The name
कुट्टक — /'kuʈʈɐkɐ/
“The pulverizer.” Sanskrit. A 1,500-year-old algorithm.
Origin · 499 CE
Aryabhata wrote it down at 23
In 499 CE, in the city of Kusumapura (modern Patna), a 23-year-old astronomer named Aryabhata published the Aryabhatiya — a compact 121-verse treatise that, among many other things, proposed an algorithm for solving a class of problems that had stumped mathematicians for centuries: finding integer solutions to equations like ax ≡ 1 (mod n). He called it Kuttaka — “the pulverizer” — because it worked by breaking a problem down through repeated division, much like grinding grain.
Used for · planetary cycles
Why anyone needed it: to predict the sky
Aryabhata's day job was astronomy. Indian astronomers needed to answer questions like: If Jupiter returns to a given position every 4,332 days, and Saturn every 10,759 days, when will they meet here again? Or: given the lunar cycle and the solar cycle, when do they re-synchronise to mark a new year? These were calendar and almanac problems, and they all boiled down to one mathematical shape: ax + by = c — finding whole-number solutions. The Kuttaka algorithm solved them, exactly, by hand, on palm leaves.
What it actually does
A small example, gently
Imagine you owe ₹3 each to several friends and you only have ₹7 notes. You want a number of ₹7 notes (let's call it x) that you can hand out so that after each friend's ₹3 is removed, exactly nothing is left over — say, after seven friends. Kuttaka finds the smallest x that works. It looks trivial here. But scale it to numbers in the hundreds of digits and the same algorithm — re-derived by Euclid in Greece, by Brahmagupta in India, rediscovered as the Extended Euclidean Algorithm in the 19th century West — turns out to be the central machinery of modern cryptography.