Ramanujan's century-old math turns up in a Bangalore physics paper
On 22 December 2025 a paper from researchers at the Indian Institute of Science (IISc) in Bangalore appeared in Physical Review Letters with a simple, striking claim: some of the exotic formulae Srinivasa Ramanujan wrote down in 1914 are not merely human inventions for calculating digits of pi — they show up naturally inside physical theories. The authors, led by Aninda Sinha with former student Faizan Bhat, argue that those classical identities are mirrored by the mathematics that describes scale‑invariant systems. In short, the same structures that let mathematicians compute pi to trillions of digits also govern phenomena as different as fluid turbulence, percolation and aspects of black‑hole physics.
Ramanujan's formulas meet physics
Ramanujan is famous for producing hundreds of deep and often mysterious formulae—many discovered without proofs—that connect modular forms, hypergeometric series and other parts of number theory. Later mathematicians repackaged several of his identities into algorithms that are extraordinarily efficient for computing pi. What Sinha and Bhat set out to do was not to re‑compute pi, but to ask why those algebraic identities appear so repeatedly across unrelated branches of mathematics and computation.
Their answer, presented in Physical Review Letters, is that those Ramanujan structures are natural outputs of a class of physical theories called logarithmic conformal field theories (logarithmic CFTs). These are mathematical frameworks physicists use to describe systems that look the same at different length scales — a property known as scale invariance. The surprising upshot is that a bridge exists from century‑old pure mathematics to concrete models of physical behaviour.
Logarithmic conformal field theory and scale symmetry
Conformal field theory (CFT) is the language physicists use to describe critical points — the special parameter values where a system undergoes a phase transition and shows scale invariance. Classic CFTs have powered progress in particle physics, condensed matter and statistical mechanics. Logarithmic CFTs are a more exotic cousin: correlation functions in these theories feature logarithms and a different sort of operator algebra, reflecting extra degeneracies and subtle long‑range behaviours that standard CFTs do not capture.
Why does that matter for pi? The point is not that a logarithmically behaving field theory spits out the digits of pi, but that the special functions and series Ramanujan wrote down are natural solutions or invariants inside these theories. When a physical system sits at a critical point with scale symmetry — for example, the threshold where a porous material suddenly conducts through percolation or the statistical limits of a turbulent cascade — the mathematical objects you use to describe it can be the very same q‑series or modular constructs Ramanujan studied.
Put another way: scale symmetry organizes physical correlations into patterns that mathematics already knew how to describe, decades before physicists framed those particular systems.
Where pi shows up: turbulence, percolation and black holes
The IISc paper highlights three domains where the Ramanujan structures appear especially naturally. The first is turbulence — the chaotic, multiscale motion of fluids — where scale invariance in certain statistical regimes leads to analytic behaviour that echoes Ramanujan's identities. The second is percolation, the probabilistic model for connectivity in random media: at the critical threshold, the geometry of connected clusters is fractal and described by conformal invariance, and logarithmic CFTs are one of the correct effective languages to capture its correlations.
From Ramanujan to Chudnovsky: the computing link
People often equate pi with the familiar classroom number 3.14, but mathematically pi is an irrational constant with infinitely many nonrepeating digits. Practical computation of pi to high precision relies on clever series and algorithms. Several of the fastest methods trace their conceptual roots to identities Ramanujan discovered; later refinements, such as the Chudnovsky algorithm, package those ideas into extremely efficient routines that have been used to push pi computations into the hundreds of trillions of digits.
Aninda Sinha pointed out that the widespread use of Ramanujan‑style identities in algorithms is why the connection to physical theories matters: those algebraic patterns are not only computationally powerful, they are also natural outcomes of the same symmetry principles that govern certain physical systems. In other words, the mathematics that helps us crunch digits of pi is not a contrived trick — it reflects patterns that nature uses in its own calculations.
What this does — and doesn't — mean
It is important to be precise about what the IISc study does not claim. The research does not change the numerical value of pi. It does not make pi equal to 3.14 — that decimal is merely a low‑precision truncation familiar from school. What the work does is offer a conceptual explanation for why a particular family of formulae that produce pi also appear as natural objects in several physically meaningful theories.
The result is best understood as a unifying insight: mathematics and physics often mirror each other, and identities discovered in one realm frequently reappear in another. Showing that Ramanujan's 1914 formulae arise inside logarithmic CFTs is a striking example of that cross‑disciplinary resonance. For mathematicians, it adds intuition about why certain q‑series and modular objects are so robust; for physicists it supplies new analytic tools to handle problems in turbulence, percolation and simplified black‑hole models.
Next steps: theory, numerics and experiments
The immediate next steps are predominantly theoretical and computational. Logarithmic conformal field theories are technically demanding; the IISc paper opens a roadmap for using Ramanujan‑type identities as analytical handles inside those models. That can make some calculations cleaner and suggest new numerical checks.
On the experimental side, the implications are more indirect. Turbulence and percolation are real, measurable phenomena, so the ideas could ultimately guide new analyses of laboratory flows or materials near criticality. Black holes, by contrast, are observed astronomically through indirect signatures; translating the mathematical echoes into observable diagnostics will be a longer, more speculative project.
Whatever the timescale, the paper is a reminder that the frontier between pure mathematics and theoretical physics remains porous. A century after Ramanujan recorded his formulae on paper, contemporary physics has found those same shapes in the equations that describe how nature organizes itself at criticality.
