Editing Pythagoras (section)

=== Numerology ===
[[File:Tetractys.svg|thumb|alt=Diagram showing the tetractys, an equilateral triangle made up of ten dots, with one dot in the top row, two in the second, three in the third, and four in the bottom.|Pythagoras is credited with having devised the [[tetractys]],{{sfnp|Gregory|2015|pages=28–29}} an important [[Religious symbol|sacred symbol]] in later Pythagoreanism.{{sfnp|Riedweg|2005|page=29}}{{sfnp|Kahn|2001|pages=1–2}}]]
Another belief attributed to Pythagoras was that of the "[[Musica universalis|harmony of the spheres]]",{{sfnp|Riedweg|2005|pages=29–30}}{{sfnp|Gregory|2015|pages=38–39}} which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.{{sfnp|Riedweg|2005|pages=29–30}}{{sfnp|Gregory|2015|pages=38–39}} According to Porphyry, Pythagoras taught that the seven [[Muse]]s were actually the [[Classical planet|seven planets]] singing together.{{sfnp|Riedweg|2005|page=30}}

{{cquote|The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything.|author={{harvp|Aristot. Met. 1|loc=985b}} }}

Modern scholars typically ascribe these discoveries to the later Pythagorean philosopher [[Philolaus of Croton]] ({{circa|470|385|lk=no}}&nbsp;BC), whose extant fragments are the earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras.{{sfnp|Joost-Gaugier|2006|pages=87–88}} In his landmark study ''Lore and Science in Ancient Pythagoreanism'', Walter Burkert argues that Pythagoras was a charismatic political and religious teacher,{{sfnp|Kahn|2001|pages=2–3}} but that the number philosophy attributed to him was really an innovation by Philolaus.{{sfnp|Kahn|2001|page=3}} According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics.{{sfnp|Kahn|2001|pages=2–3}} Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, [[Mathematical proof|proofless]] [[arithmetic]],{{sfnp|Burkert|1972|pages=428–433}} but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics.{{sfnp|Burkert|1972|page=465}} For the later Pythagoreans, Pythagoras was credited with devising the [[tetractys]], the triangular figure of four rows which add up to the "perfect" number, ten.{{sfnp|Gregory|2015|pages=28–29}}{{sfnp|Burkert|1972|pages=467–468}} The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance.{{sfnp|Riedweg|2005|page=29}} Iamblichus, in his ''Life of Pythagoras'', states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it.{{sfnp|Riedweg|2005|page=29}}{{sfnp|Iamblichus, Vit. Pyth|loc=§29}}

This shouldn't be confused with a simplified version known today as "[[Numerology#Pythagorean method|Pythagorean numerology]]", involving a variant of an isopsephic technique known – among other names – as {{lang|grc|pythmenes}} {{gloss|roots}}<ref name="pythmenes1">{{harvp|Gregory|2015|pp=32–34}}</ref> or {{gloss|base numbers}},<ref>{{harvp|Zhmud|2012|p=277}}</ref> by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word.<ref name="pythmenes1" />