Pythagoras is in the left foreground of Raphael's
fresco and is depicted writing on a tablet. Although none of his
writings have survived, he is regarded as one of the founders
of mathematics. Pythagoras or his followers are credited with
discovering many principles of mathematics, particularly in the
area of numerical relationships, that form the basis of current
mathematics.
He founded a school in what is now southern Italy.
Among the beliefs he held and taught were that the world around
us, at its deepest level, is mathematical in nature and that philosophy
(including mathematics) was a means to purify the soul and enable
it to unite with the divine.
To read more about Pythagoras, examine the following
web pages:
Ptolemy is standing with his back to the viewer
in the right foreground of Raphael's fresco. he is holding an
earth sphere and is facing Zoroaster who is holding a celestial
sphere.
Ptolemy is a controversial figure. Some regard him
as a great mathematician and astronomer and others (including
the great scientist Newton) accused him of fraud. He is credited
with developing a mathematical theory of the motion of the sun,
moon and planets and his famous treatise on the subject survived
as an authoritative source until the publication of the theories
of Copernicus in the 16th century.
To read more about Pytolemy and to study his writings,
examine the following web pages: