Indian scholar at Cambridge claims to solve a 2,500-yr-old Panini Sutra puzzle
December 5, 2025
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Indian scholar at Cambridge claims to solve a 2,500-yr-old Panini Sutra puzzle

A PhD scholar, Rishi Atul Rajpopat at the faculty of Asian and Middle Eastern Studies at St. John’s College, Cambridge, has cracked a grammatical problem posed by the texts authored by ancient Sanskrit scholar Paṇini.

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Indian scholar at Cambridge solves 2,500-yr-old Sanskrit algorithm problem in Panini’s text
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A PhD scholar, Rishi Atul Rajpopat at the faculty of Asian and Middle Eastern Studies at St. John’s College, Cambridge, has cracked a grammatical problem posed by the texts authored by ancient Sanskrit scholar Paṇini.

Paṇini’s text Aṣṭādhyāyī, which includes a set of rules to derive or form new words from root words, often has conflicting rules for creating new words, with many scholars confused about which rules to use.

Cracking such conflicts in this linguistic algorithm of a book was the subject of many scholars’ interests. Paṇini himself wrote a meta-rule to fix rule conflicts, which so far scholars have interpreted as: In the event of a conflict between two rules of equal strength, the rule that comes later in the grammar’s serial order wins.

In his dissertation, Rajpopat claims that this metarule was historically mistaken— instead, what Paṇini meant was that between rules applicable to the left and right sides of a word, he wanted the reader to choose the rule applicable to the right side.

With this logic, Rajpopat finds that Paṇini’s algorithms produce grammatically correct words and sentences without errors.

For example, in the sentence jñānaṁ dīyate guruṇā — knowledge (jñānaṁ) is given (dīyate) by the guru (guruṇā) — there is a rule conflict when trying to form the word guruṇā, which means ‘by the guru’ and is a known word.

The word comprises the roots, guru + ā. Following Paṇini’s rules to create the word that will mean “by the guru”, two rules become applicable — one to the word guru, and one to ā. This is decided by choosing the rule that is applicable to the word on the right, resulting in the correct new form guruṇā.

Rajpopat’s work is a refusal to scholars over the course of two and a half millennia.

Scholars who attempted to resolve Paṇini’s rule conflicts include Jayaditya and Vamana in their writing treatise Kāśikāvṛttī, Patanjali in his Mahābhāṣya, and Katyayana in his Vārttikakāra.

“After Pāṇini wrote his text, Kātyāyana expounded upon it, followed by Patanjali,” Rajpopat told ThePrint. “Several months after I started working on my thesis, I discovered that Kātyāyana had also deduced the same logic in a remote corner of his work. However, he too seemed to have decided to use alternate interpretations for rule conflict as well. Since in the Sanskrit tradition, scholars build up on the previous expert’s work more than the canonical text, this interpretation of the rule seems to have fallen through the cracks.”

Topics: patanjaliRishi Atul RajpopatPaṇini’s text AṣṭādhyāyīSt. John’s CollegeKāśikāvṛttīSanskrit algorithmCambridge
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