History of Science and Mathematics Stack Exchange is a question and answer site for people interested in the history and origins of science and mathematics. It only takes a minute to sign up.
Sign up to join this community
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.
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.
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.
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,
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 .
