This manuscript page discusses the philosophical concept of avyakta (the unmanifest) as understood in Samkhya philosophy, explaining it as the pradhana (primordial matter) and the material cause of the manifest world. The text explores the Samkhya definition of true intellect and the great principle (mahat-tattva), connecting these to mental modifications and self-knowledge. It also presents an interpretation from the Bijaganita (algebra) perspective, where Samkhyas are defined as calculators who know particular numbers, and avyakta is described as the one seed and principal cause of the entire manifest world. The page includes grammatical analysis of Sanskrit terms, discussion of the fourfold accomplishment of means such as discrimination (viveka), and references to the Siromani text and the role of the true teacher (sadguru) in producing knowledge.

Sanskrit

Bījagaṇita Kī Ṭīkā

This Sanskrit manuscript presents a sophisticated treatise on *bījagaṇita* (algebra), specifically addressing the foundational concept of *avyakta* (the unknown/invisible) as the generative principle of mathematical knowledge. The text uniquely synthesizes Sāṃkhya philosophical terminology—where *avyakta* denotes primordial matter—with algebraic methodology, establishing the unknown quantity as the "single seed" (*eka-bīja*) from which all manifest mathematical operations proceed. The excerpt demonstrates the systematic exposition of algebraic operations including addition and subtraction of positive (*dhana*) and negative (*ṛṇa*) quantities, multiplication, division, squaring, and root extraction, with worked examples (*udāharaṇa*) illustrating the rules for sign manipulation. The manuscript's interlinear and marginal notations, including a later Hindi identification of the text as belonging to the *Bījagaṇita*, attest to its sustained scholarly engagement across centuries.

Opening verse on the unmanifest (avyakta) as pradhāna

MathematicsJune 20, 2026

Avyakta: The Unmanifest Seed of Indian Algebra

An ancient Sanskrit algebra treatise grounds the unknown in Sāṃkhya philosophy, treating invisible quantities as seeds from which all calculation grows.

From: Bījagaṇita Kī ṬīkāRead moreeast