**Plato
427 BC – 347 BC
**

**I believe it is important to note how we know what we know about Plato. The knowledge
we have on Plato comes from letters, supposedly written by him. It is important
that we consider the possibilities: 1.) that the letters were written by him
and are, therefore accurate of his life, 2.) that the letters were written by
someone who had accurate knowledge of his life, and 3.) that the letters were
made up by someone as pure fiction. Hopefully, the last of which is not the case.
**

**It is almost certain that Plato was friends with Socrates. In fact,
the death of Socrates had a profound affect on Plato; Plato decided to no
longer pursue
a career in politics in Athens. When Socrates died, Plato decided to travel
to Egypt, Sicily, and Italy. He introduced the Greeks to the water clock,
which he learned of in Egypt. He learned of the work of Pythagoras while
in Italy.
This made him begin to appreciate the value of mathematics. The things he
learned from studying Pythagoras’s work helped him form his idea that “the
reality which scientific thought is seeking must be expressible in mathematical
terms, mathematics being the most precise and definite kind of thinking of
which we are capable.”
**

**After serving in the military (and not for the first time), Plato returned to
Athens and founded his Academy (about 387 BC). This academy was an institution
dedicated to research and instruction of philosophy and the sciences. Through
the academy, Plato had hopes of training young men there who would eventually
become statesmen. He thought that, through his own training, these men would
improve the political leadership of Greece once they became involved in the politics.
**

**Plato considered mathematical objects as perfect forms. For example,
a line “is
an object having length but no breadth.” No matter how thin we make a line,
it will not be this perfect mathematical form, because it will always have breadth.
He discusses how objects in the real world try to be like their perfect forms
but never quite reach it. “The instance taken there is the mathematical
relation of equality, and the contrast is drawn between the absolute equality
we think of in mathematics and the rough, approximate equality which is what
we have to be content with in dealing with objects with our senses.” Plato
did not make any important mathematical discoveries, but he believed
that mathematics provides the finest training for the mind. This belief
was
important to the
development of mathematics.
**

**In fact, over the door of his academy, the sentence “Let no one unversed
in geometry enter here.” was written. Within the academy, Plato concentrated
on the idea of proof, and insisted on clear and concise definitions and hypotheses.
This is what laid the foundations of Euclid’s systematic approach
to mathematics.
**

**The most important mathematical work of the 4th century was done by
friends or students of Plato. For example, the first students of
conic sections
and the
creator of solid geometry were members of Plato’s academy. Plato’s
name is also connected with Platonic solids.
**

**It is interesting to note what Plato believed the first ten years
of a person’s
education should consist of: arithmetic, plane and solid geometry,
astronomy, and harmonics.**

References:

Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries:

Development and History. 3rd ed. New York: W.H. Freeman and Company,

1993. 6-19.

Historical Topics for the Mathematics Classroom. Washington D.C.:

National Council of Teachers of Mathematics, 1969.

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Thales.html (March 2005)

http://geometryalgorithms.com/history.htm (March 2005)