# To what extent can the invention of zero in India as a number be tied to Buddhist philosophy, if at all?

The Wikipedia entry on zero suggests that the ancient Greeks were unsure about the ontological status of zero. They asked themselves, 'How can nothing be something?' whereas in Buddhism, Sunyata or void appears to have positive value (not in an arithmetic sense, but in the sense of beneficial). Is there any evidence that Buddhist philosophy helped usher in the invention of zero as a number in its own right, other than the fact that it arose in India when Buddhism was vital force there?

Further, zero is often called the identity, or (very much) less often the neutral element in mathematical circles. Is that a telling coincidence, rather than simply a curious one?

Zero is used as a placeholder in the decimal/Arabic number system, but for the purposes of the argument I'm developing here, the more important 'positive' virtue is that it allowed the invention of negative numbers. Without zero they wouldn't be possible.

We can then picture two numbers of the same absolute value but of opposite sign put together (i.e. addition) vanishing into the void, and the opposite process of the void separating into two somethings. So we could answer the Greeks, not only is nothing a something, but somethings (in the plural) can dissolve into nothing as well as arise from it.

• I'm not sure that the usage of 'identity' is significant. It is the additive identity, but working in abstract algebra, 'identity' without further qualification much more frequently refers to 1 or a closely related object. – Niel de Beaudrap Mar 28 '13 at 12:00
• @deBeaudrap: I'm just making the point that nothing aka zero is useful. Whereas on the face of it nothing is not useful at all since you don't have anything. Its useful in terms of a process (addition) and again not in stasis. I agree its speculation. But I find it nonetheless interesting speculation. – Mozibur Ullah Mar 28 '13 at 15:11
• I don't have any problems with the rest of the question, I'm just noting that the modern mathematical usage of the word 'identity' is unlikely to reflect very much on 'nothingness'. – Niel de Beaudrap Mar 28 '13 at 15:16
• @deBeaudrap: True enough. Nothingness or essenceless as a buddhist concept has nothing at all to do with zero or identities. But it can be used to illuminate. – Mozibur Ullah Mar 28 '13 at 15:47
• This seems to me analogous to illustrating the concept of pride by U2's song "Pride"; some associations serve only to confuse. – Niel de Beaudrap Mar 28 '13 at 15:53

The (https://en.wikipedia.org/wiki/Bakhshali_manuscript) [Bakhshali manuscript] is one of the oldest(3rd century AD) recorded Indian mathematics. It was discovered by a local peasant in the Pakhtunkhwa region of Pakistan. The region was under the control of Buddhism (see (http://whc.unesco.org/en/list/140) [Takhtbai ruins]). It dates back from 500 years before Brahmagupta. The zero dot symbol is used in the manuscript instead of a ring symbol.

• it would have been posted a year ago but this platform did not allowed me to do so. so i made another account. – user29792 Dec 1 '17 at 10:52
• well, it would have been +100, but this platform does not allow me to do this! – Mozibur Ullah Dec 1 '17 at 11:00
• i live near that region. if you have ever to visit the relics then i can accompany you there :) cheers – user29792 Dec 1 '17 at 11:05
• btw another number that may be of interest to you geomathry.wordpress.com/2017/02/13/0-1-and-a-new-number – user29792 Dec 1 '17 at 14:13
• – Mozibur Ullah Dec 1 '17 at 14:41

I think there is a connection, but you have the relationship reversed.

Yes, one of the key terms in Buddhist philosophy is Śūnyatā (emptiness), and yes, this comes directly from the Sanskrit word for zero (śūnya). However, there is no indication that the Buddhist philosophical concept led to the mathematical concept; on the contrary, it appears that the Buddhists borrowed the existing mathematical concept for their own purposes.

It should also be remembered that within Buddhist philosophy, the emphasis on Śūnyatā only comes with the advent of Nāgārjuna (which is to say, 1st-2nd century CE). There are a handful of earlier references; see Luis O. Gomez, "Proto-Madhyamaka in the Pāli Canon", Philosophy East and West, 22(1976):2 pp137-165) for an analysis of these, along with Choong Mun-keat, The Notion of Emptiness in Early Buddhism, 1995, if you are interested.

• I don't know if I'd say that Madhyamaka borrowed the mathematical concept. After all, Śūnyatā is not the same as nothing or nothingness -- it's a so-called non-affirming negative, whereas the mathematical concept of zero is a negative, but it certainly affirms something, like all negatives other than Śūnyatā. Seems like they just needed a word. Better that than make up a new one, or use an arbitrary one. Hey, let's all meditate on Mxyzptlk, or Banana. – David Lewis Mar 15 '12 at 5:18
• Madhyamaka logic does make a distinction between implicational and non-implicational negation (i.e., prasajya vs paryudāsa), but Śūnyatā is not tied to either; rather, it is generally used to mean niḥsvabhāva, empty of essence or essential properties. – Michael Dorfman Mar 15 '12 at 7:39

Your question heads in the right direction, but you're a little off in the religion itself. The invention of zero (or rather, its acceptance as more than just a placeholder) had a lot to do with Hinduism, not Buddhism (which, granted, came directly from Hinduism).

The following explanation is entirely referenced from the excellent book Zero: The Biography of a Dangerous Idea by Charles Seife:

The void had an important place in Hindu religion. Hinduism had started off as a polytheistic religion... However, over centuries - centuries before Alexander [of Greece] arrived [in the 4th century BC] - the gods began to merge together... at its core Hinduism became monotheistic and introspective. All the gods became aspects of an all encompassing god, Brahma.

The book continues to describe the concept of Atman, and how it is "the infinite soul that suffuses the universe, at once everywhere and nowhere at the same time. It is infinity, and it is nothing."

So India, as a society that actively explored the void and the infinite, accepted zero. Indian mathematicians did more than simply accept zero. They transformed it, changing its role from mere placeholder to number.

Thus, Buddhism did not have anything to do with the idea of zero, but rather it was Hinduism that allowed for its acceptance (note "acceptance," and definitely not "invention" - zero existed long before even Hinduism became prominent, as it was used as a placeholder since Babylonian times). The Indian concept of the void, arising from Hinduism, helped usher in the Arabic numeral system and eventual mathematical applications of zero.

For further information, I strongly recommend Zero as I mentioned above.

• I'm not sure that timings is as far off as you're suggesting: The Buddha lived around the 4-6 century BC. Buddhist philosophy appears to place much more emphasis on Sunyata, or nothingness than ascetic Hinduism with its emphasis on Brahman, the absolute. Sure, both shared the idea of nothingness, Sunya after all is a Sanskrit word. – Mozibur Ullah Mar 4 '12 at 23:39
• @Mozibur Ullah Oh my, sorry about that. For whatever reason I flipped BC/AD on that one. I've fixed that in the answer, thanks. – commando Mar 4 '12 at 23:48
• To follow the thread started about the link with Hinduism, you might find interesting the opinions of the esteemed Indian mathematician S. Ramanujan, a devout Hindu, on the concept of "zero" and the concept of Nirguna-Brahman. (It is not hard to find something on this through Google search.) And if you would indulge me the freedom to go a little off-topic, even in ancient China, the Dao De Jing proclaims that "The Tao produced One; One produced Two; Two produced Three; Three produced All things." (Legge) Reference: wayist.org/ttc%20compared/chap42.htm – user1539 Mar 5 '12 at 7:02

I have thought on that issue already and I can't help but remember the ideas of Wilfred Bion (the psychoanalist born in India), particulary his concept of O, the ultimate truth. Here a quote from his work 'Transformations' (1):

"For Bion, understanding is a complex process comprising thinking and feeling. It involves a striving to get to know emotional experience, the direction he refers to as K, and the even more essential need to be in touch with emotional truth, which he denoted as O. Knowledge Bion refers to is not sterile and cold. He underlines the importance of Love, without which true understanding is not possible. Movement towards ‘O’ , which for him is making known the unknowable, depends upon a loving and passionate link with the other. The ultimate truth, reality, O is not an ideal and it is not reified. It is unknowable. As Bion puts it ‘It is impossible to know reality for the same reason that makes it impossible to sing potatoes; they may be grown, or pulled, or eaten but not sung. Reality has to be ‘been’ (from to be) (Transformations, p.148) One cannot know O, one can only attempt to become, be O. Knowing about reality is different from being reality, like knowing about psychoanalysis is different from experiencing it."

Buddhism did NOT derive directly from Hinduism, as no such thing existed at the time. The ancient Vedas did exist, though, and the Upanishads were in process. What differentiates Buddhism, among other things, is that they did NOT accept the authority of the Vedas, which is what defines 'Hinduism', something of a catch-all term. So while Hindus consider the Buddha to be the incarnation of a 'Hindu' deity, most Buddhists allow no such thing.

Apparently the word 'shunya' was in discussion among the Buddha's circle during his lifetime, becoming 'shunyata' around the time of Nagarjuna. I'm no mathematician, but there seems no question that the zero we know today was created by Indians, at or around the time of Buddha. It would be very interesting to know the interplay of ideas which produced the concept 'shunyata' as we know it, and the use of zero as we know it, which didn't come into common use until maybe 1000 years after the Buddha, and in Europe maybe another 1000 years still, as introduced by Arabs...

p.s. I have not read the book 'Zero' referenced above, but I suspect there are inaccuracies. The idea of Hinduism as a monotheistic religion is dubious. Shunyata, zero-ness, is a Buddhist term, NOT 'Hindu'.

• It would be good to provide references for any assertions made. That way others can find more information and those references if correctly used would strengthen your answer making it less of an opinion and more of a description of what others have claimed. Welcome to this SE. – Frank Hubeny Jul 1 '18 at 13:38
• Kaplan has a number of inaccuracies. – Jonathan Cender Oct 7 '20 at 19:09

All sorts of issues arise here, some of which have been mentioned. For instance, that Hinduism is monotheism is not correct. If we take the Baghavad Gita as definitive then Hinduism (as it came to be known) is an instance of the Perennial philosophy, advaita or 'nondualism'. The underlying metaphysic is explained by Nagarjuna without the use of zero as a concept.

I find the idea in the question profound and interesting. A good book on the topic is Robert Kaplan's The Nothing That Is: A History of Zero. For the most part it is a mathematical history going back to the early Indian use of zero, but the final chapter becomes metaphysical and here he makes a direct connection with Brahman when he suggest that the world may not be just more simple than we think but more simple than it would be possible for us to think - which is the claim of the Perennial philosophy. Another relevant book would be Spencer Brown's Laws of Form.

As a number zero cannot be associated with the formless. In mysticism the term 'advaita' (not-two) is used to avoid the suggestion of 'One' or 'Many' or any numerical value. Emptiness would not be zero but is also fullness. Unity is not a numerical 'Zero' or 'One' but encompasses multiplicity.

I wonder if the question works without introducing Buddhism. It seems highly likely that zero was introduced as both a mathematical and metaphysical concept, arising naturally in connection with metaphysical/religious issues and not just out of mathematical necessity. Buddhism rests on the metaphysics of the Upanishads so did not add any new ideas about nothingness. As I understand it it was the Vedic practices that had evolved through Brahmanism, (ascetism, animal sacrifice, over-respect for authority and so forth), that Buddhism was unhappy about.

What works against the idea of Buddhist influence is that zero plays no part in Buddhist metaphysics. Number and form would be part of the mundane world and zero would belong in this world. Metaphysically-speaking there would be no such thing as 'Nothing' if we mean nothing at all.

So while I can see how the use of zero might have been motivated by metaphysical considerations I can't see any need to suppose that the emergence of Buddhism had much to do with it.

The association of zero with identity is a profound issue that deserves a long essay. It relates to the 'thing-in-itself' of Kant. If we travel beyond number and form then all is identical (because of the identity of indiscernables - a point Kant seems to have missed). Thus where there is no distinction or division there are no 'things' and there is identity. This would be a state prior to zero since zero is the expression of a conceptual distinction (zero is not-one etc). That is, zero is a relative term meaningful only in the world of relativity. Mysticism often speaks of the 'Nothing' but this is not nothing at all, just an absence of things.

I'd recommend Kaplan's book. It's not a metaphysical discussion but the foundations of mathematics is the same topic in translation and he sees the connections. He carefully charts the origin and use of the term in Indian culture and beyond.

This programme: In Our Time, 'Indian Mathematics' https://www.bbc.co.uk/programmes/p0038xb0 discusses with appropriate professors the arising of geometry for Hindu altars, the contemplation of very large numbers and infinities in Jain religious practice & doctrine, and zero in Buddhist though. It should be noted that not just Hindu nationalists, suggest not without evidence, that Jainism, Buddhism & even Sikhism, should be thought of as reform movements within Hindu culture, called in India sanatam dharma, their perrenial philosophy.

It has to be noted the large scholarly culture and respect for mathematics in India, and the infrastructure for preserving disseminating and discussing philosophy and mathematics, and respect and resources provided for those who did so.

Sunyata is important because it is a view of emptiness which is generative, it has maximal possibilities. Crucial to decimals, is the idea of columns. Both of these should be contrasted with Roman numerals, which don't have zero, or columns, but require special symbols as numbers get larger.

It is doubtful how strong a causative impact can be allocated. It is strongly suggestive though. And an important correction based on history, to note that 'arabic' numerals are Indian, and some of the key mathematical ideas.