The School of Athens

The School of Athens was painted by Raphael Sanzio or Raffaello Santi (1483-1520) for Pope Julius II (1503-1513) as a part of Raphael's commission to decorate with frescoes the rooms that are now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican. In this fresco, Raphael depicts the great philosophers and mathematicians of ancient Greece as colleagues in a timeless academy:

Plato is in the center pointing his finger to the heavens while holding the Timaeus, his treatise on the origin of the world. Next to him, his younger pupil Aristotle holds a copy of his Ethics while describing the earth and the wide realm of moral teaching with his extended hand in an elegant horizontal gesture, Pythagoras contemplates his system of proportions at the lower left and Euclid draws a circle on a slate at the lower right.

To the Greeks mathematics was essentially geometry, and it was in Elements, Euclid's treatise on the subject, that the notion of an axiomatic system was first laid out In this system certain self-evident statements called axioms are assumed to be true and new statements called theorems are derived from them using the Aristotelian rules of inference.

The Fresco of Raphael's School of Athens is a masterpiece of Art. However, over the centuries it has posed many problems to know all details of the persons who are depicted. Unfortunately Raphael did not leave any personal notes on this work but some of the persons can be identified.

The identity of some of the philosophers in the picture, such as Plato or Aristotle, is uncontroversial, but scholars disagree on many of the other figures. According to Lahanas, they are usually identified as follows:
 

• Zeno of Citium or Zeno of Elea?

• Epicurus

• Frederik II of Mantua?

• Anicius Manlius Severinus Boethius or Anaximander or Empedocles

• Averroes

• Pythagoras

• Alcibiades or Alexander the Great?

• Antisthenes or Xenophon?

• Hypatia — (Francesco Maria della Rovere or Raphael's mistress Margherita.)

• Aeschines or Xenophon?

• Parmenides?

• Socrates?

• Heraclitus — (Michelangelo)

• Plato holding the Timaeus — ( Leonardo da Vinci)

• Aristotle holding the Ethics?

• Diogenes of Sinope?

• Plotinus?

• Euclid or Archimedes with students ( Bramante)?

• Strabo or Zoroaster? (Baldassare Castiglione or Pietro Bembo)

• Ptolemy? - Apelles — (Raphael)

• Protogenes — (Il Sodoma or Perugino).

Reference:
The American Heritage Dictionary. Wikipedia, Houghton Mifflin Company: Scientist. Columbia University Press: Encyclopedia. Encyclopedia Britannica.