The Hindu-Arabic Numerals Quotes

“Indian mathematics”

“Hindu–Arabic numeral system”

“A History of Mathematics by Florian Cajori”

“A Short Account of the History of Mathematics by W. W. Rouse Ball.”

“It has long been recognized that the common numerals used in daily life are of comparatively recent origin.”

“[T]herefore... the Arabs from the early ninth century on fully recognized the Hindu origin of the new numerals.”

“Bubnov holds that the forms first found in Europe are derived from ancient symbols used on the abacus, but that the zero is of Hindu origin. This theory does not seem tenable...”

“In the fifth century the Persian medical school at Jondi-Sapur admitted both the Hindu and the Greek doctrines...”

“[T]he Arabs... never laid claim to the invention, always recognizing their indebtedness to the Hindus both for the numeral forms and for the distinguishing feature of place value.”

“The number of systems of notation employed before the Christian era was about the same as the number of written languages, and in some cases a single language had several systems.”

“We thus have the numerals in Arabia, in two forms: one the form now used there, and the other the one used by Al-Khowarazmi. The question then remains, how did this second form find its way into Europe?”

“The idea that our common numerals are Arabic in origin is not an old one. The mediaeval and Renaissance writers generally recognized them as Indian, and many of them expressly stated that they were of Hindu origin.”

“We have had no theory to exploit, for the history of mathematics has seen too much of this tendency... we have weighed the testimony and have set forth what seem to be the reasonable conclusions from the evidence...”

“This story has often been told in part, but it is a long time since any effort has been made to bring together the fragmentary narrations and to set forth the general problem of the origin and development of these numerals.”

“So familiar are we with the numerals that bear the misleading name of Arabic, and so extensive is their use... that it is difficult... to realize that their general acceptance... is a matter of only the last four centuries.”

“When... we consider the rise of the numerals in the land of the Sindhu... only the large movement... is meant, and that there must... be... numerous possible sources outside of India... and long anterior to the first prominent appearance of the number symbols.”

“[T]he probability [is] that it was the trader rather than the scholar... [who] carried these numerals from their original habitat to various commercial centers... we shall never know when they first made their inconspicuous entrance into Europe.”

“Whitney places the whole of the Veda literature, including the Vedas, the Brahmanas, and the Sutras, between 1500 B.C. and 800 B.C., thus agreeing with [Albert] Bürk who holds that the knowledge of the Pythagorean theorem revealed in the Sütras goes back to the eighth century B.C.”

“In this little work we have attempted to state the history of these forms in small compass, to place before the student materials for the investigation of the problems involved, and to express as clearly as possible the results, of the labors of scholars who have studied the subject...”

“Contemporary with Al-Khowarazmi... Abū 'l-Teiyib, Sened ibn Allī... also wrote a work on Hindu arithmetic...[T]he struggle to have the Hindu numerals replace the Arabic did not cease for a long time thereafter.”