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