Usefulness of Shrinivasa Ramanujan's Work in Mathematics

 Ramanujan’s work includes Prime Number, Hyper Geometric Series, Modular function, Elliptical functions, Mock theta function, Magic square, Number theory and some geometry. Many of his results have been used in subject like particle physics, statistical mechanics, computer science, cryptography and space travel. Let me simplify the same for the young readers.

1. His work on Riemann zeta function have been applied on the theory of pyrometry aimed at making better blast furnaces.
2. His result has been used to find the better approximate value of pi.

In 1989, Chudnovsky brothers computed π to over 1 billion decimal places on a supercomputer using a variation of Ramanujan’s infinite series of π.

3. Crystallographer S. Ramaseshan has shown how Ramanujan’s partition theory sheds light on polymer technology. his work on partition has found useful in splicing telephone cables, whose shorter subunits of varying length, again add up to make a whole.

His work on partition theory has applications in a number of areas including particle physics (particularly quantum field theory) and probability.

4. Ramanujan published his paper titled “On certain arithmetical functions” in the year 1916 that investigated the properties of Fourier coefficients of modular forms. He also developed three conjectures on it and his first two conjectures helped develop the Hecke theory, which was formulated 20 years after his paper, in 1936, by German mathematician Erich Hecke.

His third conjecture played a pivotal role in the development of Langlands program in 1970 under Robert Langlands. This program aims to combine two mathematical branches Representation theory and algebraic number theory.

5. Famous Physicist Prof A K Sen has used Ramanujan’s Modular equation to analyze the concept of String theory.

6. The famous taxi cab number and the elliptical curve y^2=x^3+ ax + b that Ramanujan worked on, has a great impact on K3 surface which plays pivotal role in Quantum physics. Calabi- Yau Manifold is an example of K3 surface.

(Courtesy: - Wikipedia)

8. Ramanujan’ work on Theta Function is used to determine the critical dimensions in Bosonic string theory, superstring theory and M-theory.

9. Mathematician Ken Ono says that Ramanujan’s work on Mock Modular form is now used to compute the entropy, or level of disorder, of black holes.

10. Even the Cloud Computing we use is based on Ramanujan’s result.

Thanks for reading

Dr Rajesh Kumar Thakur