Anish Tripathi

This is the story of a french astronomer, stranded after missing the Venus transit, watches a Tamil Brahmin compute the December 1768 lunar eclipse in < 45 mins with cowries and palm-leaf booklets, matching the Paris ephemerides. In 1768, a man named Nana Moutou walked into a French astronomer's house in Pondicherry and offered to compute an eclipse in front of him. The astronomer was Guillaume Le Gentil of the Royal Academy of Sciences, Paris. He had come to India for the 1761 transit of Venus and was stuck at sea on the day. He waited 8 years for the next one. On 3 June 1769, a single cloud covered the Sun at the exact moment. Nearly 10,000 leagues, he wrote, just to be "spectator of a fatal cloud". Hidden inside the same book is a story nobody tells... Le Gentil had been in Pondicherry barely 8 days when Nana Moutou came with an interpreter. Le Gentil asked for the total lunar eclipse of December 1768. Next morning the man returned with a packet of palm leaves and a bag of cowrie shells. He sat on the floor, moved the shells with a singular speed, kept consulting his little booklet, and gave all the phases of the eclipse in less than three quarters of an hour. Le Gentil checked the numbers against the French Ephemerides. They matched. He gave him more eclipses. Same result. No pen. No paper. The shells were the counters, laid out on the ground. The rules were verses recited from memory while working, the way Europeans use formulas. Once a step was done it was wiped away. And they rarely made mistakes, he writes. Nana Moutou agreed to teach him, under strict secrecy. 4 months of hard work, he said, if the Frenchman had the aptitude. Lessons at 4.30 every evening. Le Gentil changed interpreters 3x and got nowhere. In the end it took him more than a month, an hour a day, to compute a lunar eclipse. His verdict: for lunar eclipses, the error in several he calculated never went > 25 minutes. Sources: Le Gentil, Voyage dans les mers de l'Inde, Tome 1 (1779), pp. 40, 210-211 Photos: pages 210, 211 and 40 of the same 1779 edition, Imprimerie royale, scan via Internet Archive (Getty Research Institute copy), key lines highlighted

This is a fantastic story about an East India Company mathematician claiming the Hindus understood the Binomial theorem in whole numbers. Unfortunately, we hardly were taught all of this... Year was 1790 and the city was Calcutta. Reuben Burrow, a Company surveyor, dropped a Sanskrit puzzle into Asiatic Researches. The puzzle goes like this: A raja's palace has 8 doors. Open them one at a time, two at a time, three, on up to all eight together. How many ways are possible? The Sanskrit rule goes 8, 28, 56, 70, 56, 28, 8, 1. Add it up, and we get 255. Look closely and you find those are binomial coefficients. Europe called the same pattern Pascal's triangle. Burrow was a tenant farmer's son from Leeds. Walked four days to London at 18, taught himself Sanskrit once he got to India. He worked the rule through and wrote that the Hindoos (his words) understood it in whole numbers "to the full as well as Briggs, and much better than Pascal". The paper never named the book but the puzzle matches Bhaskara's Lilavati, written around 1150 CE. Source: Asiatic Researches vol 2, Calcutta 1790, pp 487-497. Photo 1: p 494, the "much better than Pascal" line.. Photo 2: p 495, the palace puzzle and the rule setup Photo 2: p 496, the total 255 and Burrow's proof. All are 1790 print, public domain.