Pāṇini
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6th–5th century BCE , region =
Indian philosophy Indian philosophy refers to philosophical traditions of the Indian subcontinent. A traditional Hindu classification divides āstika and nāstika schools of philosophy, depending on one of three alternate criteria: whether it believes the Veda ...
, main_interests =
Grammar In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes domain ...
,
linguistics Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
, notable_works = ' ( Classical Sanskrit) , influenced= , notable_ideas=
Descriptive linguistics In the study of language, description or descriptive linguistics is the work of objectively analyzing and describing how language is actually used (or how it was used in the past) by a speech community. François & Ponsonnet (2013). All acad ...
(Devanagari: पाणिनि, ) was a
Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
philologist Philology () is the study of language in oral and written historical sources; it is the intersection of textual criticism, literary criticism, history, and linguistics (with especially strong ties to etymology). Philology is also defined as th ...
, grammarian, and revered scholar in
ancient India According to consensus in modern genetics, anatomically modern humans first arrived on the Indian subcontinent from Africa between 73,000 and 55,000 years ago. Quote: "Y-Chromosome and Mt-DNA data support the colonization of South Asia by m ...
, variously dated between the 6th and 4th century BCE. Since the discovery and publication of his work by European scholars in the nineteenth century, Pāṇini has been considered the "first descriptive linguist", François & Ponsonnet (2013: 184). and even labelled as “the father of
linguistics Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
”. Pāṇini's
grammar In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes domain ...
was influential on such foundational linguists as Ferdinand de Saussure and Leonard Bloomfield.


Legacy

Pāṇini is known for his text '' Aṣṭādhyāyī'', a sutra-style treatise on
Sanskrit grammar The grammar of the Sanskrit language has a complex verbal system, rich nominal declension, and extensive use of compound nouns. It was studied and codified by Sanskrit grammarians from the later Vedic period (roughly 8th century BCE), culminati ...
, 3,996 verses or rules on
linguistics Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
, syntax and
semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...
in "eight chapters" which is the foundational text of the '' Vyākaraṇa'' branch of the
Vedanga The Vedanga ( sa, वेदाङ्ग ', "limbs of the Veda") are six auxiliary disciplines of Hinduism that developed in ancient times and have been connected with the study of the Vedas:James Lochtefeld (2002), "Vedanga" in The Illustrated Enc ...
, the auxiliary scholarly disciplines of the
Vedic period The Vedic period, or the Vedic age (), is the period in the late Bronze Age and early Iron Age of the history of India when the Vedic literature, including the Vedas (ca. 1300–900 BCE), was composed in the northern Indian subcontinent, betwe ...
. His aphoristic text attracted numerous ''
bhashya Bhashya () is a "commentary" or "exposition" of any primary or secondary text in ancient or medieval Indian literature. Common in Sanskrit literature, ''Bhashya'' is also found in other Indian languages. Bhashya are found in various fields, ranging ...
'' (commentaries), of which Patanjali's '' Mahābhāṣya'' is the most famous. His ideas influenced and attracted commentaries from scholars of other Indian religions such as
Buddhism Buddhism ( , ), also known as Buddha Dharma and Dharmavinaya (), is an Indian religions, Indian religion or Indian philosophy#Buddhist philosophy, philosophical tradition based on Pre-sectarian Buddhism, teachings attributed to the Buddha. ...
. Pāṇini's analysis of noun compounds still forms the basis of modern linguistic theories of compounding in Indian languages. Pāṇini's comprehensive and scientific theory of grammar is conventionally taken to mark the start of Classical Sanskrit. His systematic treatise inspired and made Sanskrit the preeminent Indian language of learning and literature for two millennia. Pāṇini's theory of morphological analysis was more advanced than any equivalent Western theory before the 20th century. His treatise is generative and descriptive, uses metalanguage and meta-rules, and has been compared to the
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
wherein the logical structure of any computing device has been reduced to its essentials using an idealized mathematical model.


Date and context

Pāṇini likely lived in Śalatura in ancient
Gandhāra Gandhāra is the name of an ancient region located in the northwestern region of the Indian subcontinent, more precisely in present-day north-west Pakistan and parts of south-east Afghanistan. The region centered around the Peshawar Val ...
in the northwest
Indian subcontinent The Indian subcontinent is a list of the physiographic regions of the world, physiographical region in United Nations geoscheme for Asia#Southern Asia, Southern Asia. It is situated on the Indian Plate, projecting southwards into the Indian O ...
during the Mahājanapada era. The name Pāṇini is a
patronymic A patronymic, or patronym, is a component of a personal name based on the given name of one's father, grandfather (avonymic), or an earlier male ancestor. Patronymics are still in use, including mandatory use, in many countries worldwide, alt ...
meaning descendant of Paṇina. His full name was Dakṣiputra Pāṇini according to verses 1.75.13 and 3.251.12 of Patanjali's '' Mahābhāṣya'', with the first part suggesting his mother's name was Dakṣi.


Dating

Nothing definite is known about when Pāṇini lived, not even in which century he lived. Pāṇini has been dated between the seventh or sixth and fourth century BCE. Von Hinüber (1989) based on numismatic arguments and Falk (1993) based on his Indic script studies, place him in mid-fourth century BCE. Others use internal evidence and textual evidence in ancient Indian texts to date him in the sixth or fifth century BCE, while Bod mentions the seventh to fifth century BCE. George Cardona (1997) in his authoritative survey and review of Pāṇini-related studies, states that the available evidence strongly supports a dating no later than between 400 and 350 BCE, while earlier dating depends on interpretations and is not probative. According to Bod, Pāṇini's grammar defines Classical Sanskrit, so Pāṇini is chronologically placed in the later part of the
Vedic period The Vedic period, or the Vedic age (), is the period in the late Bronze Age and early Iron Age of the history of India when the Vedic literature, including the Vedas (ca. 1300–900 BCE), was composed in the northern Indian subcontinent, betwe ...
. According to
A. B. Keith Arthur Berriedale Keith (5 April 1879 – 6 October 1944) was a Scottish constitutional lawyer, scholar of Sanskrit and Indologist. He became Regius Professor of Sanskrit and Comparative Philology and Lecturer on the Constitution of the Brit ...
, the Sanskrit text that most matches the language described by Pāṇini is the '' Aitareya Brāhmaṇa'' (). According to Scharfe, "his proximity to the Vedic language as found in the Upanisads and Vedic sūtras suggests the 5th or maybe 6th c. B.C." Based on numismatic findings, Von Hinüber and Falk place Pāṇini in the mid-4th century BCE. Pāṇini's ''rupya'' (A 5.2.119, A 5.2.120, A. 5.4.43, A 4.3.153,) mentions a specific gold coin, the ''niṣka'', in several sutra, which was introduced in India in the 4th-century BCE. According to Houben, "the date of " for Pāṇini is thus based on concrete evidence which till now has not been refuted." According to Bronkhorst, there is no reason to doubt the validity of Von Hinüber's and Falk's argument, setting the ''
terminus post quem ''Terminus post quem'' ("limit after which", sometimes abbreviated to TPQ) and ''terminus ante quem'' ("limit before which", abbreviated to TAQ) specify the known limits of dating for events or items.. A ''terminus post quem'' is the earliest da ...
'' for the date of Pāṇini at 350 BCE or the decades thereafter. According to Bronkhorst, Cardona mentions two major pieces of internal evidence for the dating of Pāṇini. The occurrence of the word '' '' in 4.1.49, referring to a writing ( ''lipi'') c.q. cuneiform writing, or to Greek writing, suggests a date for Pāṇini after
Alexander the Great Alexander III of Macedon ( grc, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the ancient Greek kingdom of Macedon. He succeeded his father Philip II to ...
. Cardona rejects this possibility, arguing that may also refer to a Yavana woman; and that Indians had contacts with the Greek world before Alexander's conquests. Sutra 2.1.70 of Pāṇini mentions ''kumāraśramaṇa'', derived from ''
śramaṇa ''Śramaṇa'' (Sanskrit; Pali: ''𑀲𑀫𑀦'') means "one who labours, toils, or exerts themselves (for some higher or religious purpose)" or "seeker, one who performs acts of austerity, ascetic".Monier Monier-Williams, श्रमण śr ...
'', which refers to a female renunciates, c.q. " Buddhist nuns," implying that Pāṇini should be placed after
Gautama Buddha Siddhartha Gautama, most commonly referred to as the Buddha, was a wandering ascetic and religious teacher who lived in South Asia during the 6th or 5th century BCE and founded Buddhism. According to Buddhist tradition, he was born in Lu ...
. K. B. Pathak (1930) argued that ''kumāraśramaṇa'' could also refer to a
Jain Jainism ( ), also known as Jain Dharma, is an Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four tirthankaras (supreme preachers of ''Dharma''), with the first in the current time cycle being ...
nun, meaning that Pāṇini is not necessarily to be placed after the Buddha. It is not certain whether Pāṇini used writing for the composition of his work, though it is generally agreed that he knew of a form of writing, based on references to words such as '' lipi'' ("script") and ''lipikara'' ("scribe") in section 3.2 of the '' Aṣṭādhyāyī''. The dating of the introduction of writing in India may therefore give further information on the dating of Pāṇini. Pāṇini cites at least ten grammarians and linguists before him: Āpiśali, Kāśyapa, Gārgya, Gālava, Cākravarmaṇa, Bhāradvāja, Śākaṭāyana, Śākalya, Senaka and Sphoṭāyana. According to Kamal K. Misra, Pāṇini also refers to Yaska, "whose writings date back to the middle of the 4th century B.C." Both Brihatkatha and Mañjuśrī-mūla-kalpa mention Pāṇini to have been a contemporary with the Nanda king (4th c. BCE).


Location

Nothing certain is known about Pāṇini's personal life. In an inscription of Siladitya VII of Valabhi, he is called Śalāturiya, which means "man from Salatura". This means Panini lived in Salatura of ancient Gandhara (present day north-west
Pakistan Pakistan ( ur, ), officially the Islamic Republic of Pakistan ( ur, , label=none), is a country in South Asia. It is the world's fifth-most populous country, with a population of almost 243 million people, and has the world's second-lar ...
), which likely was near
Lahor Lāhor (), also known as Little Lahore (Pashto: , Urdu: ), previously known as Salatura (), is an ancient pre-historic town of Swabi District in Khyber Pakhtunkhwa, Pakistan. The town serves as the headquarters of Lahor Tehsil and is administr ...
, a town at the junction of Indus and Kabul rivers. According to the memoirs of 7th-century Chinese scholar
Xuanzang Xuanzang (, ; 602–664), born Chen Hui / Chen Yi (), also known as Hiuen Tsang, was a 7th-century Chinese Buddhist monk, scholar, traveler, and translator. He is known for the epoch-making contributions to Chinese Buddhism, the travelogue of ...
, there was a town called ''Suoluoduluo'' on the Indus where Pāṇini was born, and he composed the ''Qingming-lun'' (Sanskrit: '' Vyākaraṇa''). According to Hartmut Scharfe, Pāṇini lived in Gandhara close to the borders of the Achaemenid Empire, and Gandhara was then an Achaemenian satrapy following the
Achaemenid conquest of the Indus Valley The Achaemenid conquest of the Indus Valley occurred from the 6th to 4th centuries BCE, and saw the Persian Achaemenid Empire take control of regions in the northwestern Indian subcontinent that predominantly comprise the territory of modern-d ...
. He must, therefore, have been technically a Persian subject but his work shows no awareness of the Persian language. According to Patrick Olivelle, Pāṇini's text and references to him elsewhere suggest that "he was clearly a northerner, probably from the northwestern region".


Legends and later reception

Panini is mentioned in Indian fables and ancient texts. The '' Panchatantra'', for example, mentions that Pāṇini was killed by a lion. Pāṇini was depicted on a five-rupee Indian postage stamp in August, 2004.


''Aṣṭādhyāyī''

The most important of Pāṇini's works, the ''Aṣṭādhyāyī'' is a grammar that essentially defines the Sanskrit language. Modelled on the dialect and register of elite speakers in his time, the text also accounts for some features of the older
Vedic upright=1.2, The Vedas are ancient Sanskrit texts of Hinduism. Above: A page from the '' Atharvaveda''. The Vedas (, , ) are a large body of religious texts originating in ancient India. Composed in Vedic Sanskrit, the texts constitute the ...
language. The ''Aṣtādhyāyī'' is a prescriptive and generative grammar with algebraic rules governing every aspect of the language. It is supplemented by three ancillary texts: ''akṣarasamāmnāya'', ''dhātupāṭha'' and ''gaṇapāṭha''. Growing out of a centuries-long effort to preserve the language of the Vedic hymns from "corruption", the ''Aṣtādhyāyī'' is the high point of a vigorous, sophisticated grammatical tradition devised to arrest language change. The ''Aṣtādhyāyī'''s preeminence is underlined by the fact that it eclipsed all similar works that came before: while not the first, it is the oldest such text surviving in its entirety.Burrow, §2.1. The ''Aṣṭādhyāyī'' consists of 3,959 ''sūtras'' in eight chapters, which are each subdivided into four sections or ''pādas''. The text takes material from lexical lists (''dhātupāṭha'', ''gaṇapātha'') as input and describes algorithms to be applied to them for the generation of well-formed words. Such is its intricacy that the correct application of its rules and metarules is still being worked out centuries later. The ''Aṣṭādhyāyī'', composed in an era when oral composition and transmission was the norm, is staunchly embedded in that oral tradition. In order to ensure wide dissemination, Pāṇini is said to have preferred brevity over clarity - it can be recited end-to-end in two hours. This has led to the emergence of a great number of commentaries of his work over the centuries, which for the most part adhere to the foundations laid by Pāṇini's work.


''Bhaṭṭikāvya''

The learning of Indian curriculum in late classical times had at its heart a system of grammatical study and linguistic analysis. The core text for this study was the Aṣṭādhyāyī of Pāṇini, the ''sine qua non'' of learning. This grammar of Pāṇini had been the object of intense study for the ten centuries prior to the composition of the ''Bhaṭṭikāvya''. It was plainly Bhaṭṭi's purpose to provide a study aid to Pāṇini's text by using the examples already provided in the existing grammatical commentaries in the context of the gripping and morally improving story of the '' Rāmāyaṇa''. To the dry bones of this grammar Bhaṭṭi has given juicy flesh in his poem. The intention of the author was to teach this advanced science through a relatively easy and pleasant medium. In his own words:
This composition is like a lamp to those who perceive the meaning of words and like a hand mirror for a blind man to those without grammar. This poem, which is to be understood by means of a commentary, is a joy to those sufficiently learned: through my fondness for the scholar I have here slighted the dullard. ''Bhaṭṭikāvya'' 22.33–34.


Modern linguistics

Pāṇini's work became known in 19th-century Europe, where it influenced modern linguistics initially through
Franz Bopp Franz Bopp (; 14 September 1791 – 23 October 1867) was a German linguist known for extensive and pioneering comparative work on Indo-European languages. Early life Bopp was born in Mainz, but the political disarray in the Republic of Mai ...
, who mainly looked at Pāṇini. Subsequently, a wider body of work influenced Sanskrit scholars such as Ferdinand de Saussure, Leonard Bloomfield, and
Roman Jakobson Roman Osipovich Jakobson (russian: Рома́н О́сипович Якобсо́н; October 11, 1896Kucera, Henry. 1983. "Roman Jakobson." ''Language: Journal of the Linguistic Society of America'' 59(4): 871–883. – July 18,Frits Staal Johan Frederik "Frits" Staal (3 November 1930 – 19 February 2012) was the department founder and Emeritus Professor of Philosophy and South/Southeast Asian Studies at the University of California, Berkeley. Staal specialized in the study of V ...
(1930–2012) discussed the impact of Indian ideas on language in Europe. After outlining the various aspects of the contact, Staal notes that the idea of formal rules in language – proposed by Ferdinand de Saussure in 1894 and developed by
Noam Chomsky Avram Noam Chomsky (born December 7, 1928) is an American public intellectual: a linguist, philosopher, cognitive scientist, historian, social critic, and political activist. Sometimes called "the father of modern linguistics", Chomsky i ...
in 1957 – has origins in the European exposure to the formal rules of Pāṇinian grammar. In particular, de Saussure, who lectured on Sanskrit for three decades, may have been influenced by Pāṇini and Bhartrihari; his idea of the unity of signifier-signified in the sign somewhat resembles the notion of
Sphoṭa ( sa, स्फोट, ; "bursting, opening", "spurt") is an important concept in the Indian grammatical tradition of Vyakarana, relating to the problem of speech production, how the mind orders linguistic units into coherent discourse and meani ...
. More importantly, the very idea that formal rules can be applied to areas outside of logic or mathematics may itself have been catalysed by Europe's contact with the work of Sanskrit grammarians.Frits Staal, The science of language, Chapter 16, in Gavin D. Flood, ed. ''The Blackwell Companion to Hinduism'' Blackwell Publishing, 2003, 599 pages , . p. 357-358


De Saussure

Pāṇini, and the later Indian linguist Bhartrihari, had a significant influence on many of the foundational ideas proposed by Ferdinand de Saussure, professor of
Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
, who is widely considered the father of modern structural linguistics and with
Charles S. Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for t ...
on the other side, to
semiotics Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something ...
, although the concept Saussure used was
semiology Semiotics (also called semiotic studies) is the systematic study of sign processes (semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, ...
. Saussure himself cited Indian
grammar In linguistics, the grammar of a natural language is its set of structural constraints on speakers' or writers' composition of clauses, phrases, and words. The term can also refer to the study of such constraints, a field that includes domain ...
as an influence on some of his ideas. In his ''Mémoire sur le système primitif des voyelles dans les langues indo-européennes'' (''Memoir on the Original System of Vowels in the Indo-European Languages'') published in 1879, he mentions Indian grammar as an influence on his idea that "reduplicated aorists represent imperfects of a verbal class." In his ''De l'emploi du génitif absolu en sanscrit'' (''On the Use of the Genitive Absolute in Sanskrit'') published in 1881, he specifically mentions Pāṇini as an influence on the work. Prem Singh, in his foreword to the reprint edition of the German translation of Pāṇini's Grammar in 1998, concluded that the "effect Panini's work had on Indo-European linguistics shows itself in various studies" and that a "number of seminal works come to mind," including Saussure's works and the analysis that "gave rise to the
laryngeal theory The laryngeal theory is a theory in the historical linguistics of the Indo-European languages positing that: * The Proto-Indo-European language (PIE) had a series of phonemes beyond those reconstructable by the comparative method. That is, th ...
," further stating: "This type of structural analysis suggests influence from Panini's analytical teaching."
George Cardona George Cardona (; born June 3, 1936) is an American linguist, Indologist, Sanskritist, and scholar of Pāṇini. Described as "a luminary" in Indo-European, Indo-Aryan, and Pāṇinian linguistics since the early sixties, Cardona has been recogni ...
, however, warns against overestimating the influence of Pāṇini on modern linguistics: "Although Saussure also refers to predecessors who had taken this Paninian rule into account, it is reasonable to conclude that he had a direct acquaintance with Panini's work. As far as I am able to discern upon rereading Saussure's ''Mémoire'', however, it shows no direct influence of Paninian grammar. Indeed, on occasion, Saussure follows a path that is contrary to Paninian procedure."


Leonard Bloomfield

The founding father of American structuralism, Leonard Bloomfield, wrote a 1927 paper titled "On some rules of Pāṇini".


Rishi Rajpopat

Rishi Rajpopat elaborated in 2021 in his PhD thesis a deeper understanding of Panini's "language machine" by designing a simple system of resolving rule conflicts.


Comparison with modern formal systems

Pāṇini's grammar is the world's first
formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A form ...
, developed well before the 19th century innovations of
Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic ph ...
and the subsequent development of mathematical logic. In designing his grammar, Pāṇini used the method of "auxiliary symbols", in which new affixes are designated to mark syntactic categories and the control of grammatical derivations. This technique, rediscovered by the logician
Emil Post Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. Life Post was born in Augustów, Suwałki Gove ...
, became a standard method in the design of
computer programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming l ...
s. Sanskritists now accept that Pāṇini's linguistic apparatus is well-described as an "applied" Post system. Considerable evidence shows ancient mastery of context-sensitive grammars, and a general ability to solve many complex problems.
Frits Staal Johan Frederik "Frits" Staal (3 November 1930 – 19 February 2012) was the department founder and Emeritus Professor of Philosophy and South/Southeast Asian Studies at the University of California, Berkeley. Staal specialized in the study of V ...
has written that "Panini is the Indian
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
."


Other works

Two literary works are attributed to Pāṇini, though they are now lost. * ''Jāmbavati Vijaya'' is a lost work cited by Rajashekhara in Jalhana's '' Sukti Muktāvalī''. A fragment is to be found in Ramayukta's commentary on Namalinganushasana. From the title it may be inferred that the work dealt with Krishna's winning of Jambavati in the underworld as his bride. Rajashekhara in Jahlana's ''Sukti Muktāvalī'':
: नमः पाणिनये तस्मै यस्मादाविर भूदिह। : आदौ व्याकरणं काव्यमनु जाम्बवतीजयम्॥
: namaḥ pāṇinaye tasmai yasmādāvirabhūdiha। : ādau vyākaraṇaṃ kāvyamanu jāmbavatījayam॥
* Ascribed to Pāṇini, ''Pātāla Vijaya'' is a lost work cited by Namisadhu in his commentary on Kavyalankara of
Rudrata Rudrata ( sa, रुद्रट, ) () was a Kashmiri poet and literary theorist, who wrote a work called the ''Kavyalankara'' in the first quarter of the ninth century. Very little is known about Rudrata. From Namisadhu's commentary on the verses ...
. There are many mathematical works related to Pāṇini's works. Pāṇini came up with a plethora of ideas to organize the known grammatical forms of his day in a systematic way. Like any mathematician who models a known phenomenon in mathematical language, Pāṇini created a metalanguage and it is very close to the modern-day ideas of algebra. See
Mathematical Structures of Panini's Ashtaadhyayi" by Bhaskar Kompella


See also

* Vyākaraṇa *
Bhaṭṭikāvya ' (; "Bhatti's Poem") is a Sanskrit-language poem dating from the 7th century CE, in the formal genre of "great poem" (mahākāvya). It focuses on two deeply rooted Sanskrit traditions, the ''Ramayana'' and Panini's grammar, while incorporating nu ...
*
Pingala Acharya Pingala ('; c. 3rd2nd century BCE) was an ancient Indian poet and mathematician, and the author of the ' (also called the ''Pingala-sutras''), the earliest known treatise on Sanskrit prosody. The ' is a work of eight chapters in the la ...
* Mahajanapadas *
Seṭ and aniṭ roots Sanskrit has inherited from its parent, the Proto-Indo-European language, an elaborate system of verbal morphology, much of which has been preserved in Sanskrit as a whole, unlike in other kindred languages, such as Ancient Greek or Latin. Sanskri ...
* Tolkāppiyam *
List of Indian mathematicians chronology of Indian mathematicians spans from the Indus Valley civilisation and the Vedas to Modern India. Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians ...


Notes


Glossary


Traditional glossary and notes


References


Bibliography

*Bhate, S. and Kak, S. (1993) Panini and Computer Science. Annals of the Bhandarkar Oriental Research Institute, vol. 72, pp. 79–94. * * * * * * * * Ingerman suggests that the then-called Backus normal form be renamed to the Pāṇini–Backus form, to give due credit to Pāṇini as the earliest independent inventor. * * * * * * * T. R. N. Rao
''Pāṇini-backus form of languages''.
1998. * * * * * Tiwary, Kapil Muni 1968 Pāṇini's description of nominal compounds, University of Pennsylvania doctoral dissertation, unpublished. * *


Further reading

;Works * Pāṇini. ''Ashtādhyāyī''
Book 4
Translated by Chandra Vasu.
Benares Varanasi (; ; also Banaras or Benares (; ), and Kashi.) is a city on the Ganges river in northern India that has a central place in the traditions of pilgrimage, death, and mourning in the Hindu world. * * * * The city has a syncretic tra ...
, 1896. * Pāṇini. ''Ashtādhyāyī''
Book 6–8
Translated by Chandra Vasu.
Benares Varanasi (; ; also Banaras or Benares (; ), and Kashi.) is a city on the Ganges river in northern India that has a central place in the traditions of pilgrimage, death, and mourning in the Hindu world. * * * * The city has a syncretic tra ...
, 1897. ;Pāṇini * 2000. *Pāṇini - His work and its traditions, George Cardona. 1997.


External links


PaSSim – Paninian Sanskrit Simulator
simulates the Pāṇinian Process of word formation
Gaṇakāṣṭādhyāyī
a software on Sanskrit grammar, based on Pāṇini's Sutras
Ashtadhyayi, Work by Pāṇini
*Forizs, L
Pāṇini, Nāgārjuna and Whitehead – The Relevance of Whitehead for Contemporary Buddhist Philosophy
with the ''Mahābhāṣya'' and ''Kāśikā'' commentaries, along with the ''Nyāsa'' and ''Padamanjara'' commentaries on the ''Kāśikā''. (PDF) Sanskrit.
Pāṇinian Linguistics
{{DEFAULTSORT:Panini 6th-century BC writers 5th-century BC writers Ancient Indian mathematicians Ancient Sanskrit grammarians Vyakarana Morphologists 5th-century BC mathematicians Ancient Indian grammar works