11:3 The mighty king who arose and did as he pleased proved to be Alexander the Great (cf. 2:32, 39b; 7:6; 8:5-8, 21). He was, of course, Greek. His invasion of the Persian Empire was in large part retaliation for Xerxes' attacks against his people. He first attacked the Persians at the Granicus River near Constantinople in 334 B.C. and finally overthrew the Persian yoke at Gaugamela near Nineveh in 331 B.C. His conquest of the ancient world took only five years (334-330 B.C.).
11:4 After conquering most of the ancient world, even farther east than the Persian Empire had extended, Alexander died prematurely in Babylon, his imperial capital, in 323 B.C. His two sons, Hercules and Alexander, were both murdered when they were very young as was his uncle, Philip Arrhidaeus. Consequently his kingdom eventually was divided up between his four leading generals (cf. 7:6; 8:8, 22). Cassander ruled Macedonia-Greece, Lysimachus governed Thrace-Asia Minor, Seleucus took the rest of Asia except lower Syria and Palestine, and Ptolemy reigned over Egypt and Palestine. This Greek Empire following Alexander's demise did not retain the strength that it had previously under the centralized authority of Alexander.
