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Jayadeva (c. 11th–12th century)

Indian Mathematician and Scholar of Prosody

Jayadeva lived around the 11th–12th century CE and is remembered as a mathematician who expanded upon the combinatorial and prosodic work of earlier scholars such as Pingala (c. 3rd–2nd century BCE). Distinct from the poet of the same name, this Jayadeva belonged to the scholarly tradition where mathematics and linguistics were deeply interlinked. His contributions focus on prosody, combinatorics, and the mathematical structures underlying poetic meters.

Extension of Pingala’s Binary System

Pingala had used short (laghu) and long (guru) syllables to encode poetic patterns, equivalent to a binary system of 0 and 1. Jayadeva extended this framework, formalizing the counting of possible combinations of syllables in verses of any length.

Pascal’s Triangle and Binomial Coefficients

Jayadeva introduced recursive methods equivalent to the arrangement of binomial coefficients in a triangular form, what Europe later called Pascal’s Triangle. This allowed efficient calculation of the number of possible syllable patterns in a verse of n syllables.

Combinatorial Formulas for Meters

He developed general rules to enumerate the number of meters possible for n syllables, contributing to early combinatorial enumeration. His work ensured that the mathematical analysis of poetic structures remained robust and transmitted across generations of Indian scholars.

Selected Mathematical Expression

Jayadeva’s methods can be represented using the binomial expansion:

\

Here, the coefficients \(\binom{n}{k}\) correspond to the number of arrangements of short and long syllables in verses, mirroring the triangular arrangement later known as Pascal’s Triangle. This formula provided poets and scholars a combinatorial tool to compute all possible patterns for a verse of n syllables.

Legacy

• Bridge in Indian Combinatorial Thought: Strengthened the study of prosody by systematizing Pingala’s combinatorial ideas.
• Recursive Patterns and Probability: Laid the foundations for combinatorial reasoning that prefigures modern probability theory.
• Influence on Later Scholars: Inspired subsequent mathematicians and prosodists like Halayudha and Kedārabhaṭṭa.
• Integration of Mathematics and Literature: Demonstrates the sophisticated use of mathematics in linguistic and poetic analysis in medieval India.