Researched
Geometry (Euclid)
Euclid's Elements build geometry from a few axioms and make mathematical proof the standard method of the discipline.
Open in the interactive tree →Egyptians and Babylonians used geometry to survey fields. Euclid (about 300 BC) turned it into a logical building: a few basic postulates and theorems proven step by step from them. This idea of proof still shapes mathematics; Archimedes and Apollonius added circles, conic sections and the calculation of areas and volumes.
Prerequisites
- Number Systems & Place Value~3000-2000 BC
- Deductive Proof (Greece)~600 BCEuclid organised geometry as proofs from axioms, a practice begun by Thales and the Pythagoreans
Unlocks
- Aqueducts & Public Water~312 BC
- Road & Canal Networks312 BC
- Algorithm (Euclid)~300 BC
- Archimedes: Lever & Buoyancy~250 BC
- Earth measurement and maps~240 BC
- Mortar & Roman Concrete~200 BC
- Trigonometry~150 BC
- Roman Arch, Vault & Dome~126 AD
- Ancient astronomy~150 AD
- Zero, Decimals & Algebra~820
- Book of Optics (Alhazen)~1021
- Linear Perspective~1420
- Caravel & Circumnavigation~1450
- Scientific Method~1600-1620Ibn al-Haytham's experimental optics was built on Euclid's geometry as its model of proof
- The telescope1608
- Falling Bodies & Planet Orbits1609
- Law of Refraction (Snell)1621
- Analytic Geometry (Descartes)1637
- Calculus (Analysis)1684
- Graph Theory (Euler)1736
- Machine Tools1775
- Metric System1799
- Interchangeable Parts~1800–1850
- Non-Euclidean Geometry1829
- Cepheid distance yardstick1912
- Kepler Conjecture & Flyspeck1998-2014
- Sphere Packing in 8 & 24 Dims2016
- Kakeya Conjecture in 3D2025
- Hodge Conjectureopen
More in Mathematics · Antiquity
- Number Systems & Place Value~3000-2000 BC
- Deductive Proof (Greece)~600 BC
- Trigonometry~150 BC
- Nine Chapters (China)~100 AD