Charles Marie de la Condamine wrote in a 1737 entry of his Journal du Voyage a l’é quateur that not without cause did ‘the savant and celebrated Creole’ of Lima, the royal cosmographer Pedro Peralta, call his country ‘the Purgatory of Astronomers’. La Condamine knew best Peralta's almanacs, in which he brought together his own astronomical and geographical observations and the writings of Europeans. But the earliest accomplishments of Pedro Alejandrino de Peralta Barnuevo Rocha y Benavides (1664–1743) were in canon and civil law. He worked as a fiscal accountant for the financial wing (tribunal de cuentas) of the high court (real audiencia) and minor courts in the viceregal capital. The courtrooms of Lima, a Jesuit admirer wrote, often heard him ‘advocate with that abundant acrid burning that the reason of laws inspires, without fervour disrupting the polished adornments of his style nor lack of time to prepare rendering him less eloquent’. Among the arts and sciences that interested Peralta, he studied first ancient philosophy then modern. He mastered Latin, Castilian, French, Italian, Portuguese, Greek, English and Quechua. By 1730 Peralta had been a professor of mathematics and astronomy at the University of San Marcos for twenty years.

Peralta's expressly scientific works, along with his history and poetry, were viewed favourably in the Late Baroque by traditionalists and moderns. Hispanic humanists and their noble supporters in Madrid too knew of his achievements. Peralta corresponded with Juan Manuel Fernández Pacheco, Marquis of Villena, on medical issues in 1713. He notified the Spanish Royal Academy of Language by post after he founded the Academy of Mathematics and Eloquence in Lima and began to write Historia de España vindicada (1730). Directly after publishing the first and only surviving part of this account, Peralta wrote to a Peruvian who was residing in Madrid to request newspapers from Holland and Madrid. He also asked to be sent histories written by two humanists who had been close to Álvarez de Toledo: Vicente Bacallar y Sanna, Marquis of San Felipe, and Father Juan de Ferreras. Peralta expressed interest in the Royal Academy's Diccionario de Autoridades too.

In 1746 two humanists in Spain wrote about Peralta, seemingly unaware of the publication of Historia de España vindicada and Peralta's death.