In Alexander's company was a professional historian named Callisthenes of Olynthus (c.370-327), who had already published a Greek history of the years 387-356. The two men may have met as members of the circle around the Macedonian philosopher Aristotle of Stagira, who was an uncle of the historian and the teacher of the future king. During the campaign, Callisthenes' main duty was to write the Deeds of Alexander, but he was also sent on scientific missions. When Alexander was in Egypt, he sent his historian to Nubia, where he discovered the cause of the Nile flood; and in Babylon, Callisthenes supervised the translation of the Astronomical diaries, which were used by Callipus of Cyzicus to reform the Greek calendars. (You can read more about these missions here and here.)
In the summer of 327, Callisthenes voiced protests against the introduction of proskynesis (an aspect of the Persian court ritual) among the Macedonians, and lost Alexander's favor (more...). It is not clear what happened to Callisthenes: Aristobulus and Ptolemy, officers who were present and wrote histories of the campaign, gave different accounts - he either died in prison or was crucified.
The book of Deeds of Alexander is now lost, but underlies much of what was written later. It seems to have been the work of a professional flatterer who knew how to please a king who had developed a life-long rivalry with Achilles. For example, it contained many allusions to Homer's Iliad, a calculation of the date of the fall of Troy (exactly thousand years before Alexander's visit to the sacred city), and references to towns mentioned by Homer and visited by Alexander. Callisthenes stressed Alexander's manly behavior and the effeminate weakness of the Persians. Another story that Alexander must have appreciated is that of the sea doing obedience to the new Achilles (text). One thing is certain: Callisthenes did not object to Alexander's claim to be the son of Zeus.
It is not clear when...