This manuscript page from the Bija section of a mathematical treatise begins with an invocation to Sri Ganesha and praises the unmanifest seed (avyakta bija) as the source of all manifestation, following Samkhya philosophy. It then presents rules for arithmetic operations with positive (dhana) and negative (rna) quantities, including addition and subtraction of like and unlike signs. The text provides worked examples using symbolic notation where numbers are marked with debt-signs to indicate negative values, demonstrating how to calculate sums and differences of integers. Key terms include bija (seed/coefficient), vyakta (manifest), avyakta (unmanifest), yoga (addition), and vyavakalana (subtraction).

Sanskrit

Bījagaṇita

This Sanskrit manuscript presents a foundational treatise on Indian algebra (bīja-gaṇita), attributed to the mathematician Bhāskara II. The text systematically develops rules for operations with positive and negative quantities (dhanaṛṇa), zero (kha), and unknown quantities (avyakta), including addition, subtraction, multiplication, division, squaring, and root extraction. Notable features include the sophisticated treatment of zero as a number with defined operational properties, the use of color-coded symbols (yāvattāvat, kālaka, nīlaka) to represent unknowns, and the clear distinction between like and unlike terms in algebraic operations. The verse-commentary format, with invocatory verses to Gaṇeśa and Īśvara, exemplifies the classical Indian mathematical tradition's integration of technical content with poetic expression.

Opening of the Bījagaṇita on operations with wealth and debt

MathematicsJanuary 16, 2026

Algebra as Wealth and Debt: The Bījagaṇita's Numbers

The Bījagaṇita's metaphor of wealth and debt makes the algebra of positive and negative numbers vivid and practical — mathematics rooted in the merchant's ledger.

From: Bījagaṇita Read moreeast