Mathematical Traditions by Region
Mathematics has been discovered and developed independently across many civilisations. This page provides an overview of each major tradition and its Codex entries.
The Mathematics Codex treats every tradition as a first-class subject. Entries from Indian, Chinese, Babylonian, Mayan, and Islamic traditions receive the same editorial rigour — Tier 1 sources, three reading levels, full relationship mapping — as entries from the Greek and European traditions. Priority: equal depth, not token inclusion.
Babylonian 0 live entries
The oldest substantial mathematical record. Babylonian scribes worked in base 60, solved quadratic equations, and compiled Pythagorean triple tables (Plimpton 322) over a millennium before Pythagoras.
- Plimpton 322 — Pythagorean triples, c. 1800 BCE
- Quadratic equations solved algorithmically
- Sexagesimal (base 60) place-value system
- Astronomical prediction — eclipse cycles
Egyptian 0 live entries
Practical arithmetic and geometry for administration, surveying, and construction. The Rhind and Moscow papyri reveal sophisticated unit-fraction arithmetic and volume calculations.
- Rhind Papyrus — 87 mathematical problems, c. 1650 BCE
- Moscow Papyrus — volume of a truncated pyramid
- Unit-fraction arithmetic (all fractions as sums of 1/n)
- Practical geometry for land surveying
Greek referenced in 2 entries
The tradition that most influenced Western mathematics. Pioneered proof-based mathematics, axiomatic systems, and deductive geometry. Euclid, Archimedes, Diophantus, Pythagoras, Apollonius.
- Euclid's Elements — axiomatic geometry and number theory
- Archimedes — π bounds, proto-integral calculus
- Diophantus — early algebra and number theory
- Pythagoras school — number mysticism and geometry
Indian 1 live entry
One of the most mathematically productive traditions in history. Developed the decimal place-value system (now universal), negative numbers, zero, trigonometry (sine tables), infinite series, and the Kerala school's proto-calculus — many results independently anticipating European discoveries by centuries.
- Sulbasūtras — geometric constructions, Pythagoras theorem, c. 800 BCE
- Āryabhaṭa — sine table, π, kuṭṭaka, 499 CE
- Brahmagupta — zero and negative numbers, 628 CE
- Bhāskara II — Chakravāla algorithm, 1150 CE
- Mādhava — infinite series for π, sin, cos, c. 1400 CE
Chinese 0 live entries
Rich tradition of practical and theoretical mathematics. The Nine Chapters on the Mathematical Art systematised Chinese mathematics. Later mathematicians discovered the Chinese Remainder Theorem, Horner's method, and Pascal's triangle centuries before European attribution.
- Nine Chapters on the Mathematical Art — c. 200 BCE–200 CE
- Pascal's triangle — Yang Hui, 1261 CE (Chinese attribution)
- Chinese Remainder Theorem — Qin Jiushao, 1247 CE
- Decimal fractions — Liu Hui, 263 CE
Mayan 0 live entries
Independently developed a vigesimal (base 20) place-value system with zero. Created highly accurate astronomical calendars and predicted celestial events with remarkable precision.
- Independent invention of positional notation and zero
- Vigesimal (base 20) number system
- Long Count calendar — cycles up to 5,125 years
- Precise Venus cycle and eclipse tables
Islamic Golden Age 0 live entries
The Islamic world served as a transmission bridge between ancient traditions and Europe — and produced significant original mathematics. Al-Khwārizmī founded algebra; Al-Haytham made early contributions to analysis; Al-Kashi computed π to 16 decimal places.
- Al-Khwārizmī — algebra and the algorithm, c. 820 CE
- Al-Haytham (Alhazen) — optics and proto-analysis
- Al-Bīrūnī — trigonometry and geodesy
- Al-Kashi — π to 16 decimal places, c. 1424 CE
- Transmission of Indian numerals to Europe
European (Modern) referenced in 3 entries
The tradition that formalised calculus, modern analysis, abstract algebra, and set theory. Built substantially on transmitted knowledge from Greek, Indian, and Islamic predecessors.
- Viète, Descartes — algebraic notation, coordinate geometry
- Newton, Leibniz — calculus (independently)
- Euler — analysis, graph theory, notation
- Cantor — set theory and infinite cardinalities
- Hilbert, Gödel — foundations, incompleteness