# Discovery of zero

I have read at many places that zero was discovered by Aryabhata but when i was discussing this with my mathematics teacher he told me that zero had already been discovered before Aryabhata and it was also used by Euclid. Aryabhata just made Asians aware of it.

So my question is

• Did Aryabhata discover zero?

• If no then who discovered Zero?

I have read this post but it doesn't tell which mathematician first discovered that there is 0 in number system.

• @J.W.Perry I have edited it and hope it makes more clear. – Freddy Nov 12 '14 at 6:55
• Related to the question and answers here hsm.stackexchange.com/questions/4/… – user22 Nov 12 '14 at 8:01
• I think it is still worth to be read David Eugene Smith & Louis Charles Karpinski, The Hindu-Arabic Numerals (1911 - Dover reprint): see Ch.IV : The symbol zero, page 51. – Mauro ALLEGRANZA Nov 12 '14 at 10:24
• What do you mean by "discovered zero"? (1) a positional number system with a symbol for zero? (2) calculating with zero as if it is a number like the others? (3) Something else? – Gerald Edgar Nov 12 '14 at 15:03
• @Freddy, your teacher said the truth. In fact Babylonian, mayan , Indians civilizations invented $zero$ independently – M. A. SARKAR Jul 30 at 13:24

The first evidence of zero is from the Sumerian culture in Mesopotamia, some 5000 years ago (source: Robert Kaplan, The Nothing that is: a natural History of Zero).

It is interesting to note that different cultures discovered the concept of "zero" independently. The Babylonians, the Mayans, the Chinese and the Hindus all introduced symbols for zero. They are e.g. shown in this article on the origin of zero.

Our symbol for zero has its origin in India in the fifth century (where it was written as a dot), from where it spread to Cambodia at the end of the 7th century, and then to China and the Islamic countries in the 8th century. It reached western Europe in the 12th century. The open circle symbol for zero is originally from China.

• I am not aware of a single source concerning 0 in the Sumerian culture. And the Babylonians certainly did not develop mathematics "independently": they were the Sumerians' heirs. – user2255 Mar 20 '16 at 12:41

Like with many other inventions, this did not happen once, suddenly at a specific time. The idea gradually evolved. I am not sure about Euclid but a "zero" (place holder) is occasionally found in Ptolemy. However the use is not systematic and it does not have the modern shape. Other people used space for the same purpose.

• Certainly not Euclid. In fact, for Euclid "number" does not include 1 either. There is the "unit" and then there are "numbers" ... in modern language: two or more units. – Gerald Edgar Nov 12 '14 at 15:06
• both the answer explain same that it was not by one mathematician but it got developed with time. But i think Felix answer is detailed...... +1 – Freddy Nov 12 '14 at 17:11

Answering your first question, it was not Aryabhata. It was rather Brahmagupta and that too for first time publishing the rules governing zero.

I see three aspects about the question,

1. Concept of '0'
2. '0' as a Symbol/placeholder
3. Word 'Zero' for the symbol '0'

As already answered by @Felix the concept itself was discovered across different cultures including Babylonians, Mayans, Chinese, Hindus and many other.

When it comes to using '0' as a symbol. Wikipedia states that,

In AD 976 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 was called صفر (ṣifr, "empty") in Arabic language. That was the earliest mention of the name ṣifr that eventually became zero.[8]

The same Wikipedia article says that the Arabic word 'sifr' became 'zefiro' in Italian and then later 'zero' in Venetian.

One should distinguish between the notational zero (i.e., as placeholder in a positional system for representing numbers) and the algebraic zero (i.e., as the neutral element of addition). We use the same symbol for both (and with good reason), but they were introduced independently.

As far as I know, the first mention of the algebraic zero is in the Brāhmasphuṭasiddhānta (ca. CE 628) of the Indian mathematician Brahmagupta, specifically in the section Kuttaka ("pulverizer"), Rule §19. Quoting from Thomas Colebrooke's translation of 1817 (Section II, 31 on page 339):

[...] The sum of two affirmative quantities is affirmative; of two negative is negative; of an affirmative and a negative is their difference; or, if they be equal, nought. The sum of cipher and negative is negative; of affirmative and nought is positive; of two ciphers is cipher.

(Brahmagupta uses the two terms nought (Sanskrit खम्, /kham/) and cipher (Sanskrit शून्यम्, /śūnyam/) indiscriminately.)

For those interested, the two sentences in transliteration read

dhanayos dhanam ṛṇam ṛṇayos dhana-ṛṇayos antaram sama-aikyam #kham/

ṛṇam aikyam ca dhanam ṛṇa-dhana-#śūnyayos #śūnyayos #śūnyam//

Although as Felix says that the idea of zero is known from as early as Sumeria, and although this is true, the actual widespread first use was by the ancient Babylonians. The Greeks wrote the Babylonian zero as omicron ("o") with a slash over it. The Indians later adopted this from Hellenistic cultures in what is now Syria and Iraq.

Felix's contention that the Indian's used a dot for a zero is incorrect. A dot is the Arabic symbol for zero. As I said above, our symbol for zero comes from the Greeks.

first 0 was invented by Brahmagupta. many people were not aware of it as he was not so famous as aryabatta and other mathematicians.even he invented the rules and method of cubes and cube root, square and square roots ,integers .

• You should give some sources to back up your claims. Otherwise, the answer will be of little value. – Danu Jul 7 '16 at 6:53

The time line of Greek and Indian civilizations is given by Time line of Mathematics , Greek and Indian https://www-history.mcs.st-andrews.ac.uk/Timelines/TimelineA.html

Zero was already known during the Vedic era which includes Bhoudayana in 600BC. Atharva Veda already shows how zero is to be used. Greek maths had no zero and its arithmetic was clumsy. It is highly likely that India was the sole initiator of zero and the place value notation.

Early observational astronomy does not require fancy arithmetic, however.

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