MathematicsT1
Aryabhatiya II.22 (499 CE) gives both closed-form summation
identities: Σi² for i=1..n equals n(n+1)(2n+1)/6, and Σi³ for
i=1..n equals (Σi)² = (n(n+1)/2)². Faulhaber publishes the same
identities in 1631 (Academia Algebrae); Bernoulli systematises
power-sum formulas in 1713 (Ars Conjectandi) via what became the
Bernoulli numbers. The Sanskrit statement predates Faulhaber by
1,132 years.
The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930