⚛️ Formulas from a past Genius resurface in black hole physics

Mathematical formulas written over a hundred years ago could find an echo in the most current theories about black holes and turbulence. This observation links the work of the Indian Srinivasa Ramanujan to cutting-edge research in fundamental physics.

Scientists have just discovered that these historical equations, designed to calculate the number pi, emerge naturally in models describing critical phenomena and the properties of black holes, revealing an unexpected unity between seemingly distant fields.


These researchers from the Indian Institute of Science have shown that Ramanujan's formulas, published in 1914, are not mere archival curiosities. In fact, they reappear with surprising relevance in contemporary physical theories. Originally designed to calculate pi with remarkable efficiency for the time using few terms, they still inspire the algorithms of supercomputers that push pi's decimals to trillions of digits. Their mathematical structure proves to be much deeper than a simple calculation method.

The team questioned the reason for the existence of such elegant formulas. This investigation led them to a class of physical theories called conformal theories. These models describe systems that possess scale symmetry, meaning they keep the same appearance regardless of how they are observed.

Logarithmic conformal theories, a subfamily of these models, are particularly useful for studying turbulence, percolation, or certain aspects of black holes. It is precisely within the mathematical framework of these theories that Ramanujan's formulas reappear. The structure that serves as the starting point for his pi calculations is found in the equations describing these high-level physical phenomena.


Furthermore, this discovery not only allows for a better understanding of why these formulas exist, but it also offers practical tools. By using this link, physicists can calculate certain quantities in their theories more efficiently, which could accelerate the understanding of turbulence or material behavior. As one of the authors explains, behind every beautiful mathematical construction, a physical system is often hidden in reflection, even if the mathematician was not aware of it.

Ramanujan's work, developed in relative isolation at the beginning of the 20th century, thus anticipates structures that have become central to describing the Universe. The researchers highlight how this genius, without contact with the modern physics of his time, sensed concepts that help us today model objects as extreme as black holes. This story shows the deep interconnection between pure mathematics and the description of the physical world, where old ideas can suddenly illuminate current problems.

The publication of this work in Physical Review Letters opens new avenues for calculations in theoretical physics. It also illustrates how fundamental research, whether mathematical or physical, can reveal unexpected connections across time. The intrinsic beauty of Ramanujan's equations thus finds resonance in how we attempt to describe the fundamental laws of nature, from turbulent flows to the farthest reaches of spacetime.