# History of zero?

I learn't as a kid from my teachers that zero was discovered/invented in india and if you ask anybody here in india, the answer is simple yes it was invented in india.

Now we have something to say proudly yeah INDIA invented zero...hmm!

after few years later when i went in 11th standard my maths teacher said that. Its completly false, zero was not discovered in india even though they might say it. I don't remember exactly the history that he explained to me but As far as i remember his conclusion was that zero was invented in arab countries. and he also said that the english people started saying "zero" as "not" because they do't approve of the fact that zero was invented in india.

Every body wants to take the credit even if he has not done something great.I love my country but I don't take proud in accepting wrong things. I wanted to know what would be the honest answer for this...so that don't follow blindly what everbody says.Or is it really india.

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A similar question: math.stackexchange.com/q/12323/823 –  Baudrillard Jun 3 '11 at 8:10
The English word is "naught" and it is from Middle English so I doubt the etymology has anything to do with India. en.wiktionary.org/wiki/naught –  Dan Brumleve Jun 3 '11 at 8:34
@Dan: The use of the old word naught/nought ("nothing") to mean "zero" dates only from the early 15th century. According to sources, it's a translation of the use of "nothing" to mean "zero" in Arabic (and Sanskrit in turn). –  ShreevatsaR Jun 3 '11 at 9:11
@shreevatsaR: My point wasn't that none, nothing, etc implies that "zero" is as old as notions of none, nothing, etc...But I do not think that every mathematical concept requires a designated symbol to count as mathematical. Perhaps I wasn't very clear about the point I was trying to make. –  amWhy Jun 4 '11 at 4:40
@Dan: I meant compute in terms of being able to use "nothing" as one would use any "number")..."nothing added to A remains A", e.g., or, Consider "multiplication", and let an arbitrary non-zero number be #: number #, one time is "one #"; # + # (two times) is "two #"; # + # + ... + # (n times) = "n #". So # no times = "no #" = "none" –  amWhy Jun 4 '11 at 4:52

Disclaimer: most of the dates and historical embellishment in my answer come from the Wikipedia page on the History of the Hindu-Arabic Numeral System.

A full answer requires distinguishing between two different uses for 'zero':

• As a placeholder in a positional system of writing numbers. For example, when we write 206 we mean 'two hundreds, no tens and six units'.

• As a number in itself, for example in calculations like 5 - 3 - 2 = 0

I'll briefly give some color on these two different uses.

In the first sense of the word, the Babylonians were using a positional system since before 300BC (their system was base 60 instead of the base 10 that we use, but otherwise it is similar). However, they didn't use a zero at the end of a number. This is as if we made no distinction between the numbers 2, 20 and 200 (although they did distinguish between 16 and 106).

The oldest known text using a decimal positional system, in the sense that we understand it today, come from India: the Jain text Lokavibhaga, dated 458 AD (ref: here). The author uses the Sanskrit word for 'void' to denote the positional digit zero.

The first undisputed use of the symbol for zero (0) is an inscription on a copper plate at Gwalior, in India, dated 876 AD.

However, the transmission to Europe of the numeral zero came via the Italian mathematician Fibonacci, who got it from the Arabic mathematician al-Khwarizmi, writing around 976 AD, leading to the common English term 'Arabic numerals' and the belief that the positional system for notating numbers had been invented in the Arab world.

In the second sense, Henry's answer usefully quotes from Wikipedia:

The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe), written in 628 AD.

He listed several rules for calculating with zero which would be familiar to use today, including "the sum of zero and a positive number is positive" and "the sum of zero and zero is zero".

However, the word for zero in English again comes from Arabic, rather than Hindi.

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+1 even though not concise but clear to me –  munish Jun 3 '11 at 8:31
Does anybody really dispute that this is the same symbol? 2.bp.blogspot.com/-2IR4bRPwfQw/Ta2I0XiDrfI/AAAAAAAAAGM/… –  Dan Brumleve Jun 4 '11 at 23:49
Even though I have accepted this as my answer, I personally feel that its a pretty controversial topic.Nothing can be concluded for sure who did it as there are many many things to consider –  munish Jun 5 '11 at 1:50
@munish : It is not controversial. It is well accepted and documented math history for centuries ! That's why what we call 'Arabic digits' are called 'Indian digits' in Arabic. They were transmitted from India to the Islamic empire from India around the 9th century, and transmitted from the Islamic Empire to Europe around the 13th century. –  Frédéric Grosshans Jun 7 '13 at 16:41

The Wikipedia article 0 (number) is close to the common understanding, and shows there is not a simple claim to invention as there were many early examples of use of zero as a placeholder or number in different civilisations, as well as a philosophical concept. However the points in your debate may have been based based on these two statements:

The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe), written in 628 AD.

and

In 976 AD the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in his Keys of the Sciences, remarked that if, in a calculation, no number appears in the place of tens, then a little circle should be used "to keep the rows". This circle the Arabs called صفر ṣifr, "empty".

with ṣifr being the source of the English word zero (and also cypher).

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+1 for being much more concise than me :) –  Chris Taylor Jun 3 '11 at 8:27

This is about the words rather than the concept: I'll address only the etymological origin of the words "zero", "cipher", and "nought" in this answer. (Sources: Online Etymology Dictionary and Oxford English Dictionary.)

• zero: circa 1600, (either from Middle Latin zephirum, or French zéro or its source Italian zero, for *zefiro) in any case from Arabic sifr "cipher", translation of Sanskrit śūnya "empty place, desert, naught".

• cipher: late 14th century, from Arabic sifr, "zero", literally "empty, nothing", from safara "to be empty", loan-translation of Sanskrit śūnya "empty". (The word "cipher" came to Europe with Arabic numerals. Originally meant "zero", then "any numeral", then (c. 1520s) "coded message". OED: "The Arabic was simply a translation of the Sanskrit name śūnya, literally ‘empty’."

• nought: variant of naught which means "nothing". The meaning of "zero, cipher" is only from the early 15th century. (?c1425 Crafte Nombrynge in R. Steele The Earliest Arithmetics in English. (1922) 20: "A 0 is noȝt, And twyes noȝt is but noȝt.")

So these sources seem to agree that:

• In Sanskrit, the word for "empty" (śūnya) was used for zero.
• Correspondingly when translating into Arabic, the word sifr was coined out of the word safara, meaning "to be empty", and used for zero.
• Cipher/*zero* was imported into English, or, similar to the passing from Sanskrit to Arabic, the existing word for "nothing" (nought) was used for zero.
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• A really nice "little" book that you might be interested in is:

The Nothing That Is: A Natural History of Zero, written by Robert Kaplan, (1999, Oxford University Press).

The link will take you to Amazon.com, where you can "Look Inside" for a sample from the book, or to peruse the table of contents, etc. I found it to be quite entertaining and informative.

• One other book that comes to mind is:

Zero: The Biography of a Dangerous Idea by Charles Seife.

The link here, too, is to Amazon.com, and you can "Look Inside" this book, as well, to determine if this book is of interest.

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"Kaplan suggests that the circular symbol arose from the depression left by a counting stone removed from sand." –  Dan Brumleve Jun 3 '11 at 23:09
The second book, Zero: The Biography of a Dangerous Idea, was very enjoyable. I read it before I even "liked" math in high school -- I highly recommend it! –  Jeff Jun 4 '11 at 3:19
I think my mouse must of accidentally clicked why I was scrolling through this page, and I unintentionally downvoted your answer. Please edit if you would like the upvote instead :) (Also, I tried changing it now, but it says it is locked because I voted 8 minutes ago...) –  Eric Naslund Jun 7 '11 at 20:24
I just saw the downvote... :-( Sure, I can edit my answer, and your free to upvote if you'd like to...In any case, not a problem; I'm just glad you told me!! –  amWhy Jun 7 '11 at 20:48
$+1$ your friendship has been great here, Amy. –  Babak S. Jul 18 '13 at 17:27

Here in America schoolchildren learn that the Maya invented the number zero for their calendars in the 3rd century AD.

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+1 nice point idon't know but just a wild guess.it might be possible arabs might be taught that they invented zero.english might be taught that they did it. controversial.hmm..then at last I might think the correct answer is that given by Dan. –  munish Jun 3 '11 at 16:36
The invention of the zero by the Maya is true and well documented. It is however obviously completely independent of the invention of the zero in the old world. –  Frédéric Grosshans Jun 7 '13 at 16:43

It seems that the Indians were not the first or only ones to consider zero a number. The wikipedia article , here seems to indicate that Egypt had a notion of zero as a sort of "base point". Quoting the Wikidepia article,

Ancient Egyptian numerals were base 10. They used hieroglyphs for the digits and were not positional. By 1740 BCE the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line. (my emphasis)

Since Wikipedia is not necessarily a valid source, the passage references the following:

George Gheverghese Joseph (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton. p. 86. ISBN 978-0-691-13526-7.

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Zero is a simple and intuitive concept and it was understood by people in prehistory who didn't even understand how to write it.

EDIT: The point of the above is obtuse and has not been well-received so I will try to explain it further. The title of the question is "History of zero?" which is not a mathematical question at all, but the body of the question seems amenable to philosophy and can be seen from a mathematical viewpoint, so I am trying to answer the latter. Some things to consider:

What if we ask instead "when and where and by whom was one discovered or invented?" Or what about the empty set, or falsehood, or "no"? Is it reasonable to say that Giuseppe Peano invented or discovered arithmetic, or that Albert Einstein invented or discovered time? If Peano created arithmetic, did Kurt Gödel destroy it? Did Isaac Newton invent calculus, or did he discover calculus? What is the difference? Or was it actually Gottfried Leibniz who found it first? Are illiteracy and innumeracy the same thing? Is literacy necessary for reason? Is numeracy? To talk about the past honestly I think we have to look beyond what we know about it for certain.

I speculate that the concept of zero, the circle glyph, and the sound of the vowel "o" have a deep and primitive relationship founded on their mutual simplicity, our anatomy, and the environment. On that basis I suggest that it is likely for them to have been identified with each other many times in the unknown past.

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I downvoted. "there is no evidence of prehistory": That is part of why I do not understand why you are making this claim about prehistoric people. And it does not answer the question. –  Jonas Meyer Jun 3 '11 at 8:16
@Dan: When you don't know something for sure, isn't the honest thing to say that you don't? :-) Zero may seem simple and intuitive to you, because you have been taught it since childhood. You only have to look at history to see that it wasn't always, to everyone. The concept of "nothing" is likely intuitive (that's what your dog knows), but not the concept of "nothing" as a number just like the "actual" numbers 1, 2, 3…. (Negative numbers also seem intuitive to many of us!) The Greeks and Romans and Europeans pre-Fibonacci would have said that 5-3-2 doesn't exist, just like 5-3-3. –  ShreevatsaR Jun 3 '11 at 8:38
@Dan: I don't understand your last comment at all. OK, here's a simple question: if you want to continue to claim that zero was simple and intuitive always, can you point to a single Greek, Roman or pre-1000 European source that contains the number zero? (This would contradict what I've read in every history of mathematics, so it would be very interesting.) –  ShreevatsaR Jun 3 '11 at 8:56
You're adding more and more kooky speculation. The identification of "the vowel o" with 0 is of recent origin in America. It's hardly universal even today (and some non-Americans do find it annoying that '0' is read as 'o', for what it's worth). It's based on the similarity in the written form in the English alphabet. You're unjustifiably extrapolating from your parochial experience. Not everything you learn in childhood in your culture and enviroment actually has a "deep and primitive relationship". –  ShreevatsaR Jun 4 '11 at 4:25
It seems you're claiming that zero was known in "prehistory", but happened to be suddenly forgotten in the entire voluminous recorded Western history until 1202. Think about how likely that is. (Occam's razor may help.) By contrast, the positive integers (like "one") do occur abundantly. Would you also claim that your dog knows what the empty set is? What it knows is some concept of absence or nothingness that you with your mathematical education identify with the empty set. Similarly, just because primitive societies did have debts doesn't mean they knew and used negative numbers. –  ShreevatsaR Jun 4 '11 at 4:29