The humanist Enea Silvio Piccolomini, who became Pope Pius II, in his memoirs called Cartagena "an ornament to the prelacy".
Eugenius, learning that the bishop of Burgos was about to visit Rome, declared in full conclave that "in the presence of such a man he felt ashamed to be seated in St. Peter's chair".
His translations into the vernacular followed a clear humanistic intent, that of teaching the wisdom of the classics to gentlemen interested in the works, but not scholars themselves.
Heinrich Graetz ascribes to the influence exercised by Carthagena over Eugenius IV the latter's sudden change of attitude toward the Jews.
Besides his translations of twelve books of Seneca, in which he was particularly interested, and of the works of Cicero mentioned above, he wrote Rerum in Hispania gestarum Chronicon.
Around 1456 he wrote a history of Spain based on Flavius Josephus, Florus and Jiménez de Rada and entitled Anacephaleosis that emphasized Castilian Gothicism.
The translation was composed of a prologue and 94 chapters, of which seven contain a summary of the origins of the Spanish monarchy from Atalaric to the kings of Asturias and of Castile and León, and a genealogical tree showing their relationship to the monarchs of Navarre, Aragon and Portugal.
He also wrote Doctrinal de Caballeros (Burgos, 1487, written around 1444), which consists of an adaptation of the second Partida of Alfonso X the Wise in four books covering faith, laws, war, rewards and punishments, revolts, challenges and duels, tournaments, vassals, bad actions and privileges.
Other works include Memoriales virtutum or Memorial de virtudes, various songs, aphorisms and compositions of love that appear dispersed in songbooks; Prefación a San Juan Crisóstomo, Allegationes... super conquista insularum Canariae (Allegations About the Conquest of the Canary Islands, 1437), which defends Castilian rights to the islands; Epistula... ad comitem de Haro (c. 1440), prescribing a program of readings to educate the nobility, among them the moral texts of Cato, and Contemptus mundanorum.