Ajax was a huge man, head and shoulders larger than the other Greeks, enormously strong but somewhat slow of speech. In the Iliad, he is often called the “wall” or “bulwark” (herkos) of the Greeks. When Achilles had withdrawn from the fighting at Troy, it was Ajax who went forth to meet Hectorin single combat; by the time darkness fell the fight was still a stalemate, but Ajax had wounded Hector without sustaining injury himself
After Achilles’ death, Ajax competed with Odysseusfor the ownership of Achilles’ armor. Both men delivered speeches explaining their own merits, but Odysseus was by far the more eloquent and won the prize. Ajax was driven mad by his disappointment. According to one account, he vowed vengeance on the Greeks and began slaughtering cattle, mistaking them for his former comrades-in-arms. He finally committed suicide.
Ajax is often called “Telemonian Ajax” or “the greater Ajax,” to distinguish him from Ajax the Lesser the son of Oileus, who also fought for the Greeks at Troy.