Ajax, the name of 2 figures in Greek mythology. Ajax the Greater was the son of King Telamon and one of the greatest Greek heroes of the Trojan War. Informed that the arms of the slain Achilles had been awarded to Odysseus, Ajax went mad and committed suicide. The Greek warrior Ajax the Lesser also fought in the Trojan War. As punishment for raping Cassandra in Athena's temple, Ajax was shipwrecked and then killed.