Plato is one of the most important Greek philosophers. He founded the Academy in Athens. His works on philosophy, politics and mathematics were very influential and laid the foundations for Euclid's systematic approach to mathematics.
Mathematical Profile (Excerpt):
- The details are mostly given by Plato himself in letters which seem, on the face of it, to make them certain.
- However, it is disputed whether Plato did indeed write the letters so there are three possible interpretations.
- Firstly that Plato wrote the letters and therefore the details are accurate.
- Secondly that although not written by Plato, the letters were written by someone who knew him or at least had access to accurate information on his life.
- Next we should comment on the name 'Plato'.
- It was mostly in Pyrilampes' house that Plato was brought up.
- Aristotle writes that when Plato was a young man he studied under Cratylus who was a student of Heracleitus, famed for his cosmology which is based on fire being the basic material of the universe.
- Plato left Athens after Socrates had been executed and travelled in Egypt, Sicily and Italy.
- Again there was a period of war and again Plato entered military service.
- It was claimed by later writers on Plato's life that he was decorated for bravery in battle during this period of his life.
- Plato returned to Athens and founded his Academy in Athens, in about 387 BC.
- The Academy was an institution devoted to research and instruction in philosophy and the sciences, and Plato presided over it from 387 BC until his death in 347 BC.
- Only two further episodes in Plato's life are recorded.
- Plato did not expect the plan to succeed but because both Dion and Archytas of Tarentum believed in the plan then Plato agreed.
- Plato returned to Athens, but visited Syracuse again in 361 BC hoping to be able to bring the rivals together.
- makes it clear that the popular conception of Plato as an aloof unworldly scholar, spinning theories in his study remote from practical life, is singularly wide of the mark.
- Plato's main contributions are in philosophy, mathematics and science.
- However, it is not as easy as one might expect to discover Plato's philosophical views.
- The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote a number of dialogues (about 30) which are written in the form of conversations.
- In letters written by Plato he makes it clear that he understands that it will be difficult to work out his philosophical theory from the dialogues but he claims that the reader will only understand it after long thought, discussion and questioning.
- The dialogues do not contain Plato as a character so he does not declare that anything asserted in them are his own views.
- Through these dialogues, Plato contributed to the theory of art, in particular dance, music, poetry, architecture, and drama.
- In his theory of Forms, Plato rejected the changeable, deceptive world that we are aware of through our senses proposing instead his world of ideas which were constant and true.
- Let us illustrate Plato's theory of Forms with one of his mathematical examples.
- Plato considers mathematical objects as perfect forms.
- In the Phaedo Plato talks of objects in the real world trying to be like their perfect forms.
- Again in the Republic Plato talks of geometrical diagrams as imperfect imitations of the perfect mathematical objects which they represent.
- Plato's contributions to the theories of education are shown by the way that he ran the Academy and his idea of what constitutes an educated person.
- Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of the subject.
- Plato concentrated on the idea of 'proof' and insisted on accurate definitions and clear hypotheses.
- Eudoxus of Cnidus - author of the doctrine of proportion expounded in Euclid's "Elements", inventor of the method of finding the areas and volumes of curvilinear figures by exhaustion, and propounder of the astronomical scheme of concentric spheres adopted and altered by Aristotle - removed his school from Cyzicus to Athens for the purpose of cooperating with Plato; and during one of Plato's absences he seems to have acted as the head of the Academy.
- Archytas, the inventor of mechanical science, was a friend and correspondent of Plato.
- In mathematics Plato's name is attached to the Platonic solids.
- The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.
- Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon move round the Earth in crystalline spheres.
- Perhaps the best overview of Plato's views can be gained from examining what he thought that a proper course of education should consist.
- Dialectic is the art of conversation, of question and answer; and according to Plato, dialectical skill is the ability to pose and answer questions about the essences of things.
- Plato's Academy flourished until 529 AD when it was closed down by the Christian Emperor Justinian who claimed it was a pagan establishment.
Born 427 BC, Athens, Greece. Died 347 BC, Athens, Greece.
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Ancient Greek, Architecture, Astronomy, Geometry, Origin Greece, Physics, Puzzles And Problems, Special Numbers And Numerals
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive