History of Large Numbers - Ancient India

Ancient India

The Indians had a passion for high numbers, which is intimately related to their religious thought. For example, in texts belonging to the Vedic literature, we find individual Sanskrit names for each of the powers of 10 up to a trillion and even 1062. (Even today, the words 'lakh' and 'crore', referring to 100,000 and 10,000,000, respectively, are in common use among English-speaking Indians.) One of these Vedic texts, the Yajur Veda, even discusses the concept of numeric infinity (purna "fullness"), stating that if you subtract purna from purna, you are still left with purna.

The Lalitavistara Sutra (a Mahayana Buddhist work) recounts a contest including writing, arithmetic, wrestling and archery, in which the Buddha was pitted against the great mathematician Arjuna and showed off his numerical skills by citing the names of the powers of ten up to 1 'tallakshana', which equals 1053, but then going on to explain that this is just one of a series of counting systems that can be expanded geometrically. The last number at which he arrived after going through nine successive counting systems was 10421, that is, a 1 followed by 421 zeros.

There is also an analogous system of Sanskrit terms for fractional numbers, capable of dealing with both very large and very small numbers.

Larger number in Buddhism works up to Bukeshuo bukeshuo zhuan (不可說不可說轉) or 1037218383881977644441306597687849648128, which appeared as Bodhisattva's maths in the Avataṃsaka Sūtra., though chapter 30 (the Asamkyeyas) in Thomas Cleary's translation of it we find the definition of the number "untold" as exactly 1010*2122, expanded in the 2nd verses to 1045*2121 and continuing a similar expansion indeterminately.

A few large numbers used in India by about 5th century BCE (See Georges Ifrah: A Universal History of Numbers, pp 422–423):

• lakṣá (लक्ष) —105
• kōṭi (कोटि) —107
• ayuta (अयुता) —109
• niyuta (नियुता) —1013
• pakoti (पकोटि) —1014
• vivara (विवारा) —1015
• kshobhya (क्षोभ्या) —1017
• vivaha (विवाहा) —1019
• kotippakoti (कोटिपकोटी) —1021
• bahula (बहूला) —1023
• nagabala (नागाबाला) —1025
• nahuta (नाहूटा) —1028
• titlambha (तीतलम्भा) —1029
• vyavasthanapajnapati (व्यवस्थानापज्नापति) —1031
• hetuhila (हेतुहीला) —1033
• ninnahuta (निन्नाहुता) —1035
• hetvindriya (हेत्विन्द्रिया) —1037
• samaptalambha (समाप्तलम्भा) —1039
• gananagati (गनानागती) —1041
• akkhobini (अक्खोबिनि) —1042
• niravadya (निरावाद्य) —1043
• mudrabala (मुद्राबाला) —1045
• sarvabala (सर्वबाला) —1047
• bindu (बिंदु or बिन्दु) —1049
• sarvajna (सर्वज्ञ) —1051
• vibhutangama (विभुतन्गमा) —1053
• abbuda (अब्बुदा) —1056
• nirabbuda (निर्बुद्धा) —1063
• ahaha (अहाहा) —1070
• ababa (अबाबा). —1077
• atata (अटाटा) —1084
• soganghika (सोगान्घीका) —1091
• uppala (उप्पाला) —1098
• kumuda (कुमुदा) —10105
• pundarika (पुन्डरीका) —10112
• paduma (पद्मा) —10119
• kathana (कथाना) —10126
• mahakathana (महाकथाना) —10133
• asaṃkhyeya (असंख्येय) —10140
• dhvajagranishamani (ध्वजाग्रनिशमनी) —10421
• bodhisattva (बोधिसत्व or बोधिसत्त) —1037218383881977644441306597687849648128
• lalitavistarautra (ललितातुलनातारासूत्र) —10200infinities
• matsya (मत्स्य) —10600infinities
• kurma (कुरमा) —102000infinities
• varaha (वरहा) —103600infinities
• narasimha (नरसिम्हा) —104800infinities
• vamana (वामन) —105800infinities
• parashurama (परशुराम) —106000infinities
• rama (राम) —106800infinities
• khrishnaraja (कृष्णराज) —10infinities
• kaiki (काईकी or काइकी) —108000infinities
• balarama (बलराम) —109800infinities
• dasavatara (दशावतारा) —1010000infinities
• bhagavatapurana (भागवतपुराण) —1018000infinities
• avatamsakasutra (अवताम्सकासुत्रा) —1030000infinities
• mahadeva (महादेव) —1050000infinities
• prajapati (प्रजापति) —1060000infinities
• jyotiba (ज्योतिबा) —1080000infinities