Editing Plato (section)

===Later philosophical development===
After the death of Socrates, Plato remained in Athens for roughly three years.{{sfn|Waterfield|2023|p=71}} 
==== Heraclitus and Parmenides ====
{{main|Heraclitus|Parmenides}}
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| image1 = Hendrik ter Brugghen - Heraclitus.jpg
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| caption1 = ''Heraclitus'' (1628) by [[Hendrick ter Brugghen]]. Heraclitus saw a world in [[flux]], with everything always in conflict, constantly changing.
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| caption2 = Bust of Parmenides from [[Velia]]. Parmenides saw the world as [[Eternity of the world|eternal]] and unchanging, that all change was an illusion.
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In Athens, Plato studied with [[Cratylus]], a philosopher who followed the early Greek philosopher [[Heraclitus]], and also [[Hermogenes]], an [[Eleatic]] philosopher in the tradition of [[Parmenides]].{{sfn|Nails|2002|p=248}} Heraclitus viewed all things as [[Impermanence|continuously changing]], that one cannot "step into the same river twice" due to the ever-changing waters flowing through it, and all things exist as a contraposition of opposites, while Parmenides adopted an altogether contrary vision, arguing for the idea of a changeless, eternal universe and the view that change is an illusion. Heraclitus's views are expounded by Cratylus himself in Plato's dialogue ''[[Cratylus]]'' and deconstructed in the ''[[Theaetetus (dialogue)|Theaetetus]]'' by Socrates. Plato would go on to depict both Parmenides and Parmenides' student [[Zeno of Elea|Zeno]] in the ''Parmenides'', and an "Eleatic Stranger" also appears in the ''[[Sophist (dialogue)|Sophist]]'' and ''[[Statesman (dialogue)|Statesman]]''.

In roughly 396 BC, Plato left Athens and studied in [[Megara]] with [[Euclid of Megara]], founder of the Megarian school of philosophy, and other Socratics.{{sfn|Waterfield|2023|p=72}} 

==== Mathematics ====
Around 394 BC or earlier, he returned to Athens, where, as an Athenian male of military age he would have needed to be available to serve in the [[Corinthian war]], which Athens participated in from 395 to 386 BC.{{sfn|Waterfield|2023|p=73}} Other than potential military service, Plato spent his time studying mathematics with [[Archytas of Tarentum]], [[Theaetetus (mathematician) | Theaetetus]], [[Leodamas of Thasos]], and [[Neoclides]] in the grove of [[Hecademus]],{{sfn|Nails|2006|pp=5-6}} named after an [[Attica|Attic]] hero in [[Greek mythology]], northwest of the city of [[Athens]], where he would later found his Academy.{{sfn|Waterfield|2023}} During this time, Plato likely began work on some of his earliest works; including the ''[[Apology (Plato)|Apology]]'', possibly early drafts of the ''[[Gorgias (dialogue)|Gorgias]]'' and ''[[Republic (Plato)|Republic]]'' Book I, and an early form of the ''Republic'' books II-IV, in the form of a speech rather than a dialogue, which was ridiculed by Aristophanes in the ''[[Ecclesiazusae]]'' in 391 BC.{{sfn|Nails|2006|p=6}} [[Speusippus]], the son of Plato's sister Potone, who took over the academy after Plato's death, joined the group in about 390 BC, and [[Eudoxus of Cnidus]], another early mathematician, arrived around 385 BC.{{sfn|Nails|2006|pp=5-6}}

==== Pythagoreanism ====
{{main|Pythagoreanism}}
[[File:Kapitolinischer Pythagoras adjusted.jpg|right|upright|thumb|The mathematical and mystical teachings of the followers of Pythagoras, pictured above, exerted a strong influence on Plato.]]
After the conclusion of the [[Corinthian War]], Plato travelled to southern Italy to study with [[Archytas]] and other Pythagoreans.{{sfn|Waterfield|2023|p=112}} The influence of these Pythagoreans appears to have been significant. According to [[R. M. Hare]], this influence consists of three points:
# The platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton.
# The idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in [[science]] and [[morals]]".
# They shared a "mystical approach to the soul and its place in the material world".<ref>R.M. Hare, Plato in C.C.W. Taylor, R.M. Hare and Jonathan Barnes, Greek Philosophers, Socrates, Plato, and Aristotle, Oxford: Oxford University Press, 1999 (1982), 103–189, here 117–119.</ref>

Pythagoras held that all things are number, and the cosmos comes from numerical principles. He introduced the concept of form as distinct from matter, and that the physical world is an imitation of an eternal mathematical world.<ref>{{Cite book |last=Calian |first=Florin George |url=https://brill.com/display/book/9789004467224/BP000010.xml |title=Numbers, Ontologically Speaking: Plato on Numerosity |year=2021 |publisher=Brill |isbn=978-90-04-46722-4 |language=en |access-date=10 April 2023 |archive-date=7 May 2023 |archive-url=https://web.archive.org/web/20230507230433/https://brill.com/display/book/9789004467224/BP000010.xml |url-status=live }}</ref>