History of Algebra

Hindu Algebra

800 BCE

When solving problems they only stated steps – no proof or reasoning was provided
•First to recognize that quadratic equations have two roots
•Known for invention of decimal system which we use today

Egyptian Algebra

300 BCE

Solve algebra problems equivalent to linear equations and 1 unknown
Algebra was rhetorical – use of no symbols
Problems were stated and solved verbally
Cairo Papyrus (300 B.C.) – solve systems of 2 degree equations

Babylonian Algebra

300 BCE

Babylonians were more advanced than Egyptians
Like Egyptians, algebra was also rhetorical
Could solve quadratic equations
Method of solving problems was rhetorical, taught through examples
No explanations to findings were given
Recognized on positive rational numbers

Rhetorical Algebra

200 BCE

Early Babylonian and Egyptian algebras were both rhetorical
•In Greece, the wording was more geometric but was still rhetorical.
•The Chinese also started with rhetorical algebra and used it longer.

Greek Algebra

100

The Greeks originally learned algebra from Egypt as indicated in their writings of the 6th century BCE. Later they learned Mesopotamian geometric algebra from the Persians. They studied number theory, beginning with Pythagoras

Fundamental Limitations of Greek Algebra

200

Negative and complex solutions of equations were rejected as “absurd” or “impossible”.

Diophantine Algebra

300

Represents the end of a movement among Greeks away from geometrical algebra to a system of algebra that did not depend on geometry

European Algebra

1540

Algebra was still largely rhetorical, slightly syncopated
•Solution to cubic and quartic equations
•Negative numbers were known, but not fully accepted
•No one could solve 5th degree equation
•Algebraists were called “cossists” and algebra was called “cossic art”