierre de Fermat publishes "Diophantus' Arithmetica" and claims to have proven Fermat's Last Theorem.

1572

1619

Analytic geometry is discovered by René Descartes.

1682

Characteristica Generalis, a manipulation of algebraic symbols, is formulated by Gottfried Wilhelm Leibniz.

1685

General cubic equations, some quartic and quintic equations are solved by Kowa Saki.

1683

Japanese Mathematician Kowa Seki discovers determinant, discriminant, and Bernoulli numbers.

1693

Simultaneous linear equations begin to be formed and solved by Gottfried Wilhelm Leibniz .

1722

1797

Gabriel Cramer studies algebraic curves, matrices and determinants

1799

Abel–Ruffini theorem, a theory that quintic or higher equations can be solved by a general formula, was discovered by Abel–Ruffini theorem.

1799

The fundamental theorem of algebra is proven by Carl Friedrich Gauss.

1806

The Argand diagram and the Fundamental Theorem of Algebra was published by Jean-Robert Argand.

1832

Évariste Galois develops the Galois Theory when working with abstract algebra.

1847

George Boole creates Boolean Algebra and publishes "The Mathematical Analysis of Logic"

1878

A general quintic equation is solved by Charles Hermite by using elliptic and modular functions.

2007

Research teams from North America and Europe work using a computer system to map E8 (mathematics) or closely related linear equations.

1981

The theory of hyperbolic groups was discovered by French-Russian Mathematician, Mikhail Gromov.

Abraham de Moivre creates "de Moivre's formula", which connected trigonometric formulas with complex numbers.

1750

Gabriel Cramer studies algebraic curves, matrices and determinants

The solution of cubic and quartic equations.

The use of letters for known constants.

The marriage of algebra and geometry.

The modern day theory of equations

**European Key Contributions**

Works CitedCardan Portraits. Digital image. Cardan Portraits. N.p., Nov. 2008. Web. 26 Sept. 2012. <http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Cardan.html>.Francois Viete, French Mathematician. Digital image. Science Photo Library. N.p., n.d. Web. 26 Sept. 2012. <http://www.sciencephoto.com/media/89268/view>.Images of the Pantheon, 125-28 C. E., Rome. Digital image. Bluffton University. N.p., n.d. Web. 26 Sept. 2012. <http://www.bluffton.edu/~sullivanm/romanpantheon/pantheon.html>.Parthenon. Digital image. Suny Oneonta. N.p., n.d. Web. 26 Sept. 2012.<http://employees.oneonta.edu/farberas/arth/arth200/politics/parthenon.html>.Pierre De Fermat. Digital image. Wikipedia. Wikimedia Foundation, 24 Sept. 2012. Web. 26 Sept. 2012. <http://en.wikipedia.org/wiki/Pierre_de_Fermat>."The History of Algebra." Highlights in the History of Algebra. N.p., n.d. Web. 26 Sept. Wikipedia contributors. "François Viète." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 1 Sep. 2012. Web. 26 Sep. 2012.Wikipedia contributors. "Gerolamo Cardano." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 26 Sep. 2012. Web. 26 Sep. 2012.Wikipedia contributors. "Pierre de Fermat." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Sep. 2012. Web. 26 Sep. 2012.Wikipedia Contributors. René Descartes. Digital image. Wikipedia, The Free Encyclopedia., 25 Sept. 2012. Web. 26 Sept.2012.<http://en.wikipedia.org/w/index.php?title=Ren%C3%A9_Descartes&oldid=514529276>.Wikipedia contributors. "René Descartes." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 25 Sep. 2012. Web. 26 Sep. 2012.Wikipedia contributors. "Timeline of algebra." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 23 Sep. 2012. Web. 26 Sep. 2012.

Descartes' La Géométrie (Book)

Parthenon (Building)

Pathenon (Building)

François Viète (1540-1603): French Mathematician, the author of "Diophantus' Arithmetica"

Gerolamo Cardano (1501-1576): Italian Mathematician, physician, astrologer, and gambler. Through his gambling he became the founder of probability.

Pierre de Fermat (1601-1665): Founder of "Fermat's Last Theorem", a document stating that in the equation "a^n + b^n = c^n" it is impossible that three of the number could be a positive number.

René Descartes (1596-1650): French philosopher, Mathematician, and Writer. Most know as the "Father of Modern Philosophy" and the first to use the term "imaginary number".

European Mathematicians that Contributed to Algebra

Pierre de Fermat

Gerolamo Cardano

François Viète