The repercussion of José Anastácio da Cunha in Britain and USA in the nineteenth century

Abstract

José Anastácio da Cunha (1744-1787) is usually recognized as one of the most important Portuguese mathematicians ever. Nevertheless, his work does not seem to have had much repercussion abroad. His Principios mathematicos (Lisbon, 1790) were translated into French, but with very limited impact. However, thanks to a review by John Playfair, an English textbook by John Radford Young featured a proof by Anastácio da Cunha (of a proposition on parallels) and a definition of proportion influenced by the one used by Cunha. This proof on parallels also made its way to an American textbook by Benjamin Greenleaf. Young's and Greenleaf's are, so far, the only known cases of actual use (instead of mere reference to) of Cunha's work outside Portugal.To Maria Fernanda Estrada, with friendship.José Anastácio da Cunha's Principios Mathematicos and their reception abroad P edro Nunes (1502-1578) and José Anastácio da Cunha (1744-1787) are arguably the two most famous mathematicians born in Portugal (for instance, they are the only Portuguese mathematicians with biographies in Katz's popular textbook (1993)). But while Nunes was a highly regarded mathematician in Europe in his lifetime, Cunha's international recognition is purely historical and not older than Youschkevitch (1973).Coming from a modest background but with some good connections, José Anastácio da Cunha studied at an Oratorian school in Lisbon, his hometown. At the age of nineteen he joined the army, and was stationed in an Artillery Regiment at Valença do Minho (on the northern border with Spain). Having been recognized in the army as a gifted mathematician, in 1773 the Marquis of Pombal, prime minister to king Joseph, invited Cunha to be a professor at the new Faculty of Mathematics, founded in the University of Coimbra the previous year. But this situation did not last too long: in 1777 the king died, the political climate changed (Pombal was dismissed) and in 1778 Cunha was arrested and convicted by the Inquisition, on charges of libertinism, deism, toleration and indifferentism (believing that all religions are equivalent). He was not, however, without influential protectors, and his sentence was not only relatively light but also commuted in 1781. He was then free and appointed to the Casa Pia (a school for poor boys in Lisbon) as director of studies and substitute teacher of mathematics. It is not known how long this position lasted-the preface to Cunha (1811) tells us that Cunha lost it, but not when. Health problems ensued, and Cunha died on 1 January 1787, aged forty-two. This research was financed by FEDER Funds through Programa Operacional Factores de Competitividade -COMPETE and by Portuguese Funds through FCT -Fundação para a Ciência e a Tecnologia, within the Project Est-C/MAT/UI0013/2011.