THE COMPASS CHRONICLES Infinity versus Ramchundra

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

ary a beacon of light illuminates rohit gupta the history of Indian science under British colonial rule. A dark gulf stretches for the 150 years between MaharajaN Sawai Jaisingh and Sir JC Bose. How- ever, ‘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 mathe- matician — now almost completely forgotten. In the mid-1800s, many illustrious Victor- ians bridged the empire from Rangoon to Lon- don — including the surveyor George Everest after he had mapped . His niece was later married to the logician , and Boole’s friend was none other than the father of computing — . But most important in this episode was another great intellect of this time — , who was born in Madurai (1806) to a colonel in the . 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 ap- pearance seemed to spring out of Charles Dickens’ Pickwick Papers…” In addition, De Morgan belonged to that minute set of Victor- ians who were aware of India’s mathematical legacy, when Master Ramchundra entered the stage. As a populariser of science, Ramchun- dra had taken upon himself the task of trans- lating and writing works on geography, ensuper/shutterstock agriculture and astronomy, including the works of Sir Isaac Newton, in Urdu (“the clos- the ancient tradition of Hindu algebra, as into Urdu, Ramchundra wrote about “a de- est thing to a national language”). started by the likes of Aryabhata, Brahmagup- scription of the diving bell, by which sunken More than a century had passed after New- ta and Bhaskara. materials may be retrieved from the sea,” ton’s death, and calculus had become the He compared the two different mathemati- “mistakes that Hindu learned men have made most powerful weapon in the hands of sci- cal cultures, saying, “The greatness of Hindoo in various sciences of the shastras”. He wrote ence. Because calculus was the mathematics invention is in algebra; the greatness of Greek on Demosthenes, Confucius, Safavid Shah Ab- of change, and everything in the Universe was invention is in geometry.” The problem which bas, Egypt, Kabul, the travels of Yusuf Khan Ka- constantly changing, either through Time or Ramchundra proposed to himself, De Morgan malposh to England, and Urdu poetry by the Space. As with any other invention, even as it suggested, others may have likes of Bahadur Shah Zafar, solved many problems easily in physics and thought — “hardly within the Mir Dard, and Shah Nasir. The astronomy — calculus created an entirely new possibilities of pure algebra” influence of Ramchundra’s breed of problems for mathematicians. Since or even “unattainable by any straightforward style has been it employed infinite series and phantom-like amount of thought”. In sum- traced by scholars to the prose infinitesimal quantities, it gave rise to numer- mation, he went on to declare of Ghalib’s letters, and the re- ous paradoxes, singularities and absurdities. that Ramchundra’s “victory formist writing of Sir Sayyid Logicians like De Morgan knew that it would over the theory of difficulty is Ahmad Khan. take decades more to put calculus on a rigor- complete.” However, the ideological ous foundation. More specifically, Ramchun- goal of Ramchundra’s mathe- It was at this time, around 1850, that the 28- dra’s book (A Treatise of Prob- matical output could not only year-old Ramchundra went to Calcutta and lems on Maxima And Minima, have been nationalistic or ped- self-published a strange textbook with solu- Solved by Algebra) was about agogical, for his book begins tions to hundreds of well-known calculus the lowest and highest values with a quotation by John Play- problems. In this extraordinary tract, howev- of changing quantities. He con- fair from the Encyclopaedia Bri- er, he solved the problems using geometry firmed mathematically in tannica (1824): “the problems and algebra alone, completely eschewing the Problem 52, for example, that which relate to the maxima use of calculus. bees have learned to use the minimum and minima... they are connected with the In Calcutta, the lawyer JE Drinkwater-Be- amount of wax in constructing their hexago- highest attainments of wisdom and the great- thune obtained several copies and sent one to nal-prismatic cells of the hive. Or, the height at est exertions of power; and seem like so many De Morgan, who himself published a Europe- which a hole in the side of a water vessel will immoveable columns erected in the infinity an edition of the book in 1859. While Ram- make the water spout to the maximum dis- of space, to mark the eternal boundary, which chundra’s career has been studied at length tance. The array of these problems demon- separates the regions of possibility and im- by contemporary historians S Irfan Habib and strate the rich spectrum of his own possibility from one another”. Dhruv Raina, De Morgan’s own preface to the intellectual pursuits. book recognised that bypassing calculus was During his diverse career as a popular sci- rohit gupta explores the history of science as Ramchundra’s attempt to revive and continue ence writer, and translator of scientific books Compasswallah t@fadesingh