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I was shocked when I read on a blog that Aryabahatta, an Indian guy born in 476 AD discovered zero.

Surely people knew about zero before that.

But his greatest contribution has to be ZERO, for which he became immortal. He certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. The supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

1) Was Aryabhatta the first to invent the place value system with zero?

2) Did he invent a new system of writing or representing numbers with zero?

3) Did he borrow any of these from others before him?

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    Any claim about who originally came up with what is bound to have some uncertainty, as someone else could have invented it first who has since been lost to history. That said, what makes you think that "surely people knew about zero before that"? – probably_someone Feb 27 '18 at 6:32
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    en.wikipedia.org/wiki/0 – MichaelK Feb 27 '18 at 6:49
  • Aryabhata is typically credited with a decimal place value system, whether or not it was original to him. He probably has less of a claim of being the first to use a zero symbol in a place value system (decimal or otherwise) – Henry Feb 27 '18 at 12:02
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You are correct in thinking that the Indians were the first to implement the zero as it is currently used, as a place value, and also as a number that you can use to add, subtract, and multiply. They also understood that division by zero somehow resulted in infinities. Unlike Greek mathematicians they were not disturbed by the idea of either zero or infinity.

And of course, early Christianity added its own taboos about those ideas. While they accepted the idea of "nothing", actually working with it was a different matter. It led one to entertain the idea of infinitesimals, which clashed with the power of God and his angels. As zero gives rise to infinity, it meant that infinities could arise outside God, another impossibility for early Christians.

Aryabhata was one of first of the Indian astronomers to use the concept of zero, although in a rather vague way. He had no actual symbol for zero. An even earlier mention was in the Jain astronomical work 'Lokvibhag', written around AD458, well before Aryabhata. However, there is still debate about which mention of zero is fully up to the modern meaning. There is no consensus about who made each of the steps necessary for the modern usage of zero - except that it did happen between 450AD and 800AD, and it happened in India.

Babylonians had used place values in their base-60 number system from around 3000BC, well before the Indians. Probably from around 2000BC, they also started using a "separation marker" to indicate intermediate empty places. While their usage was still a long way from the modern one, it is possible that the Indian astronomers borrowed this idea from the Babylonians. Even that early, ideas did spread widely.

More information about the invention of zero can be found in these books (and others):

The book of nothing

The nothing that is

The universal history of numbers

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    Note that division by zero is undefined, not "resulting in infinites". – DevSolar Feb 27 '18 at 10:25
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    "early Christianity added its own taboos about those ideas". Citation needed. – DJClayworth Feb 27 '18 at 15:20
  • @DevSolar Indeed, but the early Indian astronomers did not have that modern insight. – hdhondt Feb 28 '18 at 9:15
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    @DevSolar Your link doesn’t make such a strong claim. In general, defining x/0 = ±∞ for x≠0 sometimes makes perfect sense. It usually makes sense to treat it as undefined (as in the example of arithmetic, in a function on a given domain) but it can be well-defined. It’s no accident or oversight that IEEE 754 made x/0 for x≠0 well-defined. – Konrad Rudolph Mar 2 '18 at 16:45
  • @KonradRudolph I'm not aware of a reasonable definition of division in which defining x/0 makes sense, although you can of course use the expression as a sloppy shorthand for something else. This is exactly what IEEE 754 does, for engineering reasons, not mathematical ones. – Cubic Mar 9 '18 at 15:53
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Was Aryabhatta the first to invent the place value system with zero?

No. The use of a symbol as a placeholder in a place value representation predates Aryabhatta (aka Aryabhata) by millennia. The Babylonians, Chinese, Greeks, and Mayans used a place value system, and all had a way of writing a number whose place value notation had a hole.

Did he invent a new system of writing or representing numbers with zero?

Yes, but in a different language (Hindi).

Did he borrow any of these from others before him?

Most likely. The Bakhshali manuscript (also from India, but written in Sanskrit rather than Hindi) predates Aryabhata by centuries.


You didn't ask, but the placeholder zero is not a true zero. Even though the Babylonians, Chinese, and Greeks used a placeholder zero, none of those cultures managed to extend the concept of a placeholder zero to something that represents nothing. While we take this use of zero for granted nowadays (even six year olds know what five minus five is), this is a very difficult and very abstract concept. This "true zero" originated in India, but well after Aryabhata's time. Most attribute the development of a true zero to Brahmagutpa.

The Mayans came very close to having a true zero, and may have well had that concept. It's hard to tell because of the destruction of all but four four Maya codices during the Spanish conquest of Mexico and central America. What is known is that the Mayans and their predecessors had a base 20 place value notation with a turtle shell representing zero dating to about 2000 years ago.

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    Aryabhata wrote in Sanskrit. Hindi did not exist in his time. – fdb Mar 1 '18 at 13:58

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