To the area round what is now Naples came shiploads of colonists from the Greek cities of Asia Minor's Aegean coast. To the toe of Italy came migrants from the northern Peloponnese - the area near the port of Patrai. And to Sicily came eager colonists from Corinth, Megara and the Greek islands of Rhodes and Crete.
With its mainland core known by the sixth century BC as Megale Hellas (Magna Graecia in Latin), the Greek-colonised region of southern Italy and Sicily became, over the next few centuries, a powerhouse of philosophical, scientific, architectural and artistic creativity. Here lived, permanently or temporarily, the ancient Greek world's greatest inventor, its first great historian, and its greatest songwriter. It was home, also, to pioneers in medicine, drama, poetry and even religion.
Today, this region is the place to see the ancient world's best-preserved Greek temples, some of classical culture's finest bronzes, and rare surviving examples of ancient Greek wall-paintings. Superb southern Italian painted pottery - long thought, incorrectly, to have been imported from Greece - provides most of the surviving images of classical Greek drama.
Magna Graecia was definitely gaudier, brasher and less conventional than Greece itself. The good life here was very good indeed. We still describe sumptuous high living as sybaritic, a word derived from the ever-so-decadent fun and games practised in the city of Sybaris, near modern Sibari. Like Sodom and Gomorrah, Magna Graecia's sin city came to a bad end (it was destroyed by its neighbours).
On the intellectual front, ancient Greek all-time greats who hailed from the New Greece included Pythagoras, Archimedes and Herodotus. In the ancient city of Metaponto - the scattered ruins of which still survive - Pythagoras started his famous philosophy school.
The great man is now perhaps best known for his mathematical theorem, but spent most of his time running a politically powerful religious brotherhood which became one of the ancient world's most important philosophical movements. He believed that everything could be reduced to numbers - and even compared the universe to a musical scale.
He also believed in reincarnation and regarded animals as reincarnated humans. 'Don't hit that puppy,' he once told a fellow citizen. 'It's the soul of a friend of mine. I recognised the voice when I heard its cry.'
From the Sicilian Greek metropolis of Syracuse - later described by Cicero as the 'fairest of cities' - came the great inventor and mathematician Archimedes, who is said to have destroyed a Roman fleet with a mirror of fire: a sort of classical laser gun. It was through the streets of Syracuse that Archimedes - the original absent-minded professor - is reputed to have run stark naked crying 'Eureka] Eureka]' ('I've found it, I've found it'), after making a (scientific) discovery in his bath.
Syracuse was also home to Theocritus, founder of the pastoral genre of classical poetry; to Corax, founder of the great classical art of rhetoric; and to the founder of Greek comedy, the playwright Epicharmus, who, making fun of gods and heroes, portrayed Poseidon as a fishmonger, mighty Hercules as too greedy and Odysseus as an idle shirker. The greatest of ancient Greek lyricists, Pindar, also lived for a time in Syracuse, which he described as 'the queen of all towns'.
The predecessor of Syracuse's magnificent and still surviving Greek theatre - which seats 15,000 - almost certainly saw the world premieres of several plays by the first and greatest of Greek tragic dramatists, Aeschylus, who lived for a time in the city. Other temporary residents of Syracuse included a thousand Athenian PoWs. They had been foolish enough to attack the city during the great inter-Greek conflict, the Peloponnesian War, and ended up incarcerated in the massive ancient stone quarries, whose caverns and galleries still survive.
One of the most important of ancient Greek historians also lived for some years in the classical New World of southern Italy. Herodotus helped to found the little Magna Graecian town of Thurii; he later became one of the ancient world's best- travelled men, exploring the Balkans, the Middle East, North Africa and even southern Russia. He was also Europe's first real historian - and the first important European writer of prose. Whether he believed that historical knowledge could actually improve anything is extremely doubtful, since Herodotus was a confirmed fatalist. 'Not even the gods can override fate,' he once wrote.
Magna Graecia also produced the 'discovery' that our Earth is not the centre of the universe. This was the revolutionary conclusion of the astronomer Philolaus of Tarantum, who consolidated Pythagoras's ideas into a comprehensive system of beliefs. Southern Italy also saw the development of the idea that the universe is an integrated whole, a unity. The philosopher Parmenides - described by Aristotle as the founder of 'the science of truth' - established a philosophical school in the city of Elea (near Paestum); his ideas led directly to the formulation of ancient Greek atomic theory.
Elea was one of the classical world's greatest intellectual centres. Another of its philosophers, Xenophanes, became a pioneer in the development of monotheism. 'The all is one, and the one is God,' is how a fellow academic described his theological beliefs. In effect, Magna Graecia saw Parmenides's cosmological concept of the unity of our universe extrapolated by Xenophanes to produce a trend towards monotheism.
Politically, too, the Greek New World was a hotbed of activity. Agrigento, one of Sicily's greatest cities, had a democratic constitution written by the philosopher Empedocles. The ideal of the democratic city state which he espoused did not survive the demise of the ancient Greek world. But his theory that all matter consisted of four elements (fire, air, water and earth) dominated physics for more than 2,000 years, until a few centuries ago. And he was the first great medical figure in Western Europe - even if he did believe that all human intellectual activity takes place in the blood.
The spectacular ruins of his native city, Agrigento, survive to this day. It boasts no fewer than nine temples - including one of the best-preserved Greek temples in the world. Known now as the Temple of Concord, it was preserved by being utilised for many centuries as a Christian church, dedicated more prosaically to an early saint called Gregory of the Turnips. Zeus also had a temple here, and you can still admire one of the colossal statues of Atlas which once adorned its frontage.
Another great temple city, Paestum, has rare - and magnificent - ancient Greek tomb paintings. They show everyday life in the Greek New World: singing, music-making, feasting and even water sports.
The good life could not last forever. Magna Graecia shone for centuries as a beacon of intellectual achievement; but the region also witnessed the beginning of the end of Classical Greece. For it was in the New Greece - at Syracuse - that Athens was most decisively defeated late in its epic struggle with Sparta. This marked the beginning of the end for ancient Greece. It was not until the last century that Greece re-emerged as an independent force on the world stage.
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