Plato was a Greek philosopher born around 427 BCE who established an influential school called the Academy. He was greatly influenced by his teacher Socrates and wrote philosophical dialogues featuring Socrates discussing various topics. Plato believed that true knowledge came from comprehending abstract forms rather than material things perceived by the senses. He developed theories about mathematics being essential for understanding reality's highest forms. Pythagoras, who lived in the 6th century BCE, heavily influenced Plato and believed that numbers expressed the essence of all things.

1. PLATO.
LIFE AND LEGACY
 427 (?) – 348 BCE
 Lived about 200 years
after
Pythagoras
 His real name was Aristocles, but
his wrestling coach dubbed him
“Platon”, on account of his robust
figure.
 Son of a wealthy Athens family
 Served in the Athens army during
the Peloponnesian War.
 Student of Socrates, by whom he
was much influenced.
 Along with his mentor Socrates
and his student Aristotle, Plato
helped to lay the foundations of
Western Philosophy and Science.

2. PLATO
THE ACADEMY
In
387 BC, Plato established a
school for philosophy, built in a
grove dedicated to the famous
hero, Academos.
The Academy continued until it
was closed in 529 CE, by
Justinian I of Byzantium, over
900 years later.
Many intellectuals were
schooled in the Academy, the
most prominent one being
Aristotle.

3. PLATO
THE DIALOGUES
Plato’
s works span
approximately 30 “dialogues”dramatic conversations with
statesmen, citizens, and other
recognizable names from
Plato’s time and earlier.
Socrates is the main
interlocutor. It is hard to say
what are just Socrates’ own
views and what is just Plato’s
voice.

4. PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
Most
of Plato’s writings are
not about nature, but his
concepts of reality and
knowledge have had a
profound impact.
In his well-known dialogue,
The Republic, there is nicely
portrayed his overall view on
reality.

5. PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line
Everything
is being
represented as
placed on a single
line, extending
from the lowest to
the highest sense
of reality.

6. PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line
There
are two
main sections of
the line,
representing those
things
apprehended by
the senses (the
lower section) and
those things only
apprehended by
the mind (the
upper section).

7. PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line
The
upper section
(the intelligible
world) is divided
again in the purest
form of reality (the
forms and the
Good – which is
the highest form)
and

8. PLATO
PRE-EMINENCE OF MATHEMATICS
the
mathematical
objects which are an
essential
preliminary stage
on the mind’s way
to reach the
grasping of the
ultimate reality
For Plato the study
of mathematics was
a crucial step in the
path leading the
mind to the truth.

9. PLATO
PRE-EMINENCE OF MATHEMATICS
Plato
had become
convinced that the road to
knowledge lay in exact
reasoning, as in
mathematics.
The famous inscription over
the entrance of the
Academy read: let no one
who does not know
geometry enter here.

10. PYTHAGORAS
582-520 BC
All is number

11. PYTHAGORAS
EARLY LIFE
Born
in Samos, Greece,
circa 582 BC
Was taught about early
Ionian, presocratic
philophers Thales,
Anaximander and
Anaximenes.
Was drawn away from
his land because of his
disgust for tyranny of
Polycrates.

12. pythagoreanism
Pythagoras,
after
leaving his homeland
settled in Crotone, a
Dorian Greek colony
in southern Italy.
There he founded his
own cult, the
pythagoreans.
It was based on
philosophical, political
and religious beliefs.

13. The numbers
Pythagoras
(and all the
pythagoreans) adored
numbers.
Thought that numbers
express the real (and
usually secret) essence
of all things.
Accordingly, they
studied mathematics
intensively and
extensively.

14. Pythagoras mathematical
discoveries
Discovered
the
existence of
irrational numbers
His famous
pythagorean
theorem
( a2+b2=c2)
The ratios of
musical intervals

15. Pythagoras
the harmony of the spheres
Famous
is his view
that the movement of
the heavenly bodies
produces an unheard
musical harmony
based on the
mathematical
relationship of their
orbit, known as the
harmony of the
spheres.