The new pi formula was discovered by Arnab Pirya Saha and Aninda Sinha, a pair of physicists working at the Indian Institute of Science. Their formula was published in Physical Review Letters as a small detail in their larger scientific paper. Their goal was to find a unifying theory of fundamental forces in string theory, which just happened to generate the new formula.
Saha and Sinha were studying the interactions between gravity, electromagnetism, and nuclear forces as they relate to string theory. In exploring how the vibrations of tiny threads could create those interactions, the two had to investigate the mathematical formulas involved in those interactions. This mathematical exploration, looking for new ways to view complex natural phenomena, is what led them to the new pi formula.
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