Nevertheless, although the Form of a circle has never been seen -- -indeed, could never be seen -- -mathematicians and others do in fact know what a circle is. That they can define a circle is evidence that they know what it is. For Plato, therefore, the Form "circularity" exists, but not in the physical world of space and time. It exists as a changeless object in the world of Forms or Ideas, which can be known only by reason." Forms have greater reality than objects in the physical world both because of their perfection and stability and because they are models of reality (Vincent, 2005). Circularity, squareness, and triangularity are all good examples of what Plato meant by Forms. An object in the physical world may be called a circle or a square or a triangle only to the extent that it resembles the Form "circularity" or "squareness" or "triangularity."

Although Plato made no major mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of mathematics (Field, 1956).

Plato focused on the idea of 'proof' and insisted on accurate definitions and hypotheses (Field, 1956). His contributions to mathematics through his students at the Academy are apparent, as his students were responsible for all of the most important mathematical work of the 4th century.

Plato's...

When he died, Speusippus assumed the role as head of the Academy. The school existed until AD 529, when it was closed by the Byzantine emperor Justinian I, who outlawed its pagan teachings.
During the Renaissance, the main focus of Platonic influence was the Florentine Academy, founded in the 15th century near Florence (Urmson and Ree, 1991). Under the leadership of Marsilio Ficino, members of the Academy studied Plato in the original Greek. In England, Platonism was revived in the 17th century by Ralph Cudworth and others who were known as the Cambridge Platonists. Plato's influence has remained solid through modern times by such thinkers as Alfred North Whitehead, who once described the history of philosophy as simply "a series of footnotes to Plato."

Bibliography

Field, G. (1956). The philosophy of Plato. Oxford.

Grolier Multimedia Encyclopedia. (1996). Plato. Grolier Interactive, Inc.

Harris, William. (2000). Plato: Mathematician or Mystic? Middlebury College.

J.O. Urmson and Jonathan Ree, (1991). The Concise Encyclopedia of Western Philosophy and Philosophers. London: Unman Hyman.

Microsoft Encarta 98 Encyclopedia. (1998). Plato. Microsoft Corporation.

Vincent, Jay. (2005). Plato. Island of Freedom.