**ANCIENT TIMES**

**c. 3000 BCE:**Simple counting and record-keeping systems emerge in Mesopotamia and Egypt.**c. 2000-1900 BCE:**Babylonians develop sophisticated arithmetic, early forms of algebra, and geometry concepts (Plimpton 322).**c. 1800 BCE:**Egyptians have a grasp of fractions, basic algebra, and can calculate areas and volumes (Rhind Mathematical Papyrus).**c. 600 BCE:**Thales of Miletus introduces the concept of deductive reasoning and geometric theorems.**c. 530 BCE:**Pythagoras and his followers explore the relationship between numbers and geometry, including the famous Pythagorean Theorem.**c. 400 BCE:**Discovery of irrational numbers poses challenges to the Pythagorean view of the world.**c. 300 BCE:**Euclid's*Elements*compiles and systematizes Greek geometrical knowledge, laying the foundation for geometrical reasoning for centuries.**c. 250 BCE:**Archimedes makes significant discoveries in geometry (calculating areas and volumes), mechanics, and early concepts of calculus.

**MEDIEVAL PERIOD**

**c. 200 CE:**Diophantus writes*Arithmetica*, a major work on early algebra.**5th-6th centuries CE:**Indian mathematicians like Aryabhata formalize the decimal system, introduce the concept of zero, and make advances in trigonometry.**700-1200 CE:**The Islamic Golden Age sees scholars like Al-Khwarizmi lay the foundations of algebra and algorithms.

**RENAISSANCE AND ENLIGHTENMENT**

**1202:**Fibonacci introduces Hindu-Arabic numerals and the Fibonacci Sequence to Europe.**1545:**Gerolamo Cardano publishes*Ars Magna*, containing solutions for cubic and quartic equations.**16th century:**Development of symbolic notation makes algebraic manipulation easier.**1614:**John Napier invents logarithms, revolutionizing calculations.**1637:**Rene Descartes publishes*La Géométrie,*linking algebra and geometry.**Mid-17th century:**Pierre de Fermat and Blaise Pascal lay the groundwork for probability theory.**Late 17th century:**Isaac Newton and Gottfried Wilhelm Leibniz independently develop calculus.

**18TH & 19TH CENTURIES**

**18th century:**Calculus is rigorously formalized, and applied to solve problems in physics and astronomy. New areas like complex analysis and differential equations emerge.**1736:**Leonhard Euler solves the Seven Bridges of Königsberg problem, considered the birth of graph theory.**Early 19th century:**Carl Friedrich Gauss, the "Prince of Mathematicians", makes contributions across various fields (number theory, geometry, statistics).**1820s:**Development of non-Euclidean geometries challenges traditional understanding of space.**Late 19th century:**Georg Cantor develops set theory, revolutionizing notions of infinity.

**20TH CENTURY AND BEYOND**

**1900:**David Hilbert poses his famous 23 problems, greatly influencing the direction of mathematical research.**Early 20th century:**The rise of mathematical logic and work by Gödel, Turing, and Church on computability.**1931:**Kurt Gödel demonstrates the limits of formal mathematical systems with his incompleteness theorems.**Mid-20th century:**The advent of computers revolutionizes computation and opens new areas of study, such as numerical analysis.**Late 20th century:**Wiles' proof of Fermat's Last Theorem (1994) and the proof of the Poincaré Conjecture (2003) are landmark achievements.