Srinivasa Ramanujan (1887–1920)
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Introduction
Srinivasa Ramanujan was an Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite little formal training, he produced results that were both groundbreaking and ahead of his time. His life story is a testament to raw talent, relentless passion, and intellectual brilliance.
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Early Life
Birth: Ramanujan was born on December 22, 1887, in Erode, Tamil Nadu, India, to a Brahmin family.
Parents: His father, K. Srinivasa Iyengar, was a clerk, and his mother, Komalatammal, was a homemaker.
Childhood: Ramanujan displayed a natural flair for mathematics at a young age. By age 11, he had mastered advanced mathematics textbooks meant for college students.
At 16, he encountered G.S. Carr's "Synopsis of Elementary Results in Pure Mathematics", which contained over 6,000 mathematical results. This book profoundly influenced him, and he began deriving results and creating new theorems on his own.
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Education
Ramanujan attended several schools but dropped out of college twice due to his obsession with mathematics, which distracted him from other subjects.
Despite his brilliance, he struggled to find formal recognition or stable employment because of his lack of formal academic qualifications.
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Mathematical Journey
Self-Taught Genius
Ramanujan independently developed many mathematical theories, often rediscovering results already established in Western mathematics. However, his novel insights into number theory, partitions, and infinite series stood apart.
Correspondence with G. H. Hardy
In 1913, Ramanujan sent a letter containing over 100 mathematical theorems to G. H. Hardy, a prominent mathematician at the University of Cambridge. Initially skeptical, Hardy was eventually convinced of Ramanujan’s genius and invited him to Cambridge.
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Time at Cambridge
Ramanujan moved to England in 1914 and collaborated extensively with Hardy.
During his time at Cambridge, he:
Published papers in prestigious journals.
Made significant contributions to number theory, partition functions, and modular forms.
Developed the Ramanujan Prime and Ramanujan Theta Function.
Worked on mock theta functions, which were later connected to modern string theory.
Hardy rated Ramanujan’s mathematical ability as a 100 out of 100, while he rated his own at 25.
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Major Contributions
1. Number Theory
Introduced formulas for calculating partition functions.
Contributed to the theory of highly composite numbers.
2. Infinite Series and Continued Fractions
Discovered novel infinite series for π, some of which are used in modern computer algorithms for high-precision calculations.
3. Ramanujan-Hardy Number (1729)
When Ramanujan was ill, Hardy remarked that the taxi number 1729 seemed unremarkable. Ramanujan famously replied:
> "It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways: ."
4. Modular Forms and Mock Theta Functions
His work on modular forms and mock theta functions significantly influenced modern mathematics, including string theory and quantum physics.
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Later Life
Despite his success at Cambridge, Ramanujan struggled with health problems due to poor nutrition, cold weather, and the stress of war.
He returned to India in 1919 and continued working despite his deteriorating health.
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Death
Ramanujan died on April 26, 1920, at the young age of 32, due to complications from malnutrition and a possible liver infection (suspected to be hepatic amoebiasis).
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Legacy
1. Honors
Elected a Fellow of the Royal Society (FRS) in 1918, one of the youngest to receive this honor.
A Fellow of Trinity College, Cambridge.
2. Influence
His notebooks, filled with thousands of theorems, continue to inspire mathematicians worldwide. Many of his discoveries have applications in modern fields like physics, computer science, and cryptography.
3. Posthumous Recognition
In 2012, the film "The Man Who Knew Infinity" was released, showcasing his life and work.
His birthday, December 22, is celebrated as National Mathematics Day in India.
Institutions like the Ramanujan Institute for Advanced Study in Mathematics in Chennai honor his contributions.
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Famous Quote
> "An equation for me has no meaning unless it expresses a thought of God."
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Conclusion
Srinivasa Ramanujan’s life is a story of extraordinary talent and perseverance. Despite limited resources and formal training, he made profound contributions to mathematics that continue to resonate in modern science and mathematics. His legacy is a reminder of the boundless potential of human creativity and intellect.