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New Delhi: A 100-year-old system of equations by Indian mathematical genius Srinivasa Ramanujan has shown a surprising relationship to the high-energy physics of the modern era. Scholars at the Indian Institute of Science (IISc) have found that one of the formulae of the pi-calculation Ramanujan published in 1914 spontaneously appears in sophisticated models of black holes and other extreme physical systems.
The team discovered that Ramanujan used the same mathematical structure to compute long sequences of pi that are present within the structure of modern physics to provide quicker and efficient means of solving difficult problems. Their efforts show how pure mathematics of the early 20th century is still leading the way to discoveries in advanced research now, published in the journal Physical Review Letters.
Ramanujan in 1914 gave 17 influential expressions of computing pi, which are still used to make our ultra-high-precision computations today, but some of which are still used in algorithms to reach over 200 trillion digits. IISc researchers, led by Professor Aninda Sinha, attempted to realise why such small equations do so well and whether they have a connection to the physical theory or not.
Their search took them to conformal field theory describing systems that are identical at all scales. In this area, they pay attention to logarithmic conformal field theories and mathematical instruments applied to the study of percolation, turbulent flows, and the behaviour of some black holes. All these fields were representative of these profound structures in the formulae of Ramanujan.
Using this link, the IISc group could calculate important values in high-energy physics with astonishing speed, and this closely resembles the work of Ramanujan to speed up the calculation of pi. According to the researchers, the discovery gives prominence to the fact that beautiful mathematics frequently corresponds to real physical systems.
In their results, Ramanujan, with a small exposure to modern physics, developed techniques echoing major concepts of the current understanding of the universe. The paper highlights the timeless nature of his work and its capacity to bring light to such a wide range of disciplines as turbulence, percolation, and black hole physics.
