Srinivasa Ramanujan's century-old formulas for π are finding fresh relevance in modern physics. New research from the Indian Institute of Science (IISc) suggests that the elegant infinite series he discovered in 1914 may be connected to the mathematics used to describe systems at critical points, including phase transitions and other complex phenomena.
Ramanujan's 17 formulas for 1/π became famous for their remarkable speed and precision. They remain a foundation for some of the fastest π calculations today, including methods behind record-setting computations. What had long remained unclear was why these expressions worked so efficiently.
The IISc team, led by physicist Aninda Sinha and collaborator Faizan Bhat, explored whether the structure behind Ramanujan's formulas appears naturally in physics. Their analysis points to logarithmic conformal field theories, a class of models used to study critical behavior in systems such as percolation, dense polymers, quantum Hall states, and the early stages of turbulence.
By rewriting a key mathematical identity from Ramanujan's work in the language of these theories, the researchers found that the same structure aligns with physical quantities such as correlation functions and scaling dimensions. In some cases, calculations that usually require many terms can be reduced to a much simpler form.
The study also suggests that similar patterns may appear in holographic models of black holes and in descriptions of expanding universes. While the findings do not solve open problems in number theory, they open a promising path for faster calculations and deeper links between pure mathematics and the physical world.
Ramanujan's legacy now looks even broader: formulas once seen as abstract may help illuminate how the universe organizes itself at its most fundamental level, shaping future work across mathematics and theoretical physics.
