Ramanujan Sent 120 Theorems With No Proofs to a Stranger in 1913... They Changed Mathematics

🔴 Support the channel and get exclusive content:   / meridianlabs   What if the equations that describe the inside of a black hole were written down a century before anyone knew black holes existed, by a dying man who said a goddess placed them on his tongue while he slept? In this deep dive documentary we follow the most unsettling question in the history of mathematics. Where did Srinivasa Ramanujan's mathematics actually come from? A self taught clerk from south India, with no formal training and no proofs, produced results so far ahead of their time that we are still catching up to him more than a hundred years after his death. We have spent a century proving he was right. We have spent none of it explaining how he knew. We begin in 1913, when Ramanujan mailed roughly 120 theorems with no proofs to the Cambridge mathematician G. H. Hardy, after two other professors returned the same work without a single word. We trace his impossible rise and his slow destruction. The voyage to England, the isolation and the illness, the suicide attempt, the election to the Royal Society as one of the youngest Fellows in its history, and the famous taxicab number 1729. Then we reach the strange part. The 17 mock theta functions he scrawled in his final letter in January 1920, three months before he died at 32, sat unexplained for more than 80 years, until Sander Zwegers cracked them in 2002. Ten years later, in 2012, Atish Dabholkar, Sameer Murthy and Don Zagier showed that those same functions describe the quantum states hidden inside black holes. We follow the lost notebook that was nearly burned before George Andrews found it in 1976, the tau function that Pierre Deligne could only resolve in 1974 by way of one of the deepest results in modern mathematics, and the series for pi from 1914 that still run inside every record breaking computation of pi today. Moving deeper, we confront the question underneath all of it. Did Ramanujan invent this mathematics, or did he discover something that was already there, waiting, indifferent, complete before any mind existed to find it? We examine the position held quietly by serious mathematicians, including Hardy himself, that mathematical reality lies outside us and is found rather than made. And we sit with what that would mean. That a dying man in Madras had a door into the structure of reality that the rest of us do not have, that he could not describe, and that died with him. This is not a tribute to a genius. It is an open question about where the laws underneath the universe come from, and it has never been answered. Every claim in this documentary is grounded in verified history, real results, and the words of the mathematicians and physicists who did the work. The math has been checked. The notebooks are still being read. And he may have been telling the truth about where it came from. Sources referenced in this video: G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940) Robert Kanigel, The Man Who Knew Infinity (1991) Bruce C. Berndt, Ramanujan's Notebooks, Parts 1 to 5 (Springer, 1985 to 1998) George E. Andrews and Bruce C. Berndt, Ramanujan's Lost Notebook, Parts 1 to 5 (Springer, 2005 to 2018) S. Zwegers, Mock Theta Functions, PhD thesis, Universiteit Utrecht (2002) A. Dabholkar, S. Murthy and D. Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv 1208.4074 (2012) P. Deligne, La Conjecture de Weil I, Publications Mathematiques de l'IHES 43 (1974) G. H. Hardy and S. Ramanujan, Asymptotic Formulae in Combinatory Analysis, Proceedings of the London Mathematical Society (1918) S. Ramanujan, Modular Equations and Approximations to Pi, Quarterly Journal of Mathematics 45 (1914) D. A. B. Young, Ramanujan's Illness, Notes and Records of the Royal Society of London 48 (1994) G. H. Hardy, A Mathematician's Apology (1940) #Ramanujan #SrinivasaRamanujan #Mathematics #MockThetaFunctions #BlackHoles #ModularForms #GHHardy #NumberTheory #LostNotebook #StringTheory #BlackHoleEntropy #Pi #Infinity #MathHistory #DonZagier #DiscoveredOrInvented #MathematicalUniverse #ScienceDocumentary #Documentary #TheManWhoKnewInfinity