Ethics Theory, TLP-UPSC Mains Answer Writing
Q. 3. Srinivasa Ramanujan made extraordinary contributions to mathematics with little formal training. Discuss the significance of his work and its relevance to modern science and technology. (150 words, 10 marks)
Introduction
Srinivasa Ramanujan, a self-taught mathematical genius from India, made groundbreaking contributions to number theory, infinite series, and mathematical analysis. Despite minimal formal training, his work continues to influence modern science, technology, and theoretical research.
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Significance of Ramanujan’s Work
- Contributions to Number Theory: Ramanujan’s work on partitions, highly composite numbers, and modular forms expanded the foundations of number theory.
- Discovery of Mock Theta Functions: These mysterious functions, introduced in his final letters, puzzled mathematicians for decades.
- Infinite Series and Continued Fractions: He developed elegant formulas for π and other constants using unconventional infinite series.
- Modular Forms and q-Series: His work laid groundwork for the modern theory of modular forms.
- Ramanujan Prime and Tau Function: He introduced new functions and patterns in prime numbers and integer partitions.
- Intuition over Formal Proofs: He arrived at deep truths through intuition and pattern recognition, challenging conventional methods of mathematical discovery.
Relevance to Modern Science and Technology
- Cryptography and Cybersecurity: Ramanujan’s theories on prime numbers and modular forms underpin encryption algorithms used in secure communication.
- Theoretical Physics: Concepts like mock theta functions and modularity are applied in string theory, quantum gravity, and the study of black holes.
- Computer Science: His formulas for rapidly converging series are used in algorithm development for symbolic computation and data processing.
- Artificial Intelligence: His ability to identify patterns in complex data inspires modern approaches to machine learning and intuitive problem-solving.
- Space Science: NASA scientists have used Ramanujan’s equations in orbital mechanics and signal processing.
- Pure Mathematics Research: His notebooks continue to be a source of unsolved problems and insights for mathematicians worldwide.
Conclusion
Ramanujan’s legacy proves that genius can thrive beyond formal education. His intuition driven discoveries not only reshaped mathematics but also continue to influence cutting-edge research in physics, computer science, and cryptography in the 21st century.
