Nicomachus of Gerasa

Ancient Jerash’s pioneering mathematician, music theorist

Plato (left) and Nicomachus (right), as inventors of music, from a 12th-century manuscript. WIKIMEDIA COMMONS
Plato (left) and Nicomachus (right), as inventors of music, from a 12th-century manuscript. (Photo: WIKIMEDIA COMMONS)
AMMAN — Jerash, a once magnificent city in the Roman period and now a bustling archaeological park, has a rich history that is lesser known to the general public. Among its residents was Nicomachus, a leading mathematician and music theorist born in Jerash around 60 CE.اضافة اعلان

Mathematical contributionsNicomachus was a Neo-Pythagorean philosopher who made a remarkable contribution to mathematics and is known for writing the oldest surviving Greek multiplication table, according to several scholars who wrote on the history of mathematics, including Eric Temple Bell and Frank J. Swetz. 

Nicomachus was also known for writing "Introduction to Arithmetic,” the first book to treat arithmetic as a separate topic from geometry. This book was translated into Latin by Ancius Boethius and was used as the standard arithmetic curriculum in European schools for 1000 years.

Not much is known about Nicomachus's life, but his writings have earned him a prominent place in the history of mathematics. 

During his lifetime, he was highly regarded as a mathematician. His name became synonymous with good calculation, at least for the ancient satirist Lucian who referred to good calculators as those who "reckoned like Nicomachus of Gerasa."

Nicomachus was also involved in the theory of numbers and their "mystical properties," such as perfect and amicable numbers. He added 8,128 to the list of perfect numbers, which at that time included 6, 28, and 496. 

His book "Introduction to Arithmetic" remarkably used Arabic numerals instead of Greek ones and was later translated into Arabic by Thabit Ibn Qurra, a mathematician, physician, astronomer, and translator that is considered the founder of statics. 

And since 1926, Nicumahcus’s book has been available in English after Martin Luther D'Oog translated it.

Additionally, as quoted by Iamblichus and Porphyry in their biographies of Pythagoras, scholars have conjectured that Nicomachus also wrote a biography of Pythagoras.

He also wrote "Theology of Numbers" on the mystic properties of numbers, although only fragments of the work have survived.

Music theoryNicomachus is also known for writing "the Manual of Harmonics", which discusses music theory and its relationship with numbers. It is considered to contain the earliest surviving record of the Pythagorean legend of discovering the musical pitch. 

It says that pitch is determined by numeric ratios, according to Henrietta O. Midonick, mathematician and author of “the Treasury of Mathematics”.

Despite all his offerings, many of Nicomachus's works are lost, including a larger piece on music that he promised to an unknown lady and several other books such as "Art of Arithmetic," "Theology of Arithmetic," and "An Introduction to Geometry". 

However, mathematicians continue to recognize Nicomachus through "Nicomachus's Theorem," a mathematical equation.

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