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Can anyone provide independent confirmation or an independent reference for any of this? Google only has pages based on Wikipedia; Britannica has nothing at all.--Niels Ø 20:00, Jun 15, 2005 (UTC)

I searched through MathSciNet and found 10 reviews mentioning Pingala including:
  • Datta, Bibhutibhusan; Singh, Awadhesh Narayan; Use of permutations and combinations in India. Indian J. Hist. Sci. 27 (1992), no. 3, 231--249.
  • Kak, Subhash; Computational aspects of the \=Aryabha\d ta algorithm. Indian J. Hist. Sci. 21 (1986), no. 1, 62--71.
However, I didn't get the papers. -- Jitse Niesen (talk) 14:29, 5 December 2005 (UTC)
  • The book Indian Mathematics and Astronomy by Dr. Chandrashekar a proffessor of Mathematics, contains Sanskrit verses from Pingalas writings unfortunatly soft copy of the same is not available.

~rAGU 16:42, 7 December 2005 (UTC)

the article seemed to confuse the 10th century commentary with the actual work. "zero as a dot" certainly refers to the 10th century work, as does Pascal's triangle. I'll try to unearth an edition or a scholarly discussion of the text, but so far the content of the article is entirely anecdotal. dab () 09:10, 8 April 2006 (UTC)

9th century or earlier?[edit]

Sorry, the "Varahamihira" in my edit summary was a mistake. I meant Brahmagupta. Most sources say that the first inscription showing the use of positional zero is from the 9th century (Gwalior). However, no historian would ever claim that this means that zero was invented in the 9th century. There are enough other convincing evidences, and most historians believe that by the 6th century, zero as a positional numeral was very much in use. For example, Brahmagupta from the 7th century explains all the arithmetic of zero that we know today (except he messes up 0/0) in his book Brahmasphutasiddhanta. It is also recognized that Al Fazali translated this book into Arabic in the 8th century. It is very likely that Brahmagupta was not the inventor either, but just reported in the text a mathematical artifice that was in contemporary use. deeptrivia (talk) 17:03, 11 April 2006 (UTC)

you are confusing positional and arithmetical zero. We have discussed this at length at the numeral system articles. Brahmagupta in the 6th century certainly knew the arithmetical concept. There is still no evidence of positional zero predating the 9th c., and I am very doubtful that "most historians" believe that positional zero dates to the 6th c.; while it is not inconceivable that positional zero was introduced earlier than the 9th c., say 8th or 7th c., it is patently false to claim that "no historian would ever claim positional zero was invented in the 9th c.", let alone because of the work of Brahmagupta , which is entirely irrelevant to the question. dab () 17:18, 11 April 2006 (UTC)

Basic ideas of Fibonacci number[edit]

I do not understand the claim that the commentary includes the "basic ideas" of the Fibonacci numbers. In what sense does it contain the basic ideas, but not a description of the numbers themselves? (You would not reasonably refer to all theory around or applications of the Fibonacci numbers; since that would disqualify Fibonacci himself.)-JoergenB (talk) 21:09, 12 January 2008 (UTC)