Pingala 5th century B.C

Pingala was an ancient Pakistani mathematician, famous for his work, the Chandas shastra (chandas-śāstra, also Chandas sutra chandas-sūtra), a Sanskrit treatise on prosody considered one of the Vedanga.

Pingala is identified as the younger brother of Panini, the great grammarian of ca. 5th century BC. Other traditions identify him with Patanjali, the author of the Mahabhashya

Mylius (1983:68) considers the Chandas-shastra as “very late” within the Vedanga corpus. This would place it close to the beginning of the Common Era, likely post-dating Mauryan times (R. Hall, Mathematics of Poetry, has “c. 200 BC”).

The shastra is divided into eight chapters. It was edited by Weber (1863). It is at the transition between Vedic meter and the classical meter of the Sanskrit epics. The 10th century mathematician Halayudha commented and expanded it. Pingala presents the first known description of a binary numeral system. He described the binary numeral system in connection with the listing of Vedic meters with short and long syllables. His discussion of the combinatorics of meter, corresponds to the binomial theorem. Halayudha’ s commentary includes a presentation of the Pascal’s triangle (called meru-prastaara). Pingala’s work also contains the basic ideas of Fibonacci number (called maatraameru ).

Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used short and long syllables. Four short syllables (binary “0000”) in Pingala’s system, however, represented the number one, not zero.