Mathematical Principles, Theories, and Things is arranged Chronologically and the country of origin is listed, where appropriate. Each entry includes a clear main heading, the person or people responsible for the discovery, birth and death dates, where relevant, followed by a short introductory paragraph explaining the concept concisely. In Some cases, the main essay it also cross referenced to linked subjects.The key on the opposite page explains the order of information in each entry.

Writing Number

Fractions

The Greatest Pyramind

Pi = ∏

The Pythagoreans

Pythagora's Theorem

Irrational Number

Perfect Number

Regular Polygons

Platonic Solids

The Golden Ratio

Trisecting The Angle

Doubling The Cube

Squaring The Circle

Zeno's Paradoxes

Plato and Platonism

Conic Secion

Euclid's Elements

The 5th Postulate

Sum of The angles in a Triangle

The Fundamental Theorem of Arithmetic

Arithmetic

The Infinity of Prime Numbers

Mesurement of a Spere

Quadratune of the Parabola

The Sand Reckoner

Trigonometry

Negative Numbers

The Earth-Centered Universe

Zero

Kitab wa al jabr wa al muqabalah (The Book of Shifting and Balancing)

Cubic equation - Geometric Solutions

Fibonacci Numbers

Perspective

Cubic Equations - Algebraic Solution

Quartic Equations

The Sun Centered Universe

Mathematical Induction

Falling Bodies

The Sun Centered Universe Again

Logarithms

Tessellations

Regularly Solid Revisited

Caculating Machine

Analytic Geometry

A Formula for prime numbers

The Probles of the points

Pascal's Triagle

The Binomial Distributions

Pascal'swager

Differentiation

Intergration

The Fundamental Theorem of Caculus

Three Laws of Motions

The Law of Gravity

The Precession of the Equinoxes

The Law of the large numbers

The Normal Distribution

The seven Bridges of Konigsberg

Goldbach's Conjecture

V+F = E +2

The Gabler's Fallacy

Complex Numbers

e

Regularly Polygons Revisited

Propressions

The Fundamental Theorem of Algebra

Fourier Series

The Difference and Analytic Engines

Quintic Equations

Non-Euclidean Geometry

Galois Theory

Constructible Lengths

Doubling the Cube & Trisecting The Angle Revisited

Quaternions

Transcendental Numbers

Kirkman's Schoolgirl Problem

The Law Of Thought

Twisted Shapes

The Riemann Hypothesis

Maxwell's equations

TheCountability of Fractions

The Uncountability of the Reals

Squaring The Circile Revisited

The Correlation Coefficient

The Continuum Hypothesis

Spac-Filling Curves

Wall Paper Patterns

"Doughnuts and Coffe Cups"

What The Tortoise Said to Achilles

The prime number Theorem

Hilbert's Problem

Quantum Mechanics

The Central Limit Theorem

Russell's Paradox

Mathematics as Part of Logic

The Snowflake Curve

Axiom of Choice

The Jordan Curve Theorem

Special Relativity

Intuitionism

Zermelo-Fraenkel Set Theory

The Hairy-Ball Problem

General Relativity

The Hilbert Program

Godel's Theorem

The Traveling Salesman

Turing Machines

Binary Numbers

The Ham Sandwich Theorem

The Engima Machine

Colossus

Game Theory

ENIAC

The Prisoner's Dilemma

Electronic Calculators

Polya's Principles

Erdos Number

Chaos Theory

The Secretary Problem

Catastrophe Theory

Life

Matiyasevich's Theorem

P=NP

Public Key Codes

Fractals

The Four-Color Theorem

The Logistic Model

Stacking Oranges

Fermat's Last Theorem

The Seven Millennium Prize

Problems

Glossary