An important and well-researched essay that unravels the myth of 'Greek origins behind Hindu mathematics' and how this was perpetuated down the ages...
The Reception of Ancient Indian Mathematics by Western Historians
By Albrecht Heeffer
Center for Logic and Philosophy of Science, Ghent University, Belgium
While there was an awareness of ancient Indian mathematics in the West since the sixteenth century, historians discuss the Indian mathematical tradi- tion only after the publication of the first translations by Colebrooke in 1817. Its reception cannot be comprehended without accounting for the way new European mathematics was shaped by Renaissance humanist writings. We show by means of a case study on the algebraic solutions to a linear problem how the understanding and appreciation of Indian mathematics was deeply influenced by humanist prej- udice that all higher intellectual culture, in particular all science, had risen from Greek soil.
During the fifteenth century Italian humanists eagerly started collecting editions of Greek mathematics. One of the most industrious was Cardinal Bessarion who lived in Venice. By his death in 1472 he had accumulated over five hundred Greek manuscripts (Rose, 1975, 44-46 and 90-109). Regiomon- tanus, who had befriended Bessarion, began to study these Greek texts around 1463, including Diophantus’ Arithmetica. He reported his find of the six books of the Arithmetica in a letter to Giovanni Bianchini (Curtze, 1902, 256-7). By then he was well-acquainted with the Arabic algebra. He owned a copy of the manuscript on algebra by al-Khw ?arizm ?i, possibly from his own pen (MS. Plimpton 188). Highly receptive to influences between traditions, he immedi- ately conjectured a relation. In his Oratio, a series of lectures at the University of Padua in 1464, he introduced the idea that Arabic algebra descended from Diophantus’ Arithmetica (Regiomontanus, 1537). This heralded the initiation of a myth cultivated by humanists for centuries. Diophantus, first considered to be the source of inspiration for Arabic algebra, became the alleged origin of European algebra. Several humanist writers such as Ramus, chose to neglect or reject the Arabic roots of Renaissance algebra altogether (Høyrup, 1998). As a matter of fact, Diophantus had almost no impact on European mathemati- cal practice before the late sixteenth century. Diophantus inspired authors on algebra such as Stevin, Bombelli and Vi`ete because by then symbolic algebra was well established. By overrating the importance of Diophantus and down- grading the achievements of Arabic algebra, humanist writers created a new mythical identity of European mathematics. Suddenly Greek mathematics be- came European mathematics. However, most Greek sources were unavailable before the sixteenth century. In fact, Greek mathematics was more foreign to the European mathematical practice than Arabic mathematics was; the lat- ter was slowly but surely appropriated with the abacus tradition. Ironically, the medieval qualitative arithmetic, which was a genuine European tradition, became completely forgotten.
Only later, European historians learned about ancient Indian mathematics and what they learned was strongly influenced by the humanist mathematical tradition. We will now give a brief overview of the first assessments of Indian algebra in the West.
Bramhagupta (598–c.670 CE)