What Made Alex Run? : THE GENIUS OF ALEXANDER THE GREAT.<i> By N.G.L. Hammond</i> .<i> University of North Carolina Press: 220 pp., $29.95</i>

Starting in May 334 BC, Alexander, the 22-year-old king of Macedon, led his victorious army through four pitched battles, two sieges and innumerable smaller engagements, conquering territory that now goes under the names of Turkey, Syria, Lebanon, Palestine, Israel, Egypt, Iraq, Iran and Afghanistan--all the way to the banks of the Beas River in Pakistan, where he reluctantly turned back, as his troops threatened mutiny. Three years later, in 323 BC, he died in Babylon, probably of malaria, just as he was planning an expedition all the way from Egypt along the North African coast to the Atlantic.

There is no disagreement among historians about the magnitude of his conquests, nor about one of their most important effects: the establishment in what we know as the Middle East of a city-based Greek colonial aristocracy which, under Greco-Macedonian monarchs, imposed its culture on the native peoples. But about the motives and character of the young man who launched and carried out this tremendous enterprise, there has been controversy ever since.

Just before he died, he answered the question put to him by one of his generals--”To whom do you leave your empire?”--with the enigmatic words, “To the strongest.” He has been credited in numerous historical analyses with a belief in and a policy establishing “the brotherhood of Mankind” and with “lifting the civilized world out of one groove and setting it down in another.” On the other hand, his expedition has been dismissed as a folie de grandeur. As for his character, scholars have compared him to “a young Nazi loose on the Alps” and denounced him as a “ruthless, calculating opportunist” and “a visionary megalomaniac serving the implacable needs of his own all-consuming ego.”

In his short lifetime, he seemed to have defied the limits set on human achievement by the gods; after his death, he became the stuff of legend, which grew richer as the centuries passed. And unfortunately for the modern historian, most of the evidence for his career and character comes to us from books written long after his death. The fullest account was composed by the Greek historian Arrian five centuries after Alexander’s death, and though he frequently cites the accounts of two members of Alexander’s staff--Ptolemy, the general who later took Egypt for his share, and Aristobulus, a military engineer who served with the army--we have no means of evaluating whatever political or personal bias their narratives may represent. The other important late witnesses--Diodorus in the first century BC and Plutarch in the first and second century after Christ--present even more problematical material since Diodorus never cites his sources and Plutarch does so only sporadically. Modern historians have for many years offered conflicting evaluations of the evidence; prominent among them is N.G.L. Hammond, the author of this short, clearly written book, the distillation of a life’s work. He already has written a book on Alexander’s father Philip and a lengthier study of Alexander, two books on the historical records, a book on the ancient Macedonian state and an authoritative three-volume history of Macedonia (the first alone, the others with collaborators). “At present,” he writes in the preface to this book, “it seems appropriate to put my conclusions together and to write an account of Alexander which may claim to be close to the actual facts of his career and the nature of his personality.”

Hammond knows not only the historical sources but also the terrain. He has been to many of the battlefields and spent time in the Middle East in World War II. As a young student fresh from Cambridge, he explored on foot the mountain trails of Northern Greece, acquiring fluent modern Greek and a command of Albanian, assets that served him well when, in February 1943, a major in the British army, he parachuted with two other soldiers on Mount Ossa on a mission to blow up an important bridge and to supply and fight with Greek guerrillas operating against the German occupying forces. He remained there until August 1944, eventually acting as commander of the Allied military mission in Greece. This military experience is put to good use in “The Genius of Alexander the Great”; its careful descriptions of military maneuvers and the diagrams illustrating successive stages of the operations have a clarity that is often sadly wanting in such accounts.

Some of the most famous Alexander stories fail to pass Hammond’s strict examination. Contrary to popular belief, his Alexander did not cut the Gordian knot; he simply disconnected the yoke from the pole by pulling out the pin that held them together, as in the account given by Aristobulus. Nor did his Alexander burn the Persian king’s great palace at Persepolis at the suggestion of the Athenian courtesan Thais at a drunken party; he did indeed burn the palace as a retaliation for the Persian desecration of Greek temples in their invasion of Greece, but it was policy, not a drunken escapade. “Excavation has shown beyond doubt that the burning was not a random, unpremeditated act,” Hammond writes. On the other hand, the story of Alexander’s taming of the wild horse Bucephalus, the horse he later rode all the way to Pakistan, is accepted as based on valid evidence.

There is, however, one aspect of Alexander’s saga on which all parties are in agreement: He had, as has been said of the Germans, a genius for war. He was trained for it from his earliest days, as a member of the corps of royal pages. At the age of 16, left in charge as regent in Macedon while his father Philip campaigned abroad, he suppressed a tribal revolt in the north and founded Alexandropolis, the first of many cities that were to bear his name. Two years later, he led the cavalry charge that delivered the decisive blow to the Greek forces at Chaeronea, the battle that made Philip master of Greece. And at age 22, now king after the assassination of Philip, he moved with astounding speed to defeat the Getae on the Danube far to the north and then swept south to surprise and suppress a revolt of the Greek cities led by the city of Thebes, which he destroyed. He had already displayed the qualities and skills that would make him king of all Asia--a mobility that repeatedly took the enemy unawares and an uncanny knack of foreseeing his tactical moves. In the great pitched battles of the Asian plains that followed this suppression of the Greek cities, in swift maneuver among the awesome mountains of Afghanistan and in complicated siege operations and costly assaults at Tyre and Gaza, his courage in the van of his troops (he was wounded six times) and what Arrian called his “most wonderful power of grasping the right course when the situation was still in obscurity” made him aniketos, “invincible,” the word the Sibyl at Delphi screamed at him and which he adopted as an official title.

But there is no agreement about the final objective of his apparently insatiable lust for conquest. After the defeat of the Persian king’s last army at Gaugamela in 331 in what is now Iraq, and after the death of Darius shortly afterward, Alexander faced what Hammond calls “a crucial choice between two policies.” He could have called a halt there, establishing a defensible frontier that gave him control of the most fertile and prosperous areas of the Persian Empire. Against the advice of his staff, he decided to press on into unknown and fearsomely difficult terrain, most of it mountain or desert. Hammond explains this decision partly as the result of his belief that the gods had decreed that he would be king of all Asia, an idea that might serve to explain his decision to push on eastward after he defeated the Indian king, Porus, in Pakistan. He had been taught by his tutor Aristotle that the land mass of Asia met the encircling ocean not far east of where he was. But belief in the divine mission to conquer Asia will not serve to explain his preparations for a westward campaign to the Atlantic. This suggests a vaunting ambition to become king of the whole of the known world.

And yet there was a sober political realism at the base of his apparently megalomaniac designs. He realized, for instance, that he and his Macedonians, in an age when communications were no faster than a horse could ride, could never effectively govern an empire as large as the one he had acquired. As he moved east, he appointed more and more high-ranking Persian officials and commanders to positions of influence on his staff. He encouraged intermarriage between Macedonians and Persians, setting the example by marrying Roxane, daughter of a Persian regional governor, or satrap. He also instituted a program for training Persian boys for eventual service in the army. Measures such as these won him the esteem of some historians as a believer in the brotherhood of man, but they did not go down well with his older Macedonian generals. Growing resentment fueled conspiracies against him, and it was on this issue that, at a banquet where the Macedonians, as usual, drank deep, he quarreled with Cleitus, his oldest friend, who had saved his life at the battle of the Granicus, and, in a drunken fury, killed him.

When Alexander died, his empire broke up into separate kingdoms headed by his generals. But he had changed the world. In the old, now liberated Greek cities of Asia Minor--Ephesus and Pergamum--as well as in the newly founded cities of the Middle East--Alexandria and Antioch--the culture and language of the colonial aristocracy was Greek. When, three centuries after Alexander’s death, the life and teachings of a Hebrew prophet, Jesus of Nazareth, were written down, the language used was not his native Aramaic but Greek, which, thanks to Alexander’s conquests, had become the cultural lingua franca of the eastern Mediterranean.