The Pythagorion area is also the centre of the island's archaeological heritage – at least what sorry traces of it are left to us today. The place thrived under the rule of the tyrant Polykrates in the latter half of the 6th century BC.
With the aid of a gifted engineer Efplinos and around 4,000 slaves brought in from Lesbos and Naxos, he ordered some astonishing building work. He built six kilometres of defensive walls, bristling with 35 towers and 12 gates, stretching all the way from Pythagorion to Cape Fornias. He also created a huge harbour mole on which the modern harbour jetty still stands. And he drilled a one-kilometre tunnel through the mountain to bring water in and provide a secret escape route out should his walled city, as it was then, come under siege.
Slaves dug from both sides of the mountain to meet bang in the middle, a supreme technical achievement given the primitive tools and lack of scientific equipment at the time. Today, paying visitors are allowed around 100 metres inside to see their handiwork.
Unfortunately, much of this heritage has been lost over time. It is not unusual to see hotels built in the middle of archaeological ruins, and the island airport was built right across one of the most notable archaeological sites in Greece.
The tyrant Polykrates' most celebrated work was to the west at the end of a seven-kilometre-long marble-paved Sacred Way said to have been lined with around 2,000 statues from Pythagorio to Ireon. At the Ireon end of the road was a magnificent temple to the mother goddess Hera, supported by 134 columns and believed to rival the Parthenon itself.
Had it survived it would have been a wonder. But the glorious temple has been long laid to waste as fire, invasions, earthquakes, pilfering and out-and-out neglect. Excavation didn't begin until 1985, and the remains are, quite frankly, a sorry sight.
Ninety percent of the Sacred Way is now buried beneath an airport runway, a road and a crop of holiday hotels. The remarkable tunnel is collapsing, and all that remains of the temple is a single tottering pillar standing in an incoherent maze of scattered rubble.
Nevertheless, the place crawls with visitors, and there is plenty see over several acres if broken pillars and scattered ruins are your thing. Nearby are the remains of some Roman baths, said to have been used by Anthony and Cleopatra The baths are a good size but pretty dull with a few unimpressive standing columns and hypocausts.
The Archeological Museum in the town of Samos is one of the most important in Greece. Rare archaeological findings on show include the 'kouros' statue of a young man, the largest 'kouros' statue in Greece. This sculpture, three times life-size, is carved from a single piece of marble, weighing 4.5 tonnes, though it was in fragments when found.
The exhibits are housed in two buildings, the Old Museum, which as built in 1912 and the New Museum which opened in 1987 and contains the sculpture collection. As well as ancient sculptures the exhibits include pottery, bronzes, ivory carvings and clay figurines. Also of note is the marble statue of a draped female figure which dates from around 560BC.
Samos' most famous son Pythagoras didn't actually spend much time on the island. Known today mainly for his geometric theorems he was, during his lifetime, equal parts mathematician, philosopher, magician and mystic Surprisingly, he left absolutely no written records himself and what we know of his teachings comes only from his students, who did.
Pythagoras exerted a profound influence on later Greek philosophers, including Aristotle and Plato and he established a 'Pythagorean' way of life – noted for its vegetarianism, abstinence and the renouncing of all money and wordily goods.
It was a way of life that would endear the Pythagorean sect to the people, and its members were noted for honesty and incorruptibility. It also earned them enemies and Pythagoras was banished and many of his followers executed.
Pythagoras was born on Samos in the 6th century BC, the son of a wealthy sea trader. Highly intelligent, he made the most of the best education that money could buy. But his father died while Pythagoras was still a teenager and soon afterwards the tyrant Polykrates became ruler of the island.
Pythagoras left for Miletus, aged just 18 years, to be taught by the eminent, if ancient, teacher Thales who advised him to visit Egypt, then a significant seat of learning. Pythagoras lived more than 20 years in Egypt, studying astronomy and geometry with their priests and sages.
An extraordinary period followed when Egypt was invaded and Pythagoras was carried off to Babylon, supposedly into slavery. Here he mysteriously rose from captive to a disciple of the Persian magi, studying arithmetic, music and divination. No one understands how a captive Greek slave could have risen to such eminence.
He eventually returned to Samos, aged 56, and set up a school. He preferred a meditative way of life and took to living in a cave, but was always pestered by the island authorities to help with the public and political administration on Samos. Fed up with the intrusions, he gathered his most loyal followers and left for Croton in Italy.
It was here that he expounded a philosophy of simple living and meditative thought. Followers were strictly vegetarian and ascetic. Their numbers swelled to around 600, despite an arduous initiation into the sect, a process which could take many years. The most devoted followers, known as Cenobites, gave up all worldly possessions to the cause and shared everything equally. The sect slowly acquired great wealth and prestige. Pythagoreans were often asked to mediate in disputes, thanks to their reputation for honesty, fairness, thoughtfulness and complete incorruptibility.
Not surprisingly, they also had their enemies, not least those who had tried and failed to gain entry into the order. One such was the rich and powerful Cyclon of Croton who campaigned forcefully against the sect and eventually forced Pythagoras to flee to Metapontum, where he later died. His leaderless followers were pursued by their enemies and locked in a house which was burnt to the ground, leaving just two survivors.
Pythagoras is credited with a string of firsts – the first to describe higher geometric solids, the first to discover the relationship between the squares on a triangle's sides (the Pythagorean Theorem) and the first to map musical intervals. His number theories shaped much of the Kabbalah of the Jews and his mystical numbers are found in magic practices of the Renaissance.
Many regard him as the father of such wide-ranging disciplines as numerology, geometry, musical theory and psychotherapy. He was also said to be able to predict earthquakes, to talk with animals and to practise hypnosis. All this and Pythagoras left not a single book behind.