{"id":189336,"date":"2025-12-18T03:18:14","date_gmt":"2025-12-18T03:18:14","guid":{"rendered":"https:\/\/www.newsbeep.com\/nz\/189336\/"},"modified":"2025-12-18T03:18:14","modified_gmt":"2025-12-18T03:18:14","slug":"ramanujans-genius-%cf%80-formulas-from-a-century-ago-might-help-explain-the-deepest-secrets-of-the-universe","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/nz\/189336\/","title":{"rendered":"Ramanujan\u2019s Genius \u03c0 Formulas From a Century Ago Might Help Explain the Deepest Secrets of the Universe"},"content":{"rendered":"

\"\" <\/a>Credit: Space-Tech, X.<\/p>\n

In 1914, Srinivasa Ramanujan arrived at Cambridge with a notebook filled with 17 extraordinary infinite series for 1\/\u03c0. They were strikingly efficient, producing accurate digits of the world\u2019s most famous irrational number much faster than any technique of the time. For over a century, mathematicians viewed these formulas as a pinnacle of number theory, but they lacked a \u201cphysical\u201d explanation for why they worked so well.<\/p>\n

Now, researchers at the Indian Institute of Science (IISc) have uncovered a hidden bridge between Ramanujan\u2019s \u201crecipes\u201d for pi and the cutting-edge physics used to describe black holes and turbulent fluids. The study suggests that Ramanujan was intuitively using the same mathematical engine that governs how matter behaves at the edge of a total transformation.<\/p>\n

Srinivasa Ramanujan\u2019s life reads like fiction. Born into poverty in southern India and largely cut off from formal education, he taught himself mathematics by obsessively working through whatever books he could find, then pushing far beyond them. His notebooks filled with equations that seemed to arrive whole, without derivation, as if tuned in from some distant frequency. <\/p>\n

In his early twenties, he began mailing these results to British mathematicians, most of whom ignored them. One didn\u2019t. British Mathematician G.H. Hardy recognized that the strange, unproved formulas on the page could not be mere accidents. They were too original, too coherent. It was Hardy who brought Ramanujan to Cambridge, where the young mathematician produced a torrent of results before illness forced him back to India, where he died in 1920 at just 32. Ramanujan\u2019s story was turned into the 2015 film The Man Who Knew Infinity<\/a>.<\/p>\n

Seventeen Formulas That Should Not Have Worked<\/p>\n

\"Ramanujan <\/a>Ramanujan portrait and \u03c0 infinite series. Credit: Kyuriosity.<\/p>\n

In 1914, Srinivasa Ramanujan published 17 formulas for calculating 1\/\u03c0. Each looked almost magical.<\/p>\n

Add just a few terms, and \u03c0 snaps into focus with uncanny speed. Compared with older methods \u2014 such as the long, laborious series dating back to Archimedes \u2014 Ramanujan\u2019s expressions converged almost explosively.<\/p>\n

Today, they still power the fastest \u03c0 calculations on Earth. \u201cScientists have computed pi up to 200 trillion digits using an algorithm called the Chudnovsky algorithm,\u201d says Aninda Sinha<\/a>, a physicist at IISc and senior author of the new study. \u201cThese algorithms are actually based on Ramanujan\u2019s work.\u201d <\/p>\n

Yet Ramanujan offered little explanation for why his formulas worked so well.<\/p>\n

For more than a century, mathematicians treated them as isolated marvels. Sinha and his collaborator Faizan Bhat wanted to know whether that mystery pointed somewhere deeper.<\/p>\n

\u201cWe wanted to see whether the starting point of his formulae fit naturally into some physics,\u201d Sinha says. \u201cIn other words, is there a physical world where Ramanujan\u2019s mathematics appears on its own?\u201d <\/p>\n

The Physics of Things on the Brink<\/p>\n

Their search led to a class of theories with a long name and strange implications: logarithmic conformal field theories.<\/p>\n

Physicists use conformal field theories to describe systems at critical points, such as the moments when matter teeters between phases and ordinary notions of scale break down.<\/p>\n

Water provides a classic example. When water is heated to exactly 374\u00b0C under 221 atmospheres of pressure, at this precise moment, the distinction between liquid and vapor vanishes into a \u201csuperfluid\u201d state. Zoom in or out, and the system looks statistically the same.<\/p>\n

\u201cAt the critical point, you cannot actually say which is liquid and which is vapor,\u201d Sinha told The Hindu<\/a>. \u201cThat is the point where CFTs [Conformal field theories] enter: they are used to explain what happens in this kind of critical phenomena.\u201d<\/p>\n

Logarithmic versions of these theories describe even stranger systems: percolation (how fluids spread through porous materials), dense polymers, certain quantum Hall states, and the onset of turbulence. They also appear in theoretical descriptions of black holes<\/a>.<\/p>\n

What Bhat and Sinha found is that the mathematical backbone of Ramanujan\u2019s \u03c0 formulas \u2014 the same structure that makes them converge so quickly \u2014 also appears inside the equations that define these physical theories.<\/p>\n

Pi Hiding in Plain Sight<\/p>\n

\"A <\/a>A bust of Srinivasa Ramanujan in the garden of the Birla Industrial & Technological Museum, Kolkata. Credit: AshLin (CC BY-SA)<\/p>\n

At the heart of Ramanujan\u2019s work with \u03c0 series lies a mathematical identity known as the Legendre relation<\/a>. On its own, it looks abstract and apparently has nothing to do with physics. <\/p>\n

But when the IISc team rewrote it using the language of conformal field theory, something unexpected happened. The symbols began to line up with physical quantities: correlation functions, scaling dimensions, and operators that encode how systems fluctuate at criticality.<\/p>\n

In their analysis, Ramanujan\u2019s mysterious parameters map directly onto the properties of twist operators \u2014 mathematical objects that track how systems behave when boundaries or symmetries are disrupted.<\/p>\n

The result is a new computational shortcut.<\/p>\n

By borrowing Ramanujan\u2019s strategy \u2014 compressing complex behavior into compact expressions \u2014 the researchers constructed faster ways to calculate key quantities in logarithmic conformal field theories. In some cases, calculations that normally require summing many contributions collapse to just one.<\/p>\n

\u201cRemarkably,\u201d the authors write, the entire answer can emerge from what physicists call the \u201cidentity operator\u201d alone. <\/p>\n

That kind of simplification hints at a universal property of these theories, something fundamental hiding beneath the equations.<\/p>\n

Black Holes, Turbulence, and a Rubber Band<\/p>\n

The connection extends even further.<\/p>\n

In the study\u2019s appendix, the authors show that the same mathematical structure appears in models of black holes described using holography \u2014 a framework where gravity in higher dimensions maps onto quantum physics in lower ones.<\/p>\n

In this setting, Ramanujan\u2019s formulas correspond to how disturbances propagate between a black hole\u2019s horizon and the edge of spacetime. The same equations also describe how polymers stretch, how fluids turn turbulent, and how clusters form in percolating materials.<\/p>\n

Bhat sees a familiar pattern.<\/p>\n

\u201c[In] any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors the mathematics,\u201d he says. \u201cRamanujan\u2019s motivation might have been very mathematical, but without his knowledge, he was also studying black holes, turbulence, percolation, all sorts of things.\u201d <\/p>\n

Sinha offers a metaphor drawn from string theory. A string, he explains, behaves like a rubber band: stretch it different ways, and it reveals different properties. Pi, hidden inside those equations, shows up through infinitely many mathematical perspectives.<\/p>\n

When Pure Math Waits for Physics<\/p>\n

\"Old <\/a>Ramanujan (Center) as a Fellow of Trinity College, Cambridge. Credit: Public Domain.<\/p>\n

This is not the first time mathematics has anticipated physics by decades.<\/p>\n

Riemannian geometry began as a 19th-century abstraction, but Einstein later revealed that spacetime itself obeys its rules. Fourier transforms emerged from studies of heat flow and now underpin digital images, music, and data compression.<\/p>\n

Ramanujan\u2019s work fits this pattern uncannily well.<\/p>\n

Working largely in isolation in early 20th-century India, with little exposure to modern physics, he stumbled onto structures that now sit at the center of quantum field theory and cosmology.<\/p>\n

\u201cWe were simply fascinated by the way a genius working in early 20th century India, with almost no contact with modern physics, anticipated structures that are now central to our understanding of the universe,\u201d Sinha says. <\/p>\n

Beyond Pi<\/p>\n

The researchers are careful not to oversell their results. This work does not solve open problems in number theory or unlock a theory of everything.<\/p>\n

But it opens a door.<\/p>\n

The same approach could reveal fast-converging formulas for other irrational numbers. It could streamline calculations in theories that model turbulence and critical behavior. <\/p>\n

The IISc researchers are already looking toward the next horizon. The same mathematical structure they identified in Ramanujan\u2019s pi series has reappeared in their models of an expanding universe.<\/p>\n

It turns out that when we calculate the circumference of a circle, we might be using the same rules that govern the very fabric of the cosmos.<\/p>\n

The new findings appeared in the Physical Review Letters<\/a>.<\/p>\n


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