Infinity versus Ramchundra

Rohit Gupta | Updated on January 24, 2018 Published on February 27, 2015




How an Indian mathematician solved hundreds of well-known calculus problems — using geometry and algebra alone — and was forgotten

Nary a beacon of light illuminates the history of Indian science under British colonial rule. A dark gulf stretches for the 150 years between Maharaja Sawai Jaisingh and Sir JC Bose. However, ‘the absence of evidence is not evidence of absence,’ so we continue to search the attic for silhouettes. One such shadowy figure is Master Ramchundra — a teacher of science in Delhi, Urdu litterateur, translator and mathematician — now almost completely forgotten.

In the mid-1800s, many illustrious Victorians bridged the empire from Rangoon to London — including the surveyor George Everest after he had mapped India. His niece was later married to the logician George Boole, and Boole’s friend was none other than the father of computing — Charles Babbage. But most important in this episode was another great intellect of this time — Augustus De Morgan, who was born in Madurai (1806) to a colonel in the East India Company.

The historian Thony Christie writes, “De Morgan was a brilliantly eclectic polymath with a Pythonesque sense of humour who both from his personality and from his appearance seemed to spring out of Charles Dickens’ Pickwick Papers…” In addition, De Morgan belonged to that minute set of Victorians who were aware of India’s mathematical legacy, when Master Ramchundra entered the stage. As a populariser of science, Ramchundra had taken upon himself the task of translating and writing works on geography, agriculture and astronomy, including the works of Sir Isaac Newton, in Urdu (“the closest thing to a national language”).

More than a century had passed after Newton’s death, and calculus had become the most powerful weapon in the hands of science. Because calculus was the mathematics of change, and everything in the Universe was constantly changing, either through Time or Space. As with any other invention, even as it solved many problems easily in physics and astronomy — calculus created an entirely new breed of problems for mathematicians. Since it employed infinite series and phantom-like infinitesimal quantities, it gave rise to numerous paradoxes, singularities and absurdities. Logicians like De Morgan knew that it would take decades more to put calculus on a rigorous foundation.

It was at this time, around 1850, that the 28-year-old Ramchundra went to Calcutta and self-published a strange textbook with solutions to hundreds of well-known calculus problems. In this extraordinary tract, however, he solved the problems using geometry and algebra alone, completely eschewing the use of calculus.

In Calcutta, the lawyer JE Drinkwater-Bethune obtained several copies and sent one to De Morgan, who himself published a European edition of the book in 1859. While Ramchundra’s career has been studied at length by contemporary historians S Irfan Habib and Dhruv Raina, De Morgan’s own preface to the book recognised that bypassing calculus was Ramchundra’s attempt to revive and continue the ancient tradition of Hindu algebra, as started by the likes of Aryabhata, Brahmagupta and Bhaskara.

He compared the two different mathematical cultures, saying, “The greatness of Hindoo invention is in algebra; the greatness of Greek invention is in geometry.” The problem which Ramchundra proposed to himself, De Morgan suggested, others may have thought — “hardly within the possibilities of pure algebra” or even “unattainable by any amount of thought”. In summation, he went on to declare that Ramchundra’s “victory over the theory of difficulty is complete.”

More specifically, Ramchundra’s book ( A Treatise of Problems on Maxima And Minima, Solved by Algebra) was about the lowest and highest values of changing quantities. He confirmed mathematically in Problem 52, for example, that bees have learned to use the minimum amount of wax in constructing their hexagonal-prismatic cells of the hive. Or, the height at which a hole in the side of a water vessel will make the water spout to the maximum distance. The array of these problems demonstrate the rich spectrum of his own intellectual pursuits.

During his diverse career as a popular science writer, and translator of scientific books into Urdu, Ramchundra wrote about “a description of the diving bell, by which sunken materials may be retrieved from the sea,” “mistakes that Hindu learned men have made in various sciences of the shastras”. He wrote on Demosthenes, Confucius, Safavid Shah Abbas, Egypt, Kabul, the travels of Yusuf Khan Kamalposh to England, and Urdu poetry by the likes of Bahadur Shah Zafar, Mir Dard, and Shah Nasir. The influence of Ramchundra’s straightforward style has been traced by scholars to the prose of Ghalib’s letters, and the reformist writing of Sir Sayyid Ahmad Khan.

However, the ideological goal of Ramchundra’s mathematical output could not only have been nationalistic or pedagogical, for his book begins with a quotation by John Playfair from the Encyclopaedia Britannica (1824): “the problems which relate to the maxima and minima... they are connected with the highest attainments of wisdom and the greatest exertions of power; and seem like so many immoveable columns erected in the infinity of space, to mark the eternal boundary, which separates the regions of possibility and impossibility from one another”.

(Rohit Gupta explores the history of science as Compasswallah)


Published on February 27, 2015

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