Ramanujan's Pi Insights Echo Through Modern Physics

(MENAFN- The Arabian Post) A century after Srinivasa Ramanujan wrote down his striking formulas for calculating pi, the mathematics behind those expressions is shaping how scientists describe some of the Universe's most complex physical systems. Researchers at the Indian Institute of Science in Bengaluru have shown that the same mathematical structures embedded in Ramanujan's work also appear in turbulence, percolation processes and theoretical models of black holes, drawing a direct line between abstract number theory and real-world physics.

Ramanujan, largely self-taught and working under severe material constraints in the early 20th century, developed extraordinarily fast-converging series for pi that astonished contemporaries such as G H Hardy. For decades, these formulas were admired mainly for their beauty and efficiency in computation, with little expectation that they might illuminate physical phenomena. That view is now changing as physicists and mathematicians revisit the deeper structures underlying his equations.

At the centre of the renewed interest are modular forms and special functions that govern Ramanujan's pi series. These objects, long studied within pure mathematics, have turned out to be natural tools for describing systems that exhibit scale invariance and critical behaviour. At IISc, theoretical physicists examining turbulence and statistical mechanics noticed that the equations governing energy cascades and phase transitions mirrored those found in Ramanujan's notebooks.

One line of work focuses on percolation, a model used to describe how fluids seep through porous materials or how networks become connected as links are added. Near its critical point, percolation displays universal behaviour that does not depend on microscopic details. Researchers have found that the probabilities and scaling laws at this threshold can be expressed using the same modular functions that appear in Ramanujan's formulas for pi, suggesting a shared mathematical backbone.

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Similar patterns have emerged in studies of turbulence, one of the most stubborn problems in classical physics. Turbulent flows involve energy moving across scales in a way that resists simple description. By applying techniques inspired by Ramanujan's work, scientists have derived more precise relationships between fluctuations at different scales, helping to explain why certain statistical regularities appear across vastly different turbulent systems, from laboratory fluids to atmospheric flows.

Perhaps most striking is the connection to black hole physics. In certain models of quantum gravity and string theory, the microscopic states of black holes are counted using partition functions with modular symmetry. These partition functions are closely related to the same class of mathematical objects Ramanujan explored. As a result, formulas devised to compute pi now inform calculations of black hole entropy, a measure of the hidden information encoded at an event horizon.

The IISc researchers emphasise that this does not mean Ramanujan anticipated black holes or turbulence in any direct sense. Instead, his intuition led him to mathematical structures that turn out to be fundamental to how nature organises complexity. Modern physics has repeatedly shown that deep symmetries, once uncovered, tend to surface in many apparently unrelated contexts.

Internationally, the work has drawn attention from mathematicians and physicists working on conformal field theory, quantum chaos and complex systems. Several groups are extending the approach to study transport in disordered materials and the spread of information in quantum systems. The appeal lies in the unifying power of the mathematics: a single framework can describe phenomena ranging from fluid motion to cosmology.

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This renewed focus has also prompted historians of science to re-examine Ramanujan's legacy. His notebooks, filled with results often written without proof, were once seen as enigmatic curiosities. Today they are increasingly viewed as a reservoir of ideas whose relevance is still unfolding. Advances in computation and theoretical physics have made it possible to test and interpret these ideas in ways that were unimaginable during his lifetime.

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