Since long time I've heard that the number zero was invented by the great Indian mathematician Aryabhata.

Now I have two examples from Ramayana and Mahabharata:

  1. In Ramayana, Ravana had 10 heads.

  2. Similarly, in Mahabharata, we have the 100 Kauravas.

Now if zero was invented by Aryabhata in the era of Kaliyuga (according to Hindu panchānga) how does that make Ramayana and Mahabharata, the tales of previous yugas i.e., Treta yuga and Dwapara yuga respectively?

So effectively my question is:

How could ancient Hindus use the numbers 10 and 100 before the invention of zero?

  • Nice question and belongs more in philosophy.SE I think. It has to do with the concept of soonya vs. mathematical objects and their representation. I will post a detailed answer later. – user1195 Jan 6 '16 at 14:15
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    The origin of the modern decimal-based place value notation can be traced to the Aryabhatiya (c. 500), which states sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding . so zero is already there but DECIMAL -BASed PLACE value discoverd by aryabhata see this en.wikipedia.org/wiki/0_(number)#India_and_Southeast_Asia – Bhavin Patel Jan 7 '16 at 5:10
  • wiki of arybhatta also said he teach us how to work with zero like place value system , so zero (sunya) is already there but world didn't know how to use sunya in maths that is teach by arybhatta en.wikipedia.org/wiki/Aryabhata – Bhavin Patel Jan 7 '16 at 5:21
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    Aryabhatta discovered the '0' symbol and how to incorporate 0 into positional number system. It has nothing to do with how numbers existed. Before humans evolved into understanding maths, they know about basic counting. Counting to 10 isn't that tricky. – Vineet Menon Jan 7 '16 at 8:05
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    Something is called an invention when a person presents a phenomenon or something in the form of theory to the public. But it doesn't mean people before didn't knew about it. Newton explained Gravity in the form of theory to the general public but it doesn't mean it didn't existed before or people didn't knew about it. – Chinmay Sarupria Mar 15 '17 at 7:04
up vote 19 down vote accepted

I feel the your doubt is about representation

If you look at the history of representation, it starts with the story of people representing numbers with straight lines, and crossing them after sometime. Roman Numerals for example did not originally have 0. Multiplication and division might have possibly be done in form of addition and subtraction and if you look closely,you will not feel the importance of zero in them. Its implicit, why would anyone add nothing to a sum, or subtract nothing from the sum, the resultant will remain same, won't it? So simple calculation is not a problem.

Aryabhatt defined the value of 0/0 as 0 which is not in the case of modern definition. So it is possible that there was no such thing as zero and the calculation might have been totally dependent over some other notation as blanks dots etc.When you define something, does it not inherently implies 2 scenarios 1>That the one who defines is either correcting the value of a previously held concept 2>He might possibly be defining his own standard to facilitate correct calculation. **

Hence it is difficult to jump to conclusions and say that zero was there during the time when ramayana or mahabharata was written.

Here is an excerpt from wikipedia: The concept of zero as a digit in the decimal place value notation was developed in India, presumably as early as during the Gupta period (c. 5th century), with the oldest unambiguous evidence dating to the 7th century.[12] The Indian scholar Pingala (c. 200 BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to Morse code.[13] Pingala used the Sanskrit word śūnya explicitly to refer to zero.[14] The earliest text to use a decimal place-value system, including a zero, the Lokavibhāga, a Jain text surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380). In this text, śūnya ("void, empty") is also used to refer to zero.[15] The origin of the modern decimal-based place value notation can be traced to the Aryabhatiya (c. 500), which states sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding",[16][16][17][18] The rules governing the use of zero appeared for the first time in the Brahmasputha Siddhanta (7th century). This work considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers. In some instances, his rules differ from the modern standard, specifically the definition of the value of zero divided by zero as zero.[19]

So your doubt about calculation of 10 and 100 can be easily attributed to the above fact of simple addition and calculation. Now what remains is the representation part. So representation could be in various bases and various forms in the same base.In Ancient india, prakrit, sanskrit etc were used and they do have a good representation of numbers. If you want an example: Romans use the letter "C" to denote 100 and 'X' to denote 10 in decimal notation. In hexadecimal 100 is written as 64. So it can easily be seen that in the olden days, there might be a whole different representation for numbers with zeros. You can go to the following link to know more if you want. https://en.wikipedia.org/wiki/0_(number) I hope i answer you question. If any doubts, feel free to question me.

  • what difficult to jump to conclusions, as you are saying about Pingla. I think you should read your link again. – Shailendra Kaithal Jan 8 '16 at 7:10
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    Use of zero is sometimes mistakenly ascribed to Pingala due to his discussion of binary numbers, usually represented using 0 and 1 in modern discussion, while Pingala used light (laghu) and heavy (guru) syllables. As Pingala's system ranks binary patterns starting at one (four short syllables—binary "0000"—is the first pattern), the nth pattern corresponds to the binary representation of n-1 (with increasing positional values). Positional use of zero dates from c. the 7th century (Brahmagupta) and would have been known to Halāyudha but not to Pingala. – Pranav Jan 8 '16 at 7:28
  • @Pranav Does this prove eitheryway the existence of a well-recognised symbol for zero during Piṅgala’s time? – Gabe Hiemstra Sep 28 '16 at 1:23

From Wikipedia:

Place value system and zero

The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a placeholder for the powers of ten with null coefficients.

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.

Conclusion: Zero was available at that time too but with a different definition, Aryabhatta gave a perfect and universally accepted definition.

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    It is nice to mention the source when copy-pasting – user1195 Jan 11 '16 at 14:44

Since Vedic times Hindus were able to describe very large numbers by using appropriate names. The 9 numbers were already mentioned in RV like eka, dwi, tri, chatur,......., nava.

The names for 10, 20,..., 90 occurs in RV 2.18.5-6. Other numbers are described thus- for example 84 is spelled as four plus eighty. 18 is spelled as 2 less than 20 and so on.

RV 3.9.9 for example has the number 3339 spelled as three thousand, three hundred, and 39.

The YV 17.2 mentions numbers upto ten raised to the power of 12.

इमा मेऽअग्नऽइष्टका धेनवः सन्त्वेका च दश च दशु च शतं च शतं च सुहस्रं च सहस्रं चायुतं चायुतं च नियुतं च नियुतं च प्रयुतं चार्बुदं च न्यर्बुदं च समुद्रश्च मध्यं चान्तश्च परार्द्धश्चैता मेऽअग्नऽइष्टका धेनवः सन्त्वमुत्रामुष्मिँल्लोके॥॥

...............

Bhavarth. O learned person, may the materials of my yajna, like milchkine, be the givers of happiness to me. They may be one, and ten, and tentens, a hundred, and ten hundred, a thousand and ten thousand and a hundred thousand, a lac and ten lacs, a million, and ten millions, a crore, ten crores, hundred crores, thousand crores, its tentimes Maha Padma, its ten times Shankh, its tentimes Samudra, its tentimes Madhya, its tentimes Prardh.. May these bricks of my altar be a source of happiness to me, like milch-kine in this world and the next World.

For example: ayuta is 10^4 (10 raised to the power of 4), niyuta is 10^5, payuta is 10^6, arbuda is 10^7, nyarbuda is 10^8, samudra is 10^9, madhya is 10^10, anta is 10^11, pararardha is 10^12 etc.

Similar list can be found in Taittiriya Samhita 4.4.11, MaitrAyani Samhita 2.8.12, Kathaka Samhita 17.10 etc.

The AV 8.3.21 for example mentions the following number:

shatam te ayutam hyanan dwai trini chatvAri krama

Here shatam= 100, ayutam=10,000, dwai=2, trini=3, chatvari=4. The number is to be read in a reverse order by the standard convention.

Shatam te ayutam is one million. So, the number is 432 million.

Also, the Chamaka mantras found in the Yajur Veda also describe certain numbers as follows:

navadasha cha me ekavimsatih cha me

( 9 and 11)

trayodasha cha me panchadasha cha me saptadasha cha me

( 13, 15 and 17)

ekatrimshat cha me trayatrimshat cha me

(31 and 33)

........

dvatrimshat cha me shattrimshat cha me

(32 and 36)

chatvarimshat cha me chatuschatvarimshat cha me

( 40 and 44)

etc... (Mantras from YajurvEda)

Abbreviations used

RV 2.18.5 ---> Rig Veda Samhita Mandala 2, Sukta 18, Mantra 5.

YV 17.2 ----> Adyayaya 17, Mantra 2 of Yajur Veda Samhita.

AV 2.6.1 ---> Atharva Veda Samhita, Kanda 2, Sukta 6, Mantra 1.

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    Also the Chamakam section of Yajurveda consists of counting of no. in poetic way... – Tejaswee May 27 '17 at 4:41

Aryabhatta wasn't the first to use/discover zero. It's already described in other answers as well. In the recent radioactive dating also Bakshali manuscript which is before Aryabhatta time clearly show use of written zero:

The Bakhshali manuscript is a mathematical text written on birch bark that was found in 1881 in the British-ruled village of Bakhshali (near Mardan in present-day Pakistan). It is notable for being "the oldest extant manuscript in Indian mathematics", with portions dated to AD 224–383. It contains the earliest known Indian use of a zero symbol.

Thus it's clearly before Aryabhatta. Regarding scriptual sources there are already other excellent answer. I just want to quote here from portion of Mahanirvana Tantra as described in this answer:

Just like the number 0 in itself does not have any value and can regarded as indicative of the formless infinite. So is the Parabrahmayi ParAdevi. But just as when prefixed with a 1 it (0) makes the number 10, similarly when the ParAdevi (0) conjoins with her own trigunAtmika prakriti (or 1) she appears as the 10 MahAvidyAs to fulfill the wishes of the devotees.

So, does this mean we need 0 to count to 100 and beyond ?.

I think we can count indefinitely without ever using 0. 0 is a symbol, a convenience and a convention, not a mathematical priori. That's precisely the reason why it is called an invention and not a discovery.

How many times do you utter the word "zero" while counting till hundred ? Not once, right ?.

Zero is "applied" in decimal number system because it makes conducting mathematical operations incredibly easy, which other systems couldn't guarantee us.

Vedas, that were written much before Aryabhatta have verses like :

dvâdaśa pradháyaś cakrám ékaṃ, trîṇi nábhyāni ká u tác ciketa tásmin sākáṃ triśatâ ná śaṅkávo, 'rpitâḥ ṣaṣṭír ná calācalâsaḥ.

Here Dvadasa means 12, Sakam means Sixty, Trisata means Three Hundred, hence Sakam Trishata means 360.

As evident, we don't need 0 for writing/speaking 60, 300.

So, Sahasraarjun has 1000 hands, Shat Kauravas are 100 Kauravas and Dashanan is Ravana with 10 heads.

The idea of a zero-less counting system seems impossible to us because we deal with it on a daily basis and we rarely use any other system of counting.

Speaking mathematically, even the concept of zero varies with the context. You can conceive it as absence of numbers, or a neutral on an integral line, or as a source/origin in a multi-dimensional space.

Originally Answered: If ariabhatta discovered ZERO in kalyug, then how did they count a 100 kauravs and 10 heads of Raavan in Mahabharata and Ramayana respectively?

In my opinion, zero was always known to ancient Vedic Indians. Not only Ravana and Kauravas, you can find several references to 1000, lakh and crore in our texts. For example please read the following chapter from Bhagavatam which defines time from Nano second to several yugas (SB 3.11: Calculation of Time, from the Atom). Surely, this wouldn't have been possible without the knowledge of zero.

I would say Aryabhatta defined the formal definition of place value using Zero and its mathematical usage, because his work was intended to be a Mathematical treatise. Our Puranas and Itihasas on other hand were not Mathematical texts - Maths in them were incidental.

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    This looks like a copy paste answer. This is not the proper way to paste answer. You have to add your own words too by properly editing it. See How to write a good answer?. and formatting help and take a tour of help center. – Sarvabhouma Feb 1 '17 at 8:50
  • @SreeCharan How did u conclude that this is a copy-paste? – Rickross Feb 1 '17 at 8:59
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    @Rickross see the original version by the OP. you will understand. I removed that part through editing. – Sarvabhouma Feb 1 '17 at 9:00

Mahabharatha gives a quantitative description of the number of army contingents (Akshauhnees), their individual strengths, commander's rank for which strength of army (Athiradha, Maharatha etc) etc.When bridge to Lanka was made there was numerical estimate of number of days it would take to build the bridge and number of Vanaras needed to execute the work.

Also precise measurement of time. Every event was recorded with moon/sun calender which is unthinkable without a sufficiently satisfactory numbering vyavaharic system. Aryabhata just put in place a system on a sound scientific basis.

Needless to say even today we compute time for the marriages etc.as per ancient practices. Muhoortham time fixing practice would not have survived to this day if it had no evidenced/confirmed benefits.

I think they wrote zata(in Harvard-Kyoto transliteration) in Sanskrit which means hundred and they did not use Roman numerals. They knew the counting but they denoted it differently.

  • Do you mean they used Sanskrit word "Shat" for Kauravas without any representation (such as 0)? – The Destroyer Mar 15 '17 at 7:09

Aryabhat was taught about zero when he went to a vedic gurukul. The sages who taught him, took the concept of shunya from the vedas. The number system came from shukla yajurved 18/24-25.

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    Shukla yajurved 18/24-25? Do you mean Chapter 18, mantras 24, 25? Please add a clear reference. – Sarvabhouma Jul 15 '17 at 14:39

Zero is not at all used for counting. Even we today know the Natural Numbers start from 1, so as the counting. For counting 100 Kaurabs or Ravan's 10 heads 0 is not needed.

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