Ptolemy I Soter rivals after Alexander's death. For example, Arrian's account of the fall of Thebes in 335 BC ("Anabasis" , a rare section of narrative explicitly attributed to Ptolemy by Arrian) shows several significant variations from the parallel account preserved in Diodorus Siculus (17.11–12), most notably in attributing a distinctly unheroic role in proceedings to Perdiccas. More recently, J. Roisman has argued that the case for Ptolemy's blackening of Perdiccas and others has been much exaggerated. Ptolemy personally sponsored the great mathematician Euclid. He found Euclid's seminal work, the "Elements", too difficult to study, so he asked if there were an easier
Alexandria on the Caucasus the reign of Menander I the city was recorded as having a thriving Buddhist community, headed by Greek monks. In epic Sri Lankan poem Mahavamsa mentions the Greek (Pali: "Yona", lit: "Ionian") Buddhist monk Mahadhammarakkhita (), who is said to have come from “Alasandra” (thought to be Alexandria of the Caucasus), with 30,000 monks for the foundation ceremony of the Maha Thupa at Anuradhapura in Sri Lanka: Some archaeological evidence concerning Alexandria of the Caucasus was gathered by Charles Masson (1800–1853), providing insight into the history of that lost city. His findings include coins, rings, seals and other small objects.