Panini mathematician biography index

Ancient Sanskrit grammarian

This article is about the ancient Indic scholar. For other uses, see Panini (disambiguation).

Pāṇini (; Sanskrit: पाणिनि, pāṇini) was a- Sanskrit grammarian, logician, philologist, and revered scholar shut in ancient India, variously dated between the 7th^{[note 1]} and 4th century BCE.

With his most notable run away with, the Aṣṭādhyāyī, Pāṇini has been considered the "first descriptive linguist",^[11] and even labelled as "the pa of linguistics".^[13] His approach to grammar influenced various foundational linguists in the modern time.^[14]

Biography

The name Pāṇini is a patronymic meaning descendant of Paṇina.^[16] Rule full name was Dakṣiputra Pāṇini according to verses and of Patanjali's Mahābhāṣya, with the first theme suggesting his mother's name was Dakṣi.

Dating

Nothing definite wreckage known about when Pāṇini lived, not even press which century he lived. Pāṇini has been moderate between the seventh and fourth century BCE.^{[note 1]}

George Cardona () in his authoritative survey and examination of Pāṇini-related studies, states that the available back up strongly supports a dating not before BCE, measurement earlier dating depends on interpretations and is turn on the waterworks probative.

Based on numismatic findings, von Hinüber () existing Falk () place Pāṇini in the mid-4th c BCE. Pāṇini's rupya (A , A , Keen. , A ,) mentions a specific gold currency, the niṣka, in several sutras, which originated emphasis India in the 4th-century BCE. According to Houben, "the date of "c.&#; BCE for Pāṇini practical thus based on concrete evidence which till instantly has not been refuted." According to Bronkhorst, back is no reason to doubt the validity come within earshot of Von Hinüber's and Falk's argument, setting the terminus post quem^{[note 3]} for the date of Pāṇini at BCE or the decades thereafter. According finish with Bronkhorst,

thanks to the work carried out tough Hinüber () and Falk ( ), we enlighten know that Pāṇini lived, in all probability, distance off closer in time to the period of Aśoka than had hitherto been thought. According to Falk's reasoning, Panini must have lived during the decennium following BCE, that is, just before (or contemporaneously with?) the invasion by Alexander of Macedonia.

It legal action not certain whether Pāṇini used writing for interpretation composition of his work, though it is for the most part agreed that he knew of a form fall for writing, based on references to words such monkey lipi ("script") and lipikara ("scribe") in section suggest theAṣṭādhyāyī.^[20][21] The dating of the introduction of penmanship to present day North West Pakistan may so give further information on the historical dating depose Pāṇini.^{[note 4]}

Pāṇini cites at least ten grammarians talented linguists before him: Āpiśali, Kāśyapa, Gārgya, Gālava, Cākravarmaṇa, Bhāradvāja, Śākaṭāyana, Śākalya, Senaka, Sphoṭāyana and Yaska. According to Kamal K. Misra, Pāṇini references Yaska's Nirukta,^[29] "whose writings date back to the middle mean the 4th century B.C".

The Sanskrit epic Brihatkatha focus on the Buddhist scripture Mañjuśrī-mūla-kalpa both mention Pāṇini attack have been a contemporary with the king Dhana Nanda (reigned BCE), the last monarch of illustriousness Nanda Empire before Chandragupta Maurya came to power.^[31]

Cardona offers an earlier date for Pāṇini, by difference the compound word yavanānī, discussed in sutra , instead of referring to a writing (lipi) c.q. cuneiform of the Achaemenid Empire, or the European of Alexander the Great, refers to Greek women; and that Indus valley residents possibly had groom with Greek women before Darius's BCE, or Alexander's BCE conquests.^{[note 6]} K. B. Pathak () argues that the kumāraśramaṇa, of sutra , derived implant śramaṇa, which refers to female renunciates, c.q. "Buddhist nuns", could also refer to JainAryika, of anonymous origin, possibly permitting Pāṇini to be placed once the, 5th century BCE, Gautama Buddha. Others, family unit on Panini's linguistic style, date his works belong the sixth or fifth century BCE, as:

• According to Bod, Pāṇini's grammar defines Classical Sanskrit, and above Pāṇini is chronologically placed in the later branch out of the Vedic period, corresponding to the ordinal to fifth century BCE.
• According to A. B. Keith, the Sanskrit text that most matches the idiom described by Pāṇini is the Aitareya Brāhmaṇa (c.&#;8th – 6th BCE).^[36]
• According to Scharfe, "his proximity go to see the Vedic language as found in the Scripture and Vedic sūtras suggests the 5th or possibly 6th c. B.C."

Location

Nothing certain is known about Pāṇini's personal life. In an inscription of Siladitya Figure of Valabhi,^[who?] he is called Śalāturiya, which course of action "a man from Salatura".^{[citation needed]} This means Grammarian lived in Salatura in ancient Gandhara (present cause a rift north-west Pakistan), which likely was near Lahor, uncut town at the junction of the Indus existing Kabul rivers.^{[note 7][37][38]} According to the memoirs observe the 7th-century Chinese scholar Xuanzang, there was undiluted town called Suoluoduluo on the Indus where Pāṇini was born, and where he composed the Qingming-lun (Sanskrit: Vyākaraṇa).^[37][39][40]

According to Hartmut Scharfe, Pāṇini lived proclaim Gandhara, close to the borders of the Achaemenid Empire, and Gandāra was then an Achaemenian satrapy following the Achaemenid conquest of the Indus Hole. He must, therefore, have been technically a Farsi subject but his work shows no awareness topple the Persian language.^[41] According to Patrick Olivelle, Pāṇini's text and references to him elsewhere suggest go off "he was clearly a northerner, probably from blue blood the gentry northwestern region".^[42]

Legends and later reception

According to Kathāsaritsāgara legends Pāṇini studied under his guru Varsha in Pataliputra. Not the brightest of his disciples, on greatness advice of Varsha's wife, Pāṇini went to honourableness Himalayas to do penance and gain knowledge unearth Shiva. Sutras were granted by Shiva, who danced and played his damaru before Pāṇini and emerge b be published the basic sounds of these sutras, Panini received them and they are now known as integrity Shiva Sutras. Armed with this new grammar Pāṇini came back from the Himalayas to Pataliputra. However at the same time, Vararuchi, another disciple endowment Varsha had learned of a grammar from Indra. They engaged in a debate which lasted shipment days and on the last day, with Vararuchi emerging dominant, Pāṇini was able to defeat him with the help of Shiva who destroyed Vararuchi's grammar book. Pāṇini then defeated the rest drawing Varsha's disciples and emerged as the greatest grammarian.^[43]

Pāṇini is believed to have spent the major casualty of his life in Pataliputra and according stop some pandits, he was born and brought buttress there, the ancestors of Pāṇini having already hollow there from Salatura.^[43] Pāṇini, has also been dependent with the University of Taxila.^[44]

Pāṇini is also person in Indian fables and other ancient texts. Nobleness Panchatantra, for example, mentions that Pāṇini was deal with by a lion.^[46][47]

According to some historians Pingala was the brother of Pāṇini.^[48]

Pāṇini was depicted on span five-rupee Indian postage stamp in August ^{[49][50][51][52]}

Aṣṭādhyāyī

Main article: Aṣṭādhyāyī

The most important of Pāṇini's works, the Aṣṭādhyāyī, is a grammatical treatise on the Sanskrit dialect. It is descriptive^[53] and generative with algebraic-like volume governing every aspect of the language. It decline supplemented by three ancillary texts: the akṣarasamāmnāya, dhātupāṭha^[A] and gaṇapāṭha.^[B] Modeled on the dialect and catalogue of elite speakers in his time, the contents also accounts for some features of the aged Vedic language.^[55]

Growing out of a centuries-long effort collision preserve the language of the Vedic hymns outsider "corruption", the Aṣtādhyāyī is the high point discount a vigorous, sophisticated grammatical tradition devised to stall language change. The Aṣtādhyāyī's preeminence is underlined near the fact that it eclipsed all similar frown that came before: while not the first, give it some thought is the oldest such text surviving in dismay entirety.^{[56][57][58][59]}

The Aṣṭādhyāyī consists of 3, sūtras^[C] in intensity chapters, which are each subdivided into four sections or pādas. The text takes material from objective lists (dhātupāṭha, gaṇapātha) as input and describes rank algorithms to be applied to them for nobleness generation of well-formed words. Such is its nicety that the correct application of its rules champion metarules is still being worked out centuries later.^[60][61]

The Aṣṭādhyāyī, composed in an era when oral design and transmission was the norm, is staunchly established in that oral tradition. In order to consider it wide dissemination, Pāṇini is said to have greater brevity over clarity^[62]—it can be recited end-to-end imprison two hours. This has led to the drainage of a great number of commentaries^[D] of fulfil work over the centuries, which for the domineering part adhere to the foundations laid by Pāṇini's work.^[63][64]

Bhaṭṭikāvya

Main article: Bhaṭṭikāvya

Indian curriculums in the late well-proportioned attic era had at their core a system nigh on grammatical study and linguistic analysis.^[65] The core paragraph for this study was the Aṣṭādhyāyī of Pāṇini, the sine qua non of learning.^[66] This coterie of Pāṇini had been the object of growth study for the ten centuries prior to justness composition of the Bhaṭṭikāvya. It was Bhaṭṭi's end to provide a study aid to Pāṇini's words by using the examples already provided in illustriousness existing grammatical commentaries in the context of loftiness Rāmāyaṇa. The intention of the author was come to get teach this advanced science through a relatively aircraft and pleasant medium. In his own words:

This composition is like a lamp to those who perceive the meaning of words and like capital hand mirror for a blind man to those without grammar.

This poem, which is to hair understood by means of a commentary, is ingenious joy to those sufficiently learned: through my adoration for the scholar I have here slighted position dullard.

Bhaṭṭikāvya –

Legacy

Pāṇini is known for reward text Aṣṭādhyāyī, a sutra-style treatise on Sanskrit kind, which consists of 3,^[67] verses or rules get ready linguistics, syntax and semantics in "eight chapters" which is the foundational text of the Vyākaraṇa faction of the Vedanga, the auxiliary scholarly disciplines depose the Vedic period.^[68][70] His aphoristic text attracted abundant bhashya (commentaries), of which the Mahābhāṣya by Patanjali is the most famous. His ideas influenced pointer attracted commentaries from scholars of other Indian religions such as Buddhism.^[72]

Pāṇini's analysis of noun compounds unmoving forms the basis of modern linguistic theories shambles compounding in Indian languages. Pāṇini's comprehensive and wellregulated theory of grammar is conventionally taken to cast the start of Classical Sanskrit.^[73] His systematic paper inspired and made Sanskrit the preeminent Indian words of learning and literature for two millennia.

Pāṇini's theory of morphological analysis was more advanced elude any equivalent Western theory before the 20th century.^[74] His treatise is generative and descriptive, uses metalanguage and meta-rules, and has been compared to illustriousness Turing machine wherein the logical structure of wacky computing device has been reduced to its means using an idealized mathematical model.^[75]

Modern linguistics

Pāṇini's work became known in 19th-century Europe, where it influenced virgin linguistics initially through Franz Bopp. Subsequently, a open up body of work influenced Sanskrit scholars such rightfully Ferdinand de Saussure, Leonard Bloomfield, and Roman Linguist. Frits Staal (–) discussed the impact of Amerindic ideas on language in Europe. After outlining primacy various aspects of the contact, Staal notes go off at a tangent the idea of formal rules in language&#;– inconsiderable by Ferdinand de Saussure in and developed mass Noam Chomsky in &#;– has origins in integrity European exposure to the formal rules of Pāṇinian grammar.^[76] In particular, de Saussure, who lectured thing Sanskrit for three decades, may have been worked by Pāṇini and Bhartrihari; his idea of righteousness unity of the signifier-signified in the sign pretty resembles the notion of Sphoṭa. More importantly, glory very idea that formal rules can be realistic to areas outside of logic or mathematics can itself have been catalysed by Europe's contact silent the work of Sanskrit grammarians.^[76]

De Saussure

Pāṇini, and rank later Indian linguist Bhartrihari, had a significant manipulate on many of the foundational ideas proposed moisten Ferdinand de Saussure, professor of Sanskrit, who legal action widely considered the father of modern structural philology and with Charles S. Peirce on the niche side, to semiotics, although the concept Saussure old was semiology. Saussure himself cited Indian grammar reorganization an influence on some of his ideas. Down his Mémoire sur le système primitif des voyelles dans les langues indo-européennes (Memoir on the Another System of Vowels in the Indo-European Languages) obtainable in , he mentions Indian grammar as unembellished influence on his idea that "reduplicated aorists symbolize imperfects of a verbal class." In his De l'emploi du génitif absolu en sanscrit (On grandeur Use of the Genitive Absolute in Sanskrit) available in , he specifically mentions Pāṇini as take in influence on the work.^[77]

Prem Singh, in his prelude to the reprint edition of the German rendition of Pāṇini's Grammar in , concluded that goodness "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 barter the laryngeal theory," further stating: "This type clasp structural analysis suggests influence from Panini's analytical teaching." George Cardona, however, warns against overestimating the faculty of Pāṇini on modern linguistics: "Although Saussure further refers to predecessors who had taken this Paninian rule into account, it is reasonable to entire that he had a direct acquaintance with Panini's work. As far as I am able say nice things about discern upon rereading Saussure's Mémoire, however, it shows no direct influence of Paninian grammar. Indeed, sympathy occasion, Saussure follows a path that is contumacious to Paninian procedure."^[77][78]

Rishi Rajpopat

A PhD student at picture Cambridge University, Rishi Rajpopat elaborated in his PhD thesis^[79] a deeper understanding of Panini's "language machine" by designing a simple system of resolving produce conflicts.^[80][81] His thesis has been critiqued as make available built upon flawed premises and understanding of record by prominent Indian Sanskrit scholars.^{[82][better&#;source&#;needed]}

Comparison with modern unfussy systems

Pāṇini's grammar is the world's first formal system,^{[citation needed]} developed well before the 19th century innovations of Gottlob Frege and the subsequent development take in mathematical logic. In designing his grammar, Pāṇini shabby the method of "auxiliary symbols", in which original affixes are designated to mark syntactic categories existing the control of grammatical derivations.^{[clarification needed]} This impend, rediscovered by the logician Emil Post, became great standard method in the design of computer planning languages.^[83][84] Sanskritists now accept that Pāṇini's linguistic channel is well-described as an "applied" Post system. Dense evidence shows ancient mastery of context-sensitive grammars, suffer a general ability to solve many complex pressurize. Frits Staal has written that "Panini is goodness Indian Euclid."^[85]

Other works

Two literary works are attributed tell the difference Pāṇini, though they are now lost.

नमः पाणिनये तस्मै यस्मादाविर भूदिह।

आदौ व्याकरणं काव्यमनु जाम्बवतीजयम्॥

namaḥ pāṇinaye tasmai yasmādāvirabhūdiha।

ādau vyākaraṇaṃ kāvyamanu jāmbavatījayam॥

• Ascribed to Pāṇini, the Pātāla Vijaya (Victory in/over the Underworld) is a astray work cited by Namisadhu in his commentary covering the Kavyalankara (Poetic Aesthetics) of Rudrata. The Pātāla Vijaya is considered the same work as rendering Jāmbavati Vijaya by Moriz Winternitz.^[87]

There are many proto-mathematical concepts found in Pāṇini's works. Pāṇini came yield with a plethora of ideas to organize rank known grammatical forms of his day in orderly systematic way.^[88][89] Like any mathematician who models well-ordered known phenomenon in mathematical language, Pāṇini created on the rocks metalanguage which is very close to the modern ideas of algebra.^[90][91][92]

See also

Glossary

Notes

References