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Mathematical Achievements throughout the Ages

(all dates are approximate)  

Math before 400 CE    Math from 400-1400 CE     Math from 1400-1600 CE    

Math from 1600 CE to 1900 CE    Math from 1900 CE to present    Definitions

 Mathematics before the year 400

 1800 BCE-Egypt

Unit Fractions                                  Linear Equations                    

Measurement of Circle                       Lunar-Solar Calendar

Volume of a Pyramid


1700 BCE-Babylonia

Base 60 place value system               Systems of two linear equations

Measurement of Circle                       Quadratic Equations and systems

Lunar-Solar Calendar                         Square and Cube root tables

Square Root Calculations                   Pythagorean Theorem

Pythagorean Triples                          Volume of a Pyramid    


500 BCE-India

Pythagorean Theorem                        Measurement of Circle

Square Root Calculations


600-300 BCE-Greece

Proof of Theorems                             Music and Number Theory

Theories Regarding Proportions           The Elements

Paradoxes of Motion                          Logic of Syllogisms

Conic studies                                   Mathematical Models, Area and Volume

200 BCE-China

Counting Board in Base 10                 Systems of up to five linear equations

Measurement of circle                        Volume of a pyramid

Square and Cube Root Algorithms        Pythagorean Theorem

Pythagorean Triples                           Quadratic Equations and Systems


100-400 CE-Greece (Greek based algebra and Analysis)

Elementary Number Theory                 Intermediate Equations

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Mathematics in the Middle Ages


300-600 CE-China/India

Math of Surveying                              Remainder Problems

Sine Tables                                       Mathematical Methods


400-900 CE-Medieval Europe

Latin Versions of Greek Math Texts       Arithmatic Problems

Counting Boards

700-900 CE-China/India

Indeterminate Equations                     Tangent Tables

Algebra Problems                               Combinatorial Problems


700-1000 CE-Islamic Countries

Algebra                                             Practical Geometry

Quadratic Equations                           Algebra using Irrational Numbers

Centers of Gravity                              Arabic Arithmetic

Theorems of Spherical Geometry        

 1000-1400 CE-Medieval Europe

Translation of Texts in Other Languages

Geometry                                          Algebra

Trigonometry                                     Induction

Combinatorics                                    Proportions

Kinematics                                        Exponentials


1100-1300 CE-China/India

Pascalís Triangle                                 Pell Equation

Algebraic Equations for Geometry          Equation Solving Techniques

Linear Congruence                              Systems of Equations

 1100-1300 CE-Islamic Countries

Inductive Logic                                  Irrational Numbers

Sums of Integral Powers                     Trigonometry and Applications

Cubic Equations                                 Parallel Postulate

Decimals                                           Polynomials

Binomial Theorem                              Combinations and Permutations

Trigonometry Texts                            Amicable Numbers

Proof of Combinatorial Results

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Mathematics in the Renaissance Era


1400-1600 CE-Europe

Algebra evolves through the following specific areas

Abacus                                              Cubic Equations        

Roots                                                Translation improvements

Quartic Equations                               Complex Numbers

Decimal Fractions                                Equation Theory

Applied Mathematics evolves through the following specific areas

Perspective                                        Trigonometry

Geometry of Perspective                      Astronomy

Map Making                                        Logarithms

Kinematics                                         Applied Geometry

Probability                                         Analytic Geometry

Number Theory                                   Projective Geometry

Calculus evolves through the following areas

Power Series                                      Maxima

Area                                                 Volumes

Areas under hyperbola                        Normals

Extrema                                           Tangents

Logarithms and Areas                         Power series for logarithms

Algorithm for derivatives                     Arc Lengths

Series                                              Fundamental Theorem.

Celestial Mechanics                            Differentials

Calculus of exponentials

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Mathematics in the 17th-19th Centuries

Analysisí progression throughout the 17th and 18th Centuries

Integration Problems                          Partial Derivatives

Differential Equations                         Taylor Series

Criticism of Calculusís foundations        Rules for Partial Derivatives

Calculus Texts Written                        Vibrating String Problems

Calculus through Power Series

Probability, Algebra and Geometry in the 17th and 18th Centuries

Determinants                                     Combinatorics and Probability

Non-Euclidean Geometry                      Cramerís Rule

Probability                                         Topology

Surveying                                          Almanacs

Clockmaking                                      Analytic and Differential Geometry

Statistical Inference                           Number Theory

Algebra in the 19th Century

5th Degree Polynomial Equations          Number Theory

Permutations                                     Determinants

Eigenvalues                                       Symbolical Algebra

Complex Numbers                               Quaternions

Factorization                                      Matrices

Logic                                                 Abstract Groups

Solution of Linear Systems                   Vectors

Group Theory                                      

Analysis in the 19th Century

Surface integrals                                 Definition of Convergence

Geometric Representation of Complex Numbers

Analytic Probability                              Least Squares

Fourier Series                                      Complex Variables

Normal Distribution                              Continuity and Convergence

Complex Analysis                                Normal Curves

Divergence Theorem                            Vector Analysis

Regression and Correlation                   Beginning of Topology

Statistical Methods                              Partial Differential Equations

Geometry of the 19th Century

Differential Geometry                           Non-Euclidean Geometry

Geometry on Spheres                           Projected Geometry

Geometry in N Dimensions                    Surface of Negative Curvature

Postulates of Physical Space                 Vector Space Axioms

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 20th Century Mathematics

Analytical Engine                               Linear Associative Algebras

Computer Programming                      Algebraic Topology

Set Theory                                       Field Theory

Axioms for a Vector Space                  Simplexes

Vector Spaces                                   Homology Groups

Algebraic Topology                            Category Theory

Linear Programming                           Switching Circuits

Four Color Theorem                            Independence of Axiom of Choice

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The above mathematical terms and areas of specialty  definitions and/or examples can be found at the following websites: