
Period:2,700 BCEto2,300 BCE
The First Equations
Babylonians solve quadratic equations with the completing the square method.Over the course of the third millennium, these objects were replaced by cuneiform equivalents so that numbers could be written with the same stylus that was being used for the words in the text. A rudimentary model of the abacus was probably in use in Sumeria from as early as 2700  2300 BCE. 
Period:1,700 BCEto1,600 BCE
Babylonian Mathematicians
Babylonians solve quadratic equations with the completing the square method. 
Period:1,650 BCEto1,650 BCE
The Rhind Papyrus
There is an Egyptian papyrus that contained algebraic equations. It is called the Rhind Papyrus, and it includes several types of mathematical problems. It dates back to 1650 BC, so theoretically algebra has been around for a while. You can see parts of the Papyrus at the Brooklyn Museum in New York. 
Period:850 BCEto780 BCE
Solving the First Equations
In Iraq, Muhammad Ibn Musa AlKhwarizmi wrote a book containing the first clear explanation of solving equations by doing the same operation on both sides.It also contains sections on calculating areas and volumes of geometric figures and on the use of algebra to solve inheritance problems according to proportions prescribed by Islamic law. Elements of the work can be traced from the Babylonian mathematics of the early 2nd millennium BCE through Hellenistic, Hebrew, and Hindu treatises. 
Period:665 BCEto598 BCE
The X value
Bhaskara, an Indian mathematician was the first to replace the unknown value with letters, such as, X. While working in arithmetic, Brahmagupta explained how to find the cube and cube root or an integer and made rules that told us the computation of squares and square roots.As Well as that accomplishment, he gave us rules for dealing with five types of combinations of fractions.Brahmagupta established the basic mathematical rules for dealing with zero 
Period:540 BCEto250 BCE
Pythagoras
Greek mathematician Pythagoras' followers use geometric, visual strategies to solve equations. 
Period:287 BCEto211 BCE
The Surface and Volume of a Sphere
Archimedes was a greek mathematician that produced a formula that was used to find the relation between the surface and the volume of a sphere, amongst other shapes. He is also known for his Archimedes Screw, which is a method used to pump water. This is still used in developing countries. 
Period:190 BCEto150 BCE
Seleucus of Seleucia
Seleucus of Seleucla discovers that tides are caused by the moon. 
Period:1540to
The First +/ in Algebra
Francois Viete starts uses letters to replace variables and uses the +/ signs to represent addition and subtraction. Viete was a french mathematician who introduced the first systematic algebraic notation and contributed to the theory of equations. In 1579, Vete wrote “Mathematical Laws Applied to Triangles”. We still use his method today. 
Period:1551to1551
The Beginning of Algebra
The two best known “Fathers of Algebra” are Diophantus, a Greek mathematician, and Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi (Al for short), who both made contributions to the second stage of algebra. Al designed methods for reducing and balancing algebraic equations, and introduced algorithms. (Mathematical operation/rules.) Diophantus wrote 13 books called 'Arithmetica', which hold problems and solutions that have advanced algebraic notation. 
Period:1551to1551
The Word Algebra
The roots of “Algebra”, is traced back to the Arabic and Medieval Latin word, “Al Jabr”, that means “the reduction”. Its source is unknown, but many people think that either Diophantus and AlKhowarizm were the source of the name. 
Period: to
Carl Friedrich Gauss
German mathematician Carl Friedrich Gauss proves the Fundamental Theorem of Algebra. 
Period: to
Proving the Fundamental Theorem of Algebra
German mathematician Carl Friedrich Gauss proves the Fundamental Theorem of Algebra. He is known as one of the greatest mathematicians of all time, and is known for his work in algebra, number theory, geometry, probability theory, geodesy, astronomy, and the theory of functions.His thesis in 1797 gave proof of the fundamental theorem of algebra, which was that every polynomial equation, real or complex coefficients, has as many solutions as its highest power of the variable. 
Period: to
Functional Algebraic Equations
Norwegian mathematician Niels Henrik Abel proves that there is no general formula that solves all quintic equations. Abel’s first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an integral equation. 
Period: to
Amalie Noether
German mathematician Amalie Noether makes discoveries about noncommutative algebras.