# Mathematician:Nicomachus of Gerasa

## Mathematician

Neo-Pythagorean about whom very little is known.

Unusual in that he used the system of Arabic numerals rather than the then-current cumbersome Roman numerals.

Famously made some conjectures about perfect numbers which were soon shown to be false.

Appears to have had more influence than his (perhaps limited) abilities may have merited.

Some consider him to be "one of the greatest mathematicians in human history" which should perhaps be considered to be unwarranted hyperbole.

## Nationality

Graeco-Roman

## History

- Born: c. 60 CE in Gerasa, Roman Syria (now Jerash, Jordan)
- Died: c. 120 CE

## Theorems

Results named for **Nicomachus of Gerasa** can be found here.

## False Conjectures

- One Perfect Number for Each Number of Digits
- Last Digit of Perfect Numbers Alternates between $6$ and $8$

## Publications

*Introduction to Arithmetic*(Greek:*Ἀριθμητικὴ εἰσαγωγή*)*Manual of Harmonics*(Greek:*Ἐνχειρίδιον ἁρμονικῆς*)

Several other works of his are referred to by other ancient writers, but unfortunately appear not to have survived:

*Art of Arithmetic*(Greek:*Τεχνη ἀριθμητικῆ*)- A larger work on music
*An Introduction to Geometry*(may not have been Nicomachus's work)*Theology of Arithmetic*(Greek:*Θεολογούμενα ἀριθμητικῆς*). (There exists a work under this name written two centuries later which contains quotations from it.)*A Life of Pythagoras*- A collection of Pythagorean dogmata
*On Egyptian festivals*(Greek:*Περὶ ἑορτῶν Αἰγυπτίων*) (may not have been Nicomachus's work).

## Also known as

In Greek: **Νικόμαχος**.

His name can sometimes (erroneously) be seen spelled **Nichomachus**, but this is incorrect because the first **c** is a transliteration of Greek $\kappa$ not $\chi$.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Nicomachus of Gerasa": MacTutor History of Mathematics archive

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence