Archimedes's cattle problem

Archimedes. Archimède, Volume 3. Mugler, Charles, editor. Paris: Les Belles Lettres, 1971.

Open Greek and Latin · CC BY-SA 4.0

Cloned and adapted by Humanitext, with ongoing edits.

This work is an extremely challenging mathematical puzzle, attributed to Archimedes of Syracuse and sent to Eratosthenes of Alexandria, which tasks the reader with calculating the number of cattle belonging to the sun god, Helios. The text consists of a problem presented in poetic verse and an ancient commentary recording the numerical results of the calculation. In the poem, the relations between the numbers of bulls and cows of four different colors (white, black, dapple, and yellow) are presented as a series of simultaneous linear equations. The problem escalates in difficulty with additional conditions requiring the sums of certain cattle to form perfect square and triangular numbers, leading to an astronomically large integer solution. The subsequent commentary provides concrete numerical values for this complex calculation, illustrating the sophisticated level of ancient mathematics.