Question
Was Babylonian mathematics developed using Arabic numerals or Hindi numerals?
Answer
Without a library of original 7th-13th century manuscripts from India,
Arabia and Europe to look at, it's hard to say what the actual written
notation used to look like back then as the corpus of mathematical ideas grew by accretion on its journey westwards. The modern notation may or may not
have much relation to what things looked like back then. I believe there was also some Chinese notational influence on the Arabs at some point.
If someone knows a historical librarian with access to the three manuscripts listed below, they could probably provide fairly definitive answers. I could not find 'em online with a quick search.
It seems like the earliest known transmission of Hindu numerals via an Arabic work was Kitab al-fusul fi al-hisab al-Hindi from about 953 AD by Al Uqludisi.
http://www.amazon.com/Arithmetic...
The Indian work where most of the early ideas were developed was Brahmagupta's Brahmasputasiddhanta, http://en.wikipedia.org/wiki/Bra... around 628 AD (about 100 years before the first Arab invasions of South Asia) and the notation used there would have been closer to Brahmi I imagine, than modern Devanagri, which is used to write Hindi.
By the time Al Uqludisi grappled with the material in 953 AD (300 years later), I suppose the script would have been some mash up of medieval-Arabic+Brahmi.
In the West, decimal-based math started with Liber Abaci, 1202 AD. So there's another 200-300 year gap there. The Arabic script was not unified at that point, and I believe Western Arabic differed significantly from other regions.
I found this picture at http://www.archimedes-lab.org/nu... but it is rather useless since the Hindi script shown is modern Devnagri.
Modern Hindi numerals are written the way they are shown above, and this is Devnagri script which matured long after the decimal system had already diffused west-wards.
Overall I think the answer here is likely to be fundamentally murky since this was the pre-printing-press era and many scripts and notations probably existed in parallel as the ideas diffused and morphed.
Arabia and Europe to look at, it's hard to say what the actual written
notation used to look like back then as the corpus of mathematical ideas grew by accretion on its journey westwards. The modern notation may or may not
have much relation to what things looked like back then. I believe there was also some Chinese notational influence on the Arabs at some point.
If someone knows a historical librarian with access to the three manuscripts listed below, they could probably provide fairly definitive answers. I could not find 'em online with a quick search.
It seems like the earliest known transmission of Hindu numerals via an Arabic work was Kitab al-fusul fi al-hisab al-Hindi from about 953 AD by Al Uqludisi.
http://www.amazon.com/Arithmetic...
The Indian work where most of the early ideas were developed was Brahmagupta's Brahmasputasiddhanta, http://en.wikipedia.org/wiki/Bra... around 628 AD (about 100 years before the first Arab invasions of South Asia) and the notation used there would have been closer to Brahmi I imagine, than modern Devanagri, which is used to write Hindi.
By the time Al Uqludisi grappled with the material in 953 AD (300 years later), I suppose the script would have been some mash up of medieval-Arabic+Brahmi.
In the West, decimal-based math started with Liber Abaci, 1202 AD. So there's another 200-300 year gap there. The Arabic script was not unified at that point, and I believe Western Arabic differed significantly from other regions.
I found this picture at http://www.archimedes-lab.org/nu... but it is rather useless since the Hindi script shown is modern Devnagri.
Modern Hindi numerals are written the way they are shown above, and this is Devnagri script which matured long after the decimal system had already diffused west-wards.
Overall I think the answer here is likely to be fundamentally murky since this was the pre-printing-press era and many scripts and notations probably existed in parallel as the ideas diffused and morphed.