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| c. 529 BC |
| | | The Greek mathematician Pythagoras establishes himself, along with his followers, in southern Italy | |
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| 510 BC |
| | | The Roman senate becomes an executive body with two of its members elected annually as consuls, or joint heads of state | |
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| 508 BC |
| | | Cleisthenes, brought to power by popular support, puts into effect a major programme of political reform in Athens | |
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| c. 500 BC |
| | | The followers of Pythagoras discover the mathematical basis of the octave | |
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| c. 500 BC |
| | | The Greeks add a third bank of oars to their war galleys, turning the bireme into a trireme | |
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| 490 BC |
| | | The Persian fleet secures the Greek island of Euboea before making the short crossing to Marathon on the mainland – where they await the Greeks | |
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| 490 BC |
| | | At Marathon the Athenian hoplites, heavily outnumbered, win a spectacular victory against the Persians – of whom the survivors escape in their ships | |
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| 484 BC |
| | | Aeschylus wins the prize for tragedy at the City Dionysia in Athens | |
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| 483 BC |
| | | Themistocles persuades the Athenians to build up their fleet against the expected renewal of the threat from Persia | |
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| 480 BC |
| | | 300 Spartans, led by Leonidas, die attempting to hold the pass of Thermopylae against the advancing Persian army | |
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