Context:
- A recent study by an Indian Statistical Institute (ISI), Bengaluru research team has drawn connections between Srinivasa Ramanujan’s mathematical formulae for π (pi) and concepts used in modern cosmology and theoretical physics.
- The work highlights how abstract number theory and infinite series, developed over a century ago, are now relevant to understanding expanding universes, boiling fluids, and complex physical systems.
Key Highlights:
Ramanujan’s Mathematical Contributions
- Srinivasa Ramanujan (1887–1920) developed highly efficient infinite series to calculate the value of π with remarkable speed and accuracy.
- His formulae, published in 1914, remain among the fastest converging series for π even today.
- Ramanujan worked largely in isolation, without formal training in modern mathematics.
Link with Modern Physics & Cosmology
- Researchers found structural similarities between:
- Ramanujan’s π-series, and
- Correlation functions used in quantum field theory (QFT) and cosmology.
- These mathematical structures help model:
- Critical phenomena (sudden changes in physical systems)
- Phase transitions (e.g., boiling of fluids)
- Expanding universe models
Bridge Between Disciplines
- Ramanujan’s equations resemble those used to describe:
- Turbulent fluids
- Quantum fluctuations
- Cosmic expansion patterns
- The study suggests that pure mathematics and physical reality may share deeper structural connections.
Historical Significance
- Ramanujan’s work was once considered purely theoretical.
- Similar historical parallels exist, such as Riemannian geometry later becoming essential for Einstein’s General Theory of Relativity.
Relevant Prelims Points:
- Who: Srinivasa Ramanujan – Indian mathematical genius.
- Key Concept: Infinite series for calculating π.
- Institution: Indian Statistical Institute (ISI), Bengaluru.
- Scientific Fields Linked:
- Number theory
- Quantum Field Theory
- Cosmology
- Important Terms:
- Infinite series
- Correlation functions
- Critical phenomena
- Phase transition
- Significance: Demonstrates long-term relevance of pure mathematics.
Relevant Mains Points:
- Science & Technology Perspective:
- The study shows how theoretical mathematics can find applications decades later in advanced sciences.
- Highlights interdisciplinary research between mathematics and cosmology.
- Conceptual Clarity:
- Quantum Field Theory (QFT): Framework to describe fundamental forces and particles.
- Cosmology: Study of the origin, structure, and expansion of the universe.
- Critical Phenomena: Points where small changes cause large effects in systems.
- Indian Contributions to Global Knowledge:
- Ramanujan’s legacy underscores India’s historical strength in abstract science.
- Reinforces the importance of supporting basic research, even without immediate applications.
- Way Forward:
- Encourage investment in fundamental research.
- Promote interdisciplinary collaboration between mathematicians and physicists.
- Integrate history of science into STEM education to inspire innovation.
UPSC Relevance (GS-wise):
- GS I: History of science and technology
- GS III: Science & Technology, research and innovation
- GS IV: Ethics – value of intellectual pursuit and knowledge for humanity