Mathematics

T1

In Pingala's Chandahsutra (~200 BCE), four short aphorisms describe a recursive algorithm: halve the number, double when zero, square when halved, subtract one when odd. The output is 2ⁿ for n syllables of a Sanskrit metre. Leibniz publishes binary arithmetic in 1703. Modern exponentiation-by-squaring (the cryptographic core of every TLS handshake) follows the same recurrence. Pingala wrote it down 1,900 years earlier, for poetic prosody.

From the source

“multiply by two when zero ”
— History of Hindu Mathematics — A Source Book, tr. Bibhutibhusan Datta and Avadhesh Narayan Singh (1938)ch2.v12.dup2
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In Pingala's Chandahsutra (~200 BCE), four short aphorisms describe a recursive algorithm: halve the number,… — Experli