Why Pi Gets More Indian the Further Back You Calculate

Support the channel - https://ko-fi.com/withronny In most textbooks the alternating series for pi has Leibniz's name on it — Germany, the 1670s. The formula is "250 years older than Leibniz", and it wasn't written in Europe. It was etched on a palm leaf, in Sanskrit verse, by "Madhava of Sangamagrama" in the forests of Kerala, around the year 1400 — and Madhava didn't just write it down. He saw that the series was uselessly slow and fixed it: he bolted on correction terms that turn out to be the first convergents of a continued fraction for the error. Series acceleration and error-bounding, in 1400. The exact craft a numerical analyst — or a quant on a trading floor — is still wrestling with today. Two questions, one honest answer each. How did a man with no symbolic algebra, no calculus, no printing press write down a convergent infinite series for pi two and a half centuries before Newton? And — the one the internet gets very excited and very wrong about — did Europe steal it? (Short version: there is -no evidence, anyone in Europe ever saw Madhava's work. We don't say "Europe stole pi." What actually happened is quieter, and worse.) This is part one. Next time: Aryabhata and ancient Indian astronomy — the myths versus what's actually proven. ⏱️ Chapters 0:00 The Formula That Is Older Than Its Name 1:55 A Forest in Kerala, 1400 3:36 The Receipts 7:55 Why Pi Breaks People 12:34 Taming the Infinite 16:52 How Close They Got, and the Honest Limit 20:06 How the Door Closed 24:33 The Error, in a Suit 27:38 What We Un-Remembered 📚 Sources & further reading • Charles M. Whish, "On the Hindu Quadrature of the Circle," *Transactions of the Royal Asiatic Society* (1834) • Nilakantha Somayaji, Tantrasangraha (1501); Jyesthadeva, Yuktibhasa (c. 1530, in Malayalam); Shankara Variyar, Yuktidipika (arctangent series, ch. 2, vv. 206–209) • Victor J. Katz, "Ideas of Calculus in Islam and India," Mathematics Magazine (1995) • K. V. Sarma, critical editions of the Kerala texts (1977 onward) • Kim Plofker, Mathematics in India (Princeton, 2009) • A. Estrella, "Series Approximations and Risk Management Pitfalls," Federal Reserve Bank of New York (1995) • M. R. Krishnachandran et al., analysis of Madhava's correction terms (2024) ☕ If these videos are worth a few quid, the tip jar is on Ko-fi — https://ko-fi.com/withronny. No paywalls, no memberships; it just helps me keep making them. 💬 Check my citations and argue with me in the comments. I'm Ronny. Mind the remainder. #pi #Madhava #KeralaSchool #historyofmathematics #IndianMathematics