Ancient grammatical puzzle solved by University of Cambridge PhD student after 2,500 years

It has baffled scholars since the 5th century BC, but now a University of Cambridge PhD student has cracked an ancient grammatical puzzle that could “revolutionise the study of Sanskrit”

Rishi Rajpopat, an Indian student at St John’s College, made the breakthrough by decoding a rule taught by ‘the father of linguistics’, Pāṇini. The discovery makes it possible to ‘derive’ any Sanskrit word – enabling the construction of millions of grammatically correct words including ‘mantra’ and ‘guru’ – using Pāṇini’s revered ‘language machine’, which is considered one of the great intellectual achievements in history.

Sanskrit experts say Rajpopat’s discovery is “revolutionary” and could enable Pāṇini’s grammar to be taught to computers for the first time.

It was while researching his PhD - which was published on Thursday (December 15) - that Dr Rajpopat decoded a 2,500-year-old algorithm making it possible to use the ‘language machine’.

Pāṇini’s system – containing 4,000 rules detailed in his greatest work, the Aṣṭādhyāyī, is thought to have been written around 500BC. It is intended to work like a machine in which you feed in the base and suffix of a word so that it turns them into grammatically correct words and sentences through a step-by-step process.

Until the breakthrough, however, scholars have run into problems with it.

Typically, two or more of Pāṇini’s rules are simultaneously applicable at the same step, which has left them scratching their head over which one to choose.

Dr Rajpopat said: “Pāṇini had an extraordinary mind and he built a machine unrivalled in human history. He didn’t expect us to add new ideas to his rules. The more we fiddle with Pāṇini's grammar, the more it eludes us.”

Scholars have until now interpreted Pāṇini’s metarule as meaning that in the event of a conflict between two rules of equal strength, the rule that comes later in the grammar’s serial order wins.

But Dr Rajpopat rejected this, arguing instead that Pāṇini meant that between rules applicable to the left and right sides of a word respectively, Pāṇini wanted us to choose the rule applicable to the right side.

Using this interpretation, Dr Rajpopat found Pāṇini’s language machine produced grammatically correct words with almost no exceptions.

Six months before he made his discovery, his supervisor at Cambridge, Prof Vincenzo Vergiani, professor of Sanskrit, told him: “If the solution is complicated, you are probably wrong.”

Dr Rajpopat said: “I had a eureka moment in Cambridge. After nine months trying to crack this problem, I was almost ready to quit, I was getting nowhere. So I closed the books for a month and just enjoyed the summer, swimming, cycling, cooking, praying and meditating.

“Then, begrudgingly I went back to work and, within minutes, as I turned the pages, these patterns starting emerging, and it all started to make sense. There was a lot more work to do but I’d found the biggest part of the puzzle.

“Over the next few weeks I was so excited, I couldn’t sleep and would spend hours in the library including in the middle of the night to check what I’d found and solve related problems. That work took another two-and-a-half years.”

Prof Vergiani said: “My student Rishi has cracked it. He has found an extraordinarily elegant solution to a problem which has perplexed scholars for centuries. This discovery will revolutionise the study of Sanskrit at a time when interest in the language is on the rise.”