A Hundred Year Old Formula for Pi Is Quietly Sneaking Into Modern Physics

How Srinivasa Ramanujan’s strange math keeps resurfacing in black holes, turbulence, and the deep structure of reality

The Odd Persistence of an Old Equation

Every so often, science stumbles into a moment that feels almost unsettling. Something long forgotten or maybe never fully understood in the first place suddenly shows up again, right where you least expect it. Not as a historical curiosity, not as a footnote, but as a working tool. Alive. Useful.

That’s what’s happening right now with a century old mathematical formula for π.

Not a new equation. Not a flashy breakthrough powered by supercomputers or AI models. Just an old, elegant infinite series written down by a man working largely alone, with little formal training, in early 20th century India.

And yet here it is again. Turning up in black holes. In fluid turbulence. In the strange mathematics of systems that look the same no matter how closely or how distantly you examine them.

If that sounds improbable, it is. But improbability was sort of Srinivasa Ramanujan’s specialty.

Ramanujan, the Outsider Who Wouldn’t Stay Quiet

Ramanujan isn’t exactly obscure. Mathematicians know his name the way musicians know Bach or Coltrane. Still, outside of academic circles, he tends to hover in that vague category of “brilliant but tragic,” which somehow makes his work feel finished. Settled.

That impression couldn’t be more wrong.

Born in 1887, Ramanujan had almost no formal training in pure mathematics. He worked from outdated textbooks, filled notebooks with results he couldn’t always rigorously prove, and relied heavily on intuition sometimes bordering on mysticism. He famously believed that equations had no meaning unless they expressed a thought of God.

Whether you take that literally or metaphorically, it’s hard to ignore how often his equations seem to know more than he did.

He died in 1920 at the age of 32. Tuberculosis. Malnutrition. The usual, cruel combination of poverty and illness. By the time he passed away, he had already produced thousands of original results, including 17 infinite series for calculating π some of the fastest converging ever discovered.

At the time, they were admired. Then archived.

Now they’re back.

Pi: Familiar, Boring, and Apparently Not Done With Us

π is one of those numbers people think they understand. A ratio. A circle thing. Something you memorized in school, maybe to a few digits, before promptly forgetting why it mattered.

Mathematicians, of course, never stopped caring. π isn’t just a number it’s a kind of structural constant. It shows up everywhere once you start looking: waves, probability distributions, quantum mechanics.

Ramanujan’s contribution wasn’t redefining π itself, but discovering astonishingly efficient ways to compute it. His infinite series converge so fast that they remain the backbone of modern algorithms for calculating π to absurd levels of precision hundreds of trillions of digits.

That alone would be enough to secure his legacy.

But here’s where things get strange.

A New Paper, an Old Question

A recent paper published in Physical Review Letters asked a deceptively simple question: What if Ramanujan’s formulas weren’t just mathematical tricks? What if they naturally emerge from real physical systems?

Not as metaphors. Not as analogies.

As actual, structural descriptions of how parts of the universe behave.

The researchers Aninda Sinha and Faizan Bhat from the Indian Institute of Science weren’t trying to romanticize Ramanujan. They were doing something much more grounded. They wanted to see whether the starting assumptions of his π formulas appeared organically inside modern physics.

In other words: if you didn’t know about Ramanujan at all, and you studied certain physical systems deeply enough, would you eventually rediscover his mathematics anyway?

That’s a dangerous question. And a fascinating one.

Enter Logarithmic Conformal Field Theories (LCFTs)

To understand where this leads, you have to take a short detour into a branch of physics that’s not exactly dinner table conversation.

Logarithmic conformal field theories LCFTs are mathematical frameworks used to describe systems with scale invariance. That phrase sounds abstract, but the idea is surprisingly visual.

A scale invariant system looks the same no matter how much you zoom in or out.

Think of a coastline. From a satellite image, it looks jagged. From a drone, still jagged. From the ground, still jagged. The details change, but the pattern doesn’t.

In physics, similar behavior shows up at critical points moments where a system is about to change phase. Water at the exact point where liquid and vapor become indistinguishable is a classic example. There’s no characteristic size. No preferred scale.

LCFTs exist to describe systems like that.

And tucked inside certain versions of these theories, the researchers found something familiar.

Ramanujan’s mathematics.

Not a Coincidence But Not Magic Either

This is where it’s tempting to slip into poetic exaggeration. To say Ramanujan somehow “predicted” black holes or turbulence without knowing it. That’s a nice story. It’s also not quite accurate.

What’s actually happening is more subtle and more interesting.

Ramanujan was exploring mathematical structures that were internally consistent, deeply symmetrical, and, frankly, weird. Physics, it turns out, often runs on the same kinds of structures. When reality organizes itself at extreme edges near singularities, critical points, or chaotic flows it tends to reuse the same mathematical language.

The overlap isn’t mystical. It’s structural.

Still, the result is unsettling: equations written down with no physical motivation whatsoever are now describing percolation, turbulence, and even black hole geometries.

Percolation: Coffee, Filters, and Physics

Percolation sounds technical, but you’ve experienced it every morning if you drink coffee.

Water passes through coffee grounds. Some paths connect. Others don’t. At a certain threshold, the liquid suddenly finds a continuous route through the material.

Physicists study percolation to understand how fluids move through porous substances soil, rock, filters, even networks. At the critical point where a connected path forms, the system becomes scale invariant.

And guess what shows up in the math describing that transition?

Structures closely related to Ramanujan’s infinite series.

Not directly calculating π, but echoing the same logic. The same relationships.

It’s as if the universe occasionally borrows his handwriting.

Turbulence: The Problem No One Ever Really Solved

Turbulence is notorious. Richard Feynman once joked that it was the most important unsolved problem in classical physics. Fluids moving smoothly are easy. Fluids breaking into chaotic vortices? A nightmare.

Yet turbulence also exhibits scale invariance. Large swirls break into smaller swirls, which break into smaller ones still, repeating the pattern across scales.

Certain LCFTs describe this behavior surprisingly well.

And again, Ramanujan’s mathematics appears not as an add on, but as part of the underlying framework.

This doesn’t mean his equations “solve” turbulence. They don’t. But they sit uncomfortably close to the heart of the problem, which is more than anyone expected.

Black Holes: The Most Extreme Test Case

Then there are black holes.

Specifically, the researchers found connections between Ramanujan’s formulas and a generalized Schwarzschild black brane background a particular solution to Einstein’s field equations.

If that sentence feels dense, that’s because it is.

The short version: when physicists model certain black hole like objects in higher dimensional space, the mathematics describing their behavior aligns with LCFTs. And inside those theories, once again, are echoes of Ramanujan.

He wasn’t thinking about spacetime curvature. He wasn’t imagining event horizons.

But the math doesn’t care what you intended.

A Quiet Pattern Across Time

There’s a recurring theme here that physicists are hesitant to romanticize but can’t ignore.

Beautiful mathematics tends to reappear in nature.

Not always. Not reliably. Plenty of elegant math never finds a physical home. But when it does, it often shows up decades or centuries later, in places no one anticipated.

Ramanujan’s work seems to fall squarely into that category.

Faizan Bhat put it bluntly: in almost any truly beautiful piece of mathematics, you eventually find a physical system that mirrors it.

That’s not mysticism. It’s pattern recognition.

The Chudnovsky Algorithm and a Modern Resurrection

If Ramanujan’s ideas sound abstract, they’re also painfully practical.

In 1988, brothers David and Gregory Chudnovsky developed what is now the fastest known algorithm for calculating π. With the help of modern supercomputers, it has pushed π to over 200 trillion digits.

That algorithm is built directly on Ramanujan’s infinite series.

No Ramanujan, no Chudnovsky algorithm. No record breaking π calculations.

Even in the most computational, machine driven corner of mathematics, his fingerprints remain.

Was Ramanujan Ahead of His Time or Outside of It?

People often say Ramanujan was “ahead of his time.” That’s probably true, but it also feels incomplete.

He wasn’t just early. He was operating in a different mental landscape altogether. One where intuition mattered more than formalism, where results came before explanations.

Modern physics, ironically, is circling back toward that mindset. We now accept theories that work before we fully understand why they work. We tolerate black boxes, as long as the predictions hold.

In that sense, Ramanujan doesn’t feel old fashioned. He feels contemporary.

A Necessary Dose of Skepticism

It’s worth pausing here to avoid overstating the case.

Ramanujan did not “discover” black holes. His formulas don’t explain the universe in some secret, unified way. These connections are mathematical, not prophetic.

Physicists are careful about this for a reason. Patterns can be seductive. Coincidences happen. And not every overlap is meaningful.

Still, when the same structures emerge independently across math, fluid dynamics, and gravitational theory, it’s hard not to pay attention.

Why This Matters Beyond Trivia

At first glance, this all sounds like intellectual trivia. Interesting, but distant. Why should anyone outside physics care?

Because it hints at something unsettling and profound: our mathematical imagination may be more constrained and more powerful than we realize.

We don’t invent mathematics from scratch. We explore a landscape that already exists. Occasionally, someone like Ramanujan wanders into a region no one else has mapped yet.

Decades later, physics catches up.

The Unfinished Legacy

Ramanujan died young. Everyone knows that part. What’s less obvious is that his work didn’t finish when he did.

We’re still unpacking it.

Physicists are only beginning to understand how deeply his ideas resonate with modern theories. And they’re doing so with tools he never had quantum field theory, relativity, computational power orders of magnitude beyond anything imaginable in 1920.

And yet, the equations hold.

That’s the part that’s hardest to shake.

The Quiet Lesson

There’s a lesson here, though it’s not an easy one.

Progress doesn’t always look like progress. Sometimes it looks like rediscovery. Sometimes the future reaches backward, not forward, to find what it needs.

Ramanujan wasn’t trying to explain the universe. He was trying to understand numbers. The universe, apparently, took notes.

And a century later, we’re still catching up.

Open Your Mind !!!

Source: PopMech