Firstly that Plato wrote the letters and therefore the details are accurate.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.Only two further episodes in Plato's life are recorded.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.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.Plato concentrated on the idea of 'proof' and insisted on accurate definitions and clear hypotheses.