Keep in mind that we have very little primary sources (in the most fundamental definition thereof) on Alexander. Most of what we consider primary sources today are, by definition, secondary sources; many of which of differ greatly.

The epithet “The Great” is commonly acknowledged as being granted to Alexander III of Macedon first by Quintus Curtius Rufus in his famous work, Historiae Alexandri Magni (Histories of Alexander the Great). “Magni” is translated into English as “great.” In this partial history, Curtius uses sources to give a sort of biography of Alexander, his army, and his campaigns. Curtius, a Roman, wrote the works in ca. 1st century. Curtius did not write the works in a hagiographic tone as Arrian did. Unlike many Roman historians, he also did not criticize Alexander to a great extent 1. The Diadochi question is a difficult one to answer as we are not blessed with testimonies and memoirs from many of the leaders. Ptolemy I, however, did write about, not only his own experiences in the Macedonian Army, but also his experiences after becoming Pharoah of Egypt. The former is lost to us and now only exists in the writings of Arrian in his Anabasis Alexandri. Arrian used Ptolemy I and Aristobulus to a great extent in his Anabasis. The problem is, Arrian’s work is seen as hagiographic, and if you read it, I am sure you will agree. Ptolemy had little affinity with Perdiccas, a general in Alexander’s army. Many of his testimonies which are paraphrased in Arrian’s work can be viewed as biased. However, this does not make his testimony forgettable, as we are able to get a first-hand look at the politics and squabbles within Alexander’s general staff. Ptolemy seemed to model his tactics in the Diadochi Wars after that of Alexander with a few exceptions 2.

A key facet to remember regarding the Diadochi is the rift that occurred in Alexander’s circle. This rift was caused by the introduction of proskynesis as well as the lengthy campaign that continued after the defeat of Persia. Oddly enough, Alexander relieved his Thessalian allies after the defeat of Persia as he incorporated Persians into his army. The continuation of the campaign angered many Macedonians; this was compounded by proskynesis becoming prevalent and a requirement in Alexander’s army. Once the campaign ended in India, most of the supplies were shipped while the army marched back to Babylon. The food train and the army were separated and many soldiers starved enroute Babylon. The end of Alexander’s campaign was less than glorious and it caused even more dissent among his generals. So, to say that his successors remembered him fondly is likely far from true. For many successors, such as Antigonus, there is difficulty in knowing his personal opinion of Alexander. Antigonus was a satrap and not a part of Alexander’s army; although he provided a crucial victory in the early part of Alexander’s Persian campaign 3. A good source to get the ball rolling on the Diadochi Wars is Livy. This is one of the earliest histories of the Successor Wars, although I have never been a big Livy fan 4. Livy also provides insight on Roman views of Alexander in Book IX.

Your question regarding the Romans has been answered previously and the provided answer is solid and likely better than I could do. For the life of me, I am unable to find it. It was a great answer to a very similar question. Basically, Pompey was one of the first Romans to write positively of Alexander as he compared himself to Alexander. Maybe one of the moderators can link the post as I am unable to find it.

1. Quintus Curtius Rufus, Historae Alexandri Magnae
2. Arrian, Anabasis Alexandri
3. Joseph Rolisman, Alexander’s Veterans and The Early Wars of the Successors, Austin, TX, USA: university of Texas Press, 2012.
4. Livy, History of Rome, Book IX.