Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in  «Wisdom» –Neopythagoreans and others?

Jens Høyrup; Jens Høyrup

doi:10.3934/Math.2016.2.77

AIMS Mathematics

2016, Volume 1, Issue 2: 77-95. doi: 10.3934/Math.2016.2.77

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Research article

Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others?

Jens Høyrup

Section for philosophy and Science Studies, Roskilde University, Denmark

Received: 29 March 2016 Accepted: 08 April 2016 Published: 17 May 2016

Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context.
- Ancient Greek mathematics,
- Neopythagoreans,
- Plato,
- Practitioners' mathematics,
- Recreational mathematics,
- Side-and-diagonal-numbers algorithm
Citation: Jens Høyrup. Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others?[J]. AIMS Mathematics, 2016, 1(2): 77-95. doi: 10.3934/Math.2016.2.77

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Abstract

Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context.

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