History of Mathematics
Before 500 BCE
Key Regions: Mesopotamia, Ancient Egypt, Indus Valley.
Focus:Practical arithmetic, basic geometry, and astronomy for tax collection, construction, and tracking seasons.
Major Milestones: Invention of base-60 (Babylonian) and base-10 systems, creation of the earliest geometric rules for land surveying, and the Rhind Mathematical Papyrus
500 BCE – 500 CE
Key Regions: Ancient Greece, Alexandria.
Focus:The shift from practical calculation to deductive reasoning and rigorous proof. Geometry becomes the central language of math.
Major Milestones: Pythagoras introduces abstract proofs; Euclid writes The Elements (axiomatic geometry); Archimedes approximates \pi using exhaustion methods; Diophantus lays early roots for algebra.
500 – 1400
Key Regions:India, Islamic Empire, China.
Focus: Synthesis of Greek and Indian ideas, invention of modern algebra, and the spread of decimal notation.
Major Milestones:Aryabhata and Brahmagupta formalize zero and negative numbers in India; Al-Khwarizmi introduces systemic algebra (Al-Jabr) in Baghdad; development of spherical trigonometry.
1400 – 1600
Key Regions:Europe (chiefly Italy, France, Germany).
Focus:Commercial arithmetic explosion, solving higher-degree polynomial equations, and the introduction of symbolic math notation.
Major Milestones: Cardano and Ferrari solve cubic and quartic equations; introduction of complex/imaginary numbers ($\sqrt{-1}$); François Viète begins using letters to represent variables.
1600 – 1800
Key Regions:Western Europe.
Focus: Analyzing change, motion, and infinity. Math becomes deeply intertwined with physics and astronomy.
Major Milestones: Descartes unifies algebra and geometry (Analytic Geometry); Newton and Leibniz independently invent Calculus; Euler dominates the 18th century, expanding graph theory, analysis, and introducing notation like $e$ and $i$.
1800 – 1900
Key Regions: Europe (Germany, France, UK).
Focus: Placing calculus on logical foundations, breaking away from traditional Euclidean limits, and exploring higher dimensions.
Major Milestones: Gauss revolutionizes number theory; Cauchy and Weierstrass formalize limits and continuity; Bolyai and Lobachevsky discover Non-Euclidean geometry; Cantor invents Set Theory.
1900 – Present
Key Regions:Global.
Focus: Formal logic, foundational limits, computational math, and hyper-abstraction.
Major Milestones:Gödel’s Incompleteness Theorems show limits of math systems; Turing conceptualizes the universal machine, launching computer science; development of cryptography, topology, game theory, and fractals.
Which specific era or mathematical milestone are we focusing on for your article? We can use this timeline as a structural backbone if you want to explore how a particular concept evolved through these periods.