- Prehistoric Mathematics: Early man kept track of regular occurrences such as the season and phases of the moon. This is just simple counting and tallying techniques.
- Sumerian/Babylonian Mathematics: Sumerian mathematics developed as a response to bureaucratic needs. Sumerians and Babylonians were the first people to assign symbols to groups of objects in an attempt to make the description of larger numbers easier. Babylonians developed a circle character for zero.
- Egyptian Mathematics: The Egyptians created a decimal numerical system based on our ten fingers. There was a desire for the development of a notation for fractions. There is evidence that the Egyptians knew the formula for volume of a pyramid.
- Greek Mathematics: Most of Greek mathematics was based on geometry. Thales established Thales Theorem. Pythagoras becomes a legend and is credited with coming up with the Pythagorean Theorem. The most important contribution of the Greeks was the ideas of proof.
- Hellenistic Mathematics: Euclid invents Euclidean geometry. Archimedes produced formulas to calculate the areas of regular shapes. Diophantus of Alexandria was the first to recognize fractions as numbers.
- Indian Mathematics: Zero is used as a number as opposed to just a place holder. Golden Age Indian mathematicians made fundamental advances in the theory of trigonometry.
- Islamic Mathematics: The Islamic Empire used extensive, complex geometric patterns to decorate buildings. Al-Khwarizmi introduced the fundamental algebraic methods of reduction and balancing.
- Medieval Mathematics: Fibonacci spread the use of the Hindu-Arabic numeral system throughout Europe. Fibonacci is best known for the Fibonacci Sequence.
- 16th Century Mathematics: The equals, multiplication, division, radical, decimal, and inequality symbols were introduced and standardized. Tartaglia demonstrated a general algebraic formula for solving cubic equations.
- 17th Century Mathematics: Napier invented the logarithm, which was later improved by Napier and Briggs. Descartes developed analytic geometry and Cartesian coordinates. Fermat formulated several theorems that extend our knowledge of number theory. Pascal is famous for Pascal's Triangle of binomial coefficients. Newton and Leibniz developed the idea of infinitesimal calculus.
- 18th Century Mathematics: Lagrange is credited with the four-square theorem and Lagrange's Theorem. Legendre made important contributions to stats, number theory, abstract algebra and mathematical analysis. Lambert was the first to introduce hyperbolic functions into trigonometry. Euler produced the Euler Identity formula and Euler's Formula.
- 19th and 20th Century Mathematics: Was a continuous trend of furthering other mathematicians findings, increasing generalization, and increasing abstractions.

All the discoveries and findings listed above still does not cover everything that happened within these time periods, but it is a start. Mathematics has been something that has continuously progressed over the years and will continue to do so. As seen from above, mathematics was and still is something we need to operate in our everyday living. It is how mankind has made sense of the world and logical reasoning of the way life began.

__Important Mathematicians:__

- 624-546 BCE-> Thales -> Greek -> Early developments in geometry, including work on similar and right triangles
- 570-495 BCE ->Pythagoras -> Greek -> Expansion of geometry, rigorous approach building from first principles, square and triangular numbers, Pythagoras’ theorem.
- 428-348 BCE -> Plato -> Greek -> Platonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methods
- 300 BCE -> Euclid -> Greek -> Definitive statement of classical (Euclidean) geometry, use of axioms and postulates, many formulas, proofs and theorems including Euclid’s Theorem on infinitude of primes
- 287-212 BCE -> Archimedes -> Greek -> Formulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities
- 200-284 CE -> Diophantus -> Greek -> Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns
- 598-668 CE -> Brahmagupta -> Indian -> Basic mathematical rules for dealing with zero (+, - and x), negative numbers, negative roots of quadratic equations, solution of quadratic equations with two unknowns
- 780-850 CE -> Muhammad Al-Khwarizmi ->Persian -> Advocacy of the Hindu numerals 1 - 9 and 0 in Islamic world, foundations of modern algebra, including algebraic methods of “reduction” and “balancing”, solution of polynomial equations up to second degree
- 1170-1250 -> Leonardo of Pisa (Fibonacci) -> Italian -> Fibonacci Sequence of numbers, advocacy of the use of the Hindu-Arabic numeral system in Europe, Fibonacci's identity (product of two sums of two squares is itself a sum of two squares)
- 1350-1425 -> Madhava -> Indian -> Use of infinite series of fractions to give an exact formula for π, sine formula and other trigonometric functions, important step towards development of calculus
- 1499-1557 -> Niccolò Fontana Tartaglia ->Italian ->Formula for solving all types of cubic equations, involving first real use of complex numbers (combinations of real and imaginary numbers), Tartaglia’s Triangle (earlier version of Pascal’s Triangle)
- 1501-1576 -> Gerolamo Cardano -> Italian -> Published solution of cubic and quartic equations (by Tartaglia and Ferrari), acknowledged existence of imaginary numbers (based on √-1)
- 1522-1565 -> Lodovico Ferrari -> Italian -> Devised formula for solution of quartic equations
- 1596-1650 -> René Descartes -> French -> Development of Cartesian coordinates and analytic geometry (synthesis of geometry and algebra), also credited with the first use of superscripts for powers or exponents
- 1601-1665 -> Pierre de Fermat -> French -> Discovered many new numbers patterns and theorems (including Little Theorem, Two-Square Thereom and Last Theorem), greatly extending knowlege of number theory, also contributed to probability theory