In 1914, Indian mathematician Srinivasa Ramanujan made public a collection of 17 mathematical expressions for
calculating pi, an iconic constant used worldwide.
These formulations, compact yet highly potent, could yield extensive sequences of correct digits with minimal
calculation. More than a hundred years on, the mathematical community still uses these equations as the backbone for
ultra-high-precision computations of pi, reaching results with hundreds of trillions of digits.
A team from the Centre for High Energy Physics (CHEP) at the Indian Institute of Science (IISc) recently established
that Ramanujan’s formulae, crafted within the domain of pure mathematics, intertwine closely with the mathematical
architecture of contemporary high-energy physics.
In an IISc statement, Professor Aninda Sinha explained: “Scientists have computed pi up to 200 trillion digits using an
algorithm called the Chudnovsky algorithm. These algorithms are actually based on Ramanujan's work.”
Working under Sinha’s guidance, Faizan Bhat and colleagues aimed to uncover the origin of the formulae’s remarkable form
“We wanted to see whether the starting point of his formulae fit naturally into some physics,” Sinha said. “In other
words, is there a physical world where Ramanujan’s mathematics appears on its own?”
LINK WITH PHYSICS THEORIES
Their pursuit led directly to conformal field theory, a mathematical construct that models physical systems showing
scale invariance. These are systems that retain their appearance regardless of zoom or scale. One illustrative instance
is the critical point in water, a state where liquid and vapour become completely indistinct.
From the broader class, the researchers zeroed in on logarithmic conformal field theories. These models are essential
for addressing complex questions in physics: the movement of substances through media (percolation), the initiation of
turbulent flow in liquids, and particular descriptions of black holes.
Each instance revealed the same core mathematical structures found in Ramanujan’s formulae.
Taking advantage of this unexpected resonance, Sinha and Bhat managed to compute key quantities for these advanced
physical scenarios with notable efficiency, parallel to how Ramanujan’s equations accelerate the calculation of pi’s
“In any piece of beautiful mathematics, you almost always find that there is a physical system which actually mirrors
the mathematics,” said Bhat. “Ramanujan’s motivation might have been very mathematical, but without his knowledge, he
was also studying black holes, turbulence, percolation, all sorts of things.”
This research demonstrates that Ramanujan’s mathematical legacy reaches beyond the boundaries of pure calculation,
surfacing as an essential tool for streamlining work in fields such as turbulence and black hole physics. These
mathematical links now contribute to making complex calculations both faster and more approachable for physicists
Considering Ramanujan’s influence, Sinha reflected on the mathematician’s reach across time and disciplines.
“We 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,” said Sinha.