According to Wikipedia, The Darius Painter was an Apulian vase painter and the most eminent representative at the end of the “Ornate Style” in South Italian red-figure vase painting. His works were produced between 340 and 320 BC. The Darius Painter’s conventional name is derived from his name vase, the “Darius Vase”, which was discovered in 1851 near Canosa di Puglia and now on display at the Museo Archaeologico Nazionale, Naples (H3253). Many of his works, mostly volute kraters, amphorae and loutrophoroi, are of large dimensions. He most frequently depicted theatrical scenes, especially ones from the Classical tragedies by Euripides, and mythological themes. A number of mythological motifs not represented in surviving literary texts are known exclusively from his vases. On other shapes, especially pelikes, he also painted as wedding scenes, erotes, women, and dionysiac motifs. In contrast to other contemporary painters, sepulchral scenes (naiskos vases) by him are rare; where such motifs occur, they are virtually always on the back of the vessel. Some of his paintings, like those on the Darius Vase itself, show historical subjects.
The vase conserved in Naples is important because of its representation of a man counting on a board:
Nevertheless, the description of this Persian vase in the Museo Archeologio web page doesn’t mention the mathematical interest:
This volute krater with grotesque masks is undoubtedly one of the most famous vases in the collection. On the neck of side A there is a painted scene of an Amazonomachia, with Amazons wearing oriental costumes and armed with battle axes engaged in duels – which take place on two levels – against naked Greek warriors wearing crested Corinthian helmets who are equipped with a circular shield and long spear. The figurative decoration of the body is organised into three registers, in each of which there is a seated figure in a central position. In the upper register is Zeus, with a wingedNike kneeling down; to the left are Aphrodite with a swan on her lap and Artemis on a deer, while on the other side are Athena, Hellas, Achates with two torches and Asia, seated on an altar with the image of a deity. The central band shows Darius on his throne, behind whom stands figures who are presumably members of his bodyguard, carefully listening to a messenger standing erect in the king’s presence on a circular podium, surrounded by seated dignitaries and, it would seem, his pedagogue, who can be identified as the old man leaning on a stick. The last frieze shows five Orientals around a seated man, presumably the treasurer; three of them are kneeling, pleading for mercy. Side B, which has a similar structure, shows the myth of Bellerophon: in the upper part, Bellerophon rides Pegasus while a winged Nikecrowns him with a laurel wreath; to the left, a naked young man clasps a laurel branch in his hands while in front of him Poseidon, holding his trident in his left hand, sits on a rocky spur. To the right Pan, holding a pyxis and laurel branch, stands opposite Athena, seated on a rock, with a long spear in his left hand. In the middle of the central frieze is Chimera, depicted as a two-headed monster with a leonine body, the head of a lion and a goat, and the tail of a snake, while on the right two Amazons are fleeing; on the left there are two more Amazons, one of whom is attacking. The lowest register shows two fallen Amazons, armed with a spear and an axe respectively, and a marsh bird. On the neck of this side of the picture is a Dionysian scene with a group featuring a Maenad and Silenus on the left, a man and a woman on the sides of the fountain and lastly a second Maenad. The main scene has been interpreted in various ways: the identification of the characters is certain since beside each figure appears the name. What has proven more difficult is contextualising it. Some scholars have argued that it shows a scene from Phrynicos’ tragedy in which Persia is about to declare war on Hellas; more recently, an analysis of the compositional structure has led to the conclusion that the space is used symbolically to allude to the actual space of the theatre with the chorus in the lower register, theproscenium in the centre and the tribune of the gods above. Alternatively, the entire decorative layout could refer to the revolt of the Greek cities of Asia and may re-echo the troubled period of the wars against the Lucanians and the Messapians in Magna Graecia, specifically during the period in which the Darius painter was working.
The man of the picture is a tax collector counting on a special board in which we can read the letters M (= 10.000), Ψ (= 1.000), H (= 100) and Δ (= 10) and the former symbols used to represent the Greek coins (drachma, obol, half an obol and a quarter of obol). The collector has an opened book in which we can read the letters T A Λ and N. These letters correspond to another Greek coin named talent so we can suppose that this counting boards were used to make calculus with different kinds of coins.