Syracuse, Sicily in the context of "Polis"

During the Classical era and Hellenistic era of Classical Antiquity, many Hellenic city-states had adopted democratic forms of government, in which free (non-slave), native (non-foreigner) adult male citizens of the city took a major and direct part in the management of the affairs of state, such as declaring war, voting supplies, dispatching diplomatic missions and ratifying treaties. These activities were often handled by a form of direct democracy, based on a popular assembly. Others, of judicial and official nature, were often handled by large juries, drawn from the citizen body in a process known as sortition.

By far the most well-documented and studied example is the Athenian democracy in Athens. However, there are documented examples of at least fifty-two Greek city-states including Corinth, Megara, and Syracuse that also had democratic regimes during part of their history. According to Ober (2015), the proportion of Greek city-states with democratic regimes gradually increased from the mid 6th century BC to the end of the 4th century BC, when perhaps half of the one-thousand Greek city-states in existence at the time had democratic regimes.

The Second Peloponnesian War (431–404 BC), often called the Peloponnesian War, was fought between Athens and Sparta and their respective allies for the hegemony of the ancient Greek world. The war remained undecided until the later intervention of the Persian Empire in support of Sparta. Led by Lysander, the Spartan fleet (built with Persian subsidies) finally defeated Athens, which began a period of Spartan hegemony over Greece.

Historians have traditionally divided the war into three phases. The first phase (431–421 BC) was named the Ten Years War, or the Archidamian War, after the Spartan king Archidamus II, who invaded Attica several times with the full Hoplite army of the Peloponnesian League, the alliance network dominated by Sparta (then known as Lacedaemon). The Long Walls of Athens rendered this strategy ineffective, while the superior navy of the Delian League (Athens' alliance) raided the Peloponnesian coast to trigger rebellions within Sparta. The precarious Peace of Nicias was signed in 421 BC and lasted until 413 BC. Several proxy battles took place during this period, notably the battle of Mantinea in 418 BC, won by Sparta against an ad-hoc alliance of Elis, Mantinea (both former Spartan allies), Argos, and Athens. The main event was the Sicilian Expedition, between 415 and 413 BC, during which Athens lost almost all its navy in the attempt to capture Syracuse, an ally of Sparta.

Archimedes of Syracuse (/ˌɑːrkɪˈmiːdiːz/ AR-kih-MEE-deez; c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the city of Syracuse in Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and analysis by applying the concept of the infinitesimals and the method of exhaustion to derive and rigorously prove many geometrical theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.

Archimedes' other mathematical achievements include deriving an approximation of pi (π), defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy known as Archimedes' principle. In astronomy, he made measurements of the apparent diameter of the Sun and the size of the universe. He is also said to have built a planetarium device that demonstrated the movements of the known celestial bodies, and may have been a precursor to the Antikythera mechanism. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Hoplites (/ˈhɒplaɪts/ HOP-lytes) (Ancient Greek: ὁπλῖται, romanized: hoplîtai [hoplîːtai̯]) were citizen-soldiers of Ancient Greek city-states who were primarily armed with spears and shields. Hoplite soldiers used the phalanx formation to be effective in war with fewer soldiers. The formation discouraged the soldiers from acting alone, for this would compromise the formation and minimize its strengths. The hoplites were primarily represented by free citizens – propertied farmers and artisans – who were able to afford a linen or bronze armour suit and weapons (estimated at a third to a half of its able-bodied adult male population). Some states maintained a small elite professional unit, known as the epilektoi or logades ('the chosen') because they were picked from the regular citizen infantry. These existed at times in Athens, Sparta, Argos, Thebes, and Syracuse, among other places. Hoplite soldiers made up the bulk of ancient Greek armies.

In the 8th century BC, Greek armies started to adopt the phalanx formation. The formation proved successful in defeating the Persians when employed by the Athenians at the Battle of Marathon in 490 BC during the First Greco-Persian War. The Persian archers and light troops who fought in the Battle of Marathon failed because their bows were too weak for their arrows to penetrate the wall of Greek shields of the phalanx formation. The phalanx was also employed by the Greeks at the Battle of Thermopylae in 480 BC and at the Battle of Plataea in 479 BC during the Second Greco-Persian War.

The Sicilian Expedition was an Athenian military expedition to Sicily, which took place from 415–413 BC during the Peloponnesian War between Athens on one side and Sparta, Syracuse and Corinth on the other. The expedition ended in a devastating defeat for the Athenian forces, severely affecting Athens.

The expedition was hampered from the outset by uncertainty in its purpose and command structure—political maneuvering in Athens swelled a lightweight force of twenty ships into a massive armada, and the expedition's primary proponent, Alcibiades, was recalled from command to stand trial before the fleet even reached Sicily. Still, the Athenians achieved early successes. Syracuse, the most powerful state in Sicily, responded exceptionally slowly to the Athenian threat and, as a result, was almost completely invested before the arrival of reinforcements in the form of Spartan general Gylippus, who galvanized its inhabitants into action. From that point forward, however, as the Athenians ceded the initiative to their newly energized opponents, the tide of the conflict shifted. A massive reinforcing armada from Athens briefly gave the Athenians the upper hand once more, but a disastrous failed assault on a strategic high point and several crippling naval defeats damaged the Athenian soldiers' ability to continue fighting and maintain morale. The Athenians attempted a last-ditch evacuation from Syracuse. The evacuation failed, and nearly the entire expedition was captured or was destroyed in Sicily.

The province of Syracuse (Italian: provincia di Siracusa; Sicilian: pruvincia di Saragusa) was a province in the autonomous island region of Sicily, Italy. Its capital was the city of Syracuse, a town established by Greek colonists arriving from Corinth in the 8th century BC. It had an area of 2,124 square kilometres (820 sq mi) and a total population of 403,985 in 2016. Syracuse had 8% of the Sicilian population and 8.2% of Sicily's area.

Following the suppression of the Sicilian provinces, it was replaced in August 2015 by the free municipal consortium of Syracuse (Italian: libero consorzio comunale di Siracusa).

The siege of Syracuse by the Roman Republic took place in 213–212 BC. The Romans successfully stormed the Hellenistic city of Syracuse after a protracted siege, giving them control of the entire island of Sicily. During the siege, the city was protected by weapons developed by the prominent inventor and polymath Archimedes, who was slain at the conclusion of the siege by a Roman soldier, in contravention of the Roman proconsul Marcellus's instructions to spare his life.