# Nicomachus

**Nicomachus of Gerasa**[1] (Greek: Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist,[2] best known for his works *Introduction to Arithmetic* and *Manual of Harmonics* in Greek. He was born in Gerasa, in the Roman province of Syria (now Jerash, Jordan). He was a Neopythagorean, who wrote about the mystical properties of numbers.[3][4]

In number theory, the sum of the first *n* cubes is the square of the *n*th triangular number. That is,

{\displaystyle 1^{3}+2^{3}+3^{3}+\cdots +n^{3}=\left(1+2+3+\cdots +n\right)^{2}.}

The same equation may be written more compactly using the mathematical notation for summation:

{\displaystyle \sum _{k=1}^{n}k^{3}={\bigg (}\sum _{k=1}^{n}k{\bigg )}^{2}.}

This identity is sometimes called **Nicomachus’s theorem**, after Nicomachus of Gerasa (c. 60 – c. 120 CE).