Classical period (5th - 4th century B.C.)

Within this period Athens flourishes under Pericles, the Parthenon is built on the Acropolis, the tragedies of Sophocles, Aeschylus and Euripides are created, the phisolophical schools of Socrates and Plato (known as Academy) are established, and the Lyceum of Athens is founded by Aristotle. In science, the importance of the experimental method is accepted.

Philosophers-Scientists

• Socrates (Athens, 470-399 B.C.). Died from poison after the state found him guilty for corrupting the youth.
• Theodorus of Cyrene (4th century B.C.). . Pythagorean. Plato's teacher in mathematics. Shows that the square roots of 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, and 17 are irrational.
• Archytas of Tarentum (420-350 B.C.). Greek mathematician, astronomer and engineer. Last of the Pythagorians. Plato and Eudoxus was his pupils. Built a series of toys, among them a mechanical pigeon propelled by a steam jet. Developed the theory for the pulley.
• Plato (Athens, 430-350 B.C.). Greek philosopher. He was the founder of the Academy (named from the hero Academos owner of the grove where the Academy was built). Believed that mathematics played an important role in education. Disregarded practicality, a belief he passed to his students such as Eucledes. He started a three part trilogy : Timaeus, Critias, and Hemocrates. He finished only the first, Timaeus where he speaks of his theory of four basic elements: earth, water, air, and fire, and hints for a fifth: ether. He is said to have invented a water clock with an alarm.
• Eudoxus of Cnidus (408-360 B.C.). Greek astronomer and mathematician. Belonged to the school of Plato. Developed the theory of proportions and the method of exhaustion.
• Callippus (Cyzicus, 370-300 B.C.). Greek astronomer, student of Eudoxus. Showed that at least 34 spheres are needed to account for the movement of the moon, planets, and stars.
• Aristotle (Stagira, 384-322 B.C.). Considered the father of life sciences. He was the tutor of Alexander the Great. Undertook the classification of animals and plants at a large scale. His main discovery in embryology was that the mother's contribution is as important as the father's. Believed that the Earth was static and at the center of the universe. He also believed, erroneously, that motion was due to the tendency of all objects to reach there natural state. He discovered that free fall is an accelerated form of motion, but also believed that heavier objects fall faster than lighter ones. He considered chemical elements, which cannot be decomposed, to be the constituents of all bodies. He was the founder of the Lyceum in Athens, also called the peripatetic school because the philosophers were thought while walking.
• Menaechmus (4th century B.C.). Discovered the conic sections. Was also a teacher of Alexander the Great. When Alexander the Great asked him if there was an easy way to learn geometry, he answered that in mathematics there is no royal path.
• Theophrastus (3rd century B.C.). Continued Aristotle's work in plant classification. Headed the Lyceum after Aristotle.
  Link: Theophrastus, Internet Encyclopedia of Philosophy
• Heracleides (Heraclea, 390-320 B.C.). Greek astronomer. First to suggest that Venus and Mars may orbit the sun. Also suggested the the Earth rotates around its axis once every 24 hours.
• Pytheas (330 B.C.). Greek geographer and explorer. Sailed into the North Atlantic and Baltic Sea where he observed the strong Atlantic tides. He correctly assumed that these were caused by the moon.
• Theaetetus (4th century B.C.). Greek mathematician. Belonged to the school of Plato. Developed the theory of incommensurable magnitudes.