Srinivasa Ramanujan's formula for π
An infinite series from a mathematical genius
As a mathematician, I was astounded when I encountered this formula:
It is an infinite series for the reciprocal of π, and it was discovered by a mathematician named Srinivasa Ramanujan. What boggles my mind is the seemingly arbitrary integers in its components. I wondered, “How did he derive this formula?”
This is not an area of mathematics that I know well or studied deeply, so I defer to several articles that explain this formula. The underlying concepts are elliptic integrals and modular equations.
Baruah, N. D., Berndt, B. C., & Chan, H. H. Ramanujan’s Series for 1/π: A Survey. The American Mathematical Monthly, 116(7), 567-587.
Huber, T., Schultz, D., & Ye, D. (2023). Ramanujan–Sato series for 1/π. Acta Arithmetica.
Weisstein, Eric W. "Pi Formulas." From MathWorld — A Wolfram Web Resource.
Srinivasa Ramanujan was born in the Indian city of Erode (in present-day Tamil Nadu). He grew up in relative poverty, lost several siblings who died in infancy, and suffered many illnesses throughout his life. Despite being mostly self-taught in mathematics, he made ground-breaking discoveries in number theory, infinite series, and continued fractions.
I am sad that he died at the young age of 32 years. Within his short life, he established himself as one of the greatest mathematicians of all time; I mourn the additional discoveries he could have shared with us in a longer life.