Ramanujan’s Pi Formulas and Their Surprising Role in Black Hole Physics

Ramanujan’s Series: A Century-Old Tool for Computing Pi

In 1914, Srinivasa Ramanujan published 17 remarkably efficient formulas for computing π — ultra-compact series where each additional term yields dozens of correct digits at once. A century later, these very ideas became the foundation of the Chudnovsky algorithm, which has been used to calculate π to hundreds of trillions of decimal places.

From Pure Mathematics to High-Energy Physics

Now comes the unexpected part: a team at CHEP IISc (Aninda Sinha, Faizan Bhat, and colleagues) has shown that the same mathematics resurfaces in modern high-energy physics. When the world is viewed through the lens of conformal field theories — models in which the picture remains unchanged under rescaling — and especially their logarithmic variants, the same building blocks that Ramanujan used appear in problems involving percolation, the onset of turbulence, and the description of black holes: hypergeometric series, modular forms, and q-series.

How Ramanujan Series Physics Works in Practice

Put simply: formulas originally designed for blazingly fast computation of π turn out to be the same language in which key quantities in complex physical systems can be expressed efficiently and elegantly. Where heavy numerical calculations were once required, Ramanujan’s series now offer a shortcut.

The Geometry of Nature, Hidden in Numbers

Working entirely within pure mathematics, Ramanujan had a remarkable intuition for the architecture of natural law. His series are not merely about the digits of π — they are about the shape of the world itself, a shape that repeats from numerical identities all the way to the physics of black holes.