Glossary

A quantitative verse metre used in Sanskrit scientific literature. The Āryabhaṭīya is composed entirely in āryā metre, allowing extremely dense mathematical content to be encoded in a few syllables per concept.

Used by Āryabhaṭa to describe his value of π (≈ 3.1416). The term indicates awareness that the given value is not exact — an early recognition of irrational approximation.

A statement accepted without proof as the starting point of a formal system. Distinguished from a theorem (which is derived) and a postulate (the historical term in geometry). Different axiomatic systems for the same domain (e.g., ZFC vs NBG set theory) can yield different mathematical universes.

The Sanskrit term for algebra, literally "seed arithmetic." Used in Indian mathematical tradition to denote the manipulation of symbolic unknowns — as in Bhāskara II's Bījagaṇita (1150 CE).

The Mathematics Codex uses eight entry types: Theorem (proven result), Conjecture (unproven claim), Concept (defined mathematical object), Constant (named value), Person (mathematician biography), Work (text or treatise), Tradition (civilisational overview), Problem (unsolved or historical problem).

A mathematical statement believed to be true but not yet proven. Distinguished from a theorem (proven) and an open problem (which may not yet have a clear conjectured answer). Famous examples: Riemann Hypothesis, Goldbach's Conjecture, Collatz Conjecture.

The third reading level in every Codex entry. Intended for specialists: contains formal proofs, primary source analysis, historiographical debate, and technical commentary. Presupposes mathematical maturity. See also: Curious, Exploring.

The second reading level in every Codex entry. Intended for undergraduate-level readers with some mathematical background. Contains proofs of key steps, formal definitions, and civilisational context. See also: Curious, Deep Dive.

The Sanskrit term for mathematics broadly, and specifically for the computational/arithmetic branch as distinguished from geometry (kṣetragaṇita) and algebra (bījagaṇita).

Āryabhaṭa's term for half-chord — what we now call the sine function. The word entered Arabic as jiba (a meaningless transliteration), was later misread as jaib (bay, bosom), and was translated into Latin as sinus, giving us the modern word "sine."

Āryabhaṭa's algorithm for solving linear congruences of the form ax ≡ b (mod c). The earliest known general algorithm for linear Diophantine equations, using a method equivalent to the extended Euclidean algorithm.

A positional numeral system in which the value of a digit depends on its position (ones, tens, hundreds, etc.). Developed independently in Babylonian (base 60), Mayan (base 20), and Indian (base 10) traditions. The modern decimal system derives from the Indian tradition via Islamic mathematicians.

A rigorous logical argument establishing the truth of a mathematical statement from axioms and previously established theorems. Proof standards have evolved historically — Greek geometric proofs differ structurally from modern formal proofs, and Indian mathematical tradition emphasised upapatti (justification/demonstration) rather than the Euclidean two-column format.

The Mathematics Codex classifies sources into three tiers. Tier 1: peer-reviewed critical editions, major academic monographs from established publishers. Tier 2: reliable reference works, institutional archives, established encyclopaedias. Tier 3: accessible scholarly writing, well-regarded popular science from credentialled authors. Every entry must have at least one Tier 1 source.

A mathematical statement that has been proven to be true from a given set of axioms and definitions. Distinguished from a conjecture (unproven), a lemma (auxiliary theorem), and a corollary (theorem following immediately from another).

Zermelo-Fraenkel set theory with the Axiom of Choice — the standard axiomatic foundation of modern mathematics. Comprises nine axioms (Extensionality, Empty Set, Pairing, Union, Power Set, Infinity, Replacement, Regularity, Choice) that together define the set-theoretic universe in which virtually all contemporary mathematics takes place.