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 nth 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).
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