Old grammar puzzle solved after 2,500 years – Zoo House News

Old grammar puzzle solved after 2,500 years – Zoo House News

  • Science
  • December 17, 2022
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A grammatical problem that has plagued Sanskrit scholars since the 5th century B.C. was finally solved by an Indian PhD student at Cambridge University. Rishi Rajpopat made his breakthrough by deciphering a rule taught by the “Father of Linguistics” Pāṇini.

The discovery makes it possible to “derive” any Sanskrit word — to construct millions of grammatically correct words including “mantra” and “guru” — using Pāṇini’s revered “language engine,” widely regarded as one of the great intellectual achievements in the Story.

Leading Sanskrit experts have called Rajpopat’s discovery “revolutionary” and it could now mean that Pāṇini’s grammar can be taught to computers for the first time.

While researching his doctoral thesis published today, Dr. Rajpopat a 2,500-year-old algorithm that makes it possible for the first time to use Pāṇini’s “speech engine” accurately.

Pāṇini’s system – 4,000 rules described in his greatest work, the Aṣṭādhyāyī, believed to be around 500 BC. was written – is said to function like a machine. Enter the base and suffix of a word and it should convert them into grammatically correct words and sentences through a step-by-step process.

So far, however, there has been one major problem. Often two or more of Pāṇini’s rules are simultaneously applicable in the same step, leaving scholars racking their brains over which to choose.

Resolving so-called “rule conflicts” involving millions of Sanskrit words, including certain forms of “mantra” and “guru,” requires an algorithm. Pāṇini taught a meta-rule* to help us decide which rule to apply in the event of a “rules conflict,” but over the past 2,500 years scholars have misinterpreted this meta-rule, meaning that it often leads to a grammatically incorrect result came.

In an attempt to solve this problem, many scholars have painstakingly developed hundreds of other meta-rules, but Dr. Rajpopat shows that these are not only unable to solve the problem at hand – they have all produced too many exceptions – but also completely unnecessary. Rajpopat shows that Pāṇini’s “speech engine” is “self-sufficient”.

Rajpopat said: “Pāṇini had an extraordinary mind and he built a machine unparalleled in human history. He did not expect us to add new ideas to his rules. The more we play around with Pāṇini’s grammar, the more it eludes us .”

Traditionally, scholars have interpreted Pāṇini’s meta-rule to mean that in the event of a conflict between two rules of equal strength, the rule that comes later in the serial order of the grammar wins.

Rajpopat rejects this, arguing instead that Pāṇini meant that Pāṇini wanted us to choose the rule that applies to the right side of a word between rules that apply to the left and right sides respectively. Using this interpretation, Rajpopat found that Pāṇini’s language engine produced grammatically correct words almost without exception.

Take “mantra” and “guru” as examples. In the sentence “devāḥ prasannāḥ mantraiḥ” (“The gods [devāḥ] to be glad [prasannāḥ] through the mantras [mantraiḥ]’) we encounter ‘rule conflict’ when deriving mantraiḥ ‘through the mantras’. The derivation begins with “mantra + bhis”. One rule applies to the left part “mantra” and the other to the right part “bhis”. We have to select the rule applicable to the right part “bhis”, which gives us the correct form “mantraiḥ”.

And in the sentence “jñānaṁ dīyate guruṇā” (“knowledge [jñānaṁ] given is [dīyate] from the guru [guruṇā]’) we encounter a conflict of rules when deriving guruṇā ‘from the guru’. The derivation begins with ‘guru + ā’. One rule applies to the left part “guru” and the other to the right part “ā”. We have to choose the rule that applies to the right part “ā”, which gives us the correct form “guruṇā”.

eureka moment

Six months before Rajpopat made his discovery, his boss at Cambridge, Vincenzo Vergiani, a professor of Sanskrit, gave him some prescient advice: “If the solution is complicated, you’re probably wrong.”

Rajpopat said: “I had a eureka moment at Cambridge. After trying to solve this problem for 9 months I was almost ready to quit, I got nowhere. So I closed the books for a month and just enjoyed the summer, swimming, biking, cooking, praying and meditating. Then, reluctantly, I got back to work, and within minutes, as I turned the pages, these patterns began to appear and it all began to make sense. There was a lot more work to be done besides finding most of the puzzle.”

“Over the next few weeks I was so excited I couldn’t sleep and spent hours in the library, even in the middle of the night, reviewing what I found and solving related problems. This work took another two and a half years.”


Professor Vincenzo Vergiani said: “My student Rishi has cracked it – he has found an extraordinarily elegant solution to a problem that has puzzled scholars for centuries. This discovery will revolutionize the study of Sanskrit at a time when interest in the language is growing, rise up.”

Sanskrit is an ancient and classical Indo-European language from South Asia. It is the sacred language of Hinduism, but also the medium through which much of India’s greatest science, philosophy, poetry and other secular literature has been communicated for centuries. Although spoken by an estimated 25,000 people in India today, Sanskrit has had growing political importance in India and has influenced many other languages ​​and cultures around the world.

Rajpopat said: “Some of the oldest wisdoms of India were written in Sanskrit and we still don’t fully understand what our ancestors achieved. We have often been led to believe that we are not important, that we have not. I hope this discovery fills students in India with confidence and pride and hope that they too can achieve great things.”

An important implication of Dr. Rajpopat’s discovery is that now that we have the algorithm running Pāṇini’s grammar, we could potentially teach that grammar to computers.

Rajpopat said: “Computer scientists working on natural language processing abandoned rule-based approaches over 50 years ago.

“Teaching computers how to combine speaker intent with Pāṇini’s rule-based grammar to produce human speech would be an important milestone in the history of human interaction with machines, as well as in the intellectual history of India.”


RA Rajpopat, ‘In Pāṇini We Trust: Discovering the Algorithm for Rule Conflict Resolution in the Aṣṭādhyāyī’, Dissertation (University of Cambridge, 2022).DOI: 10.17863/CAM.80099


* dr Rishi Rajpopat calls Pāṇini’s meta-rule “1.4.2 vipratiṣedhe paraṁ kāryam”.

Pāṇini is believed to have lived in a region of present-day northwestern Pakistan and southeastern Afghanistan.

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