Srinivasa Ramanujan: The Enigmatic Genius of Mathematics

Early Life and Education

Srinivasa Ramanujan was born on December 22, 1887, in Erode, a small town in Tamil Nadu, India, into a traditionally religious Brahmin family. His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop, and his mother, Komalatammal, was a homemaker with a deep devotion to the Hindu deity Namagiri Thayar, to whom Ramanujan later attributed some of his mathematical insights.

From an early age, Ramanujan showed a phenomenal aptitude for numbers. At the age of five, he was already adept at basic arithmetic, and by thirteen, he had mastered advanced trigonometry from a library book. His education at Town Higher Secondary School in Kumbakonam was marked by his disinterest in subjects other than mathematics, leading to average performance in exams. 

In 1904, he entered the Government Arts College in Kumbakonam, where his obsession with mathematics over all other subjects led to academic failure; he was so engrossed in mathematics that he neglected his coursework, resulting in the loss of his scholarship and eventually failing his degree examination. He briefly attended Pachaiyappa's College in Madras but left without a degree, as his focus remained solely on mathematics.

Self-Taught Mathematics

Ramanujan's most formative education was self-taught. He borrowed a copy of George Shoobridge Carr's "Synopsis of Elementary Results in Pure and Applied Mathematics," a collection of thousands of theorems, which he studied intensely. This book, while not offering proofs, provided him with a vast compendium of results that he began to explore and expand upon. His notebooks from this period show a mind already at work on original mathematics, though much of it was rediscovered from Western mathematics.

Recognition and The Journey to Cambridge

Living in poverty in Madras (now Chennai), Ramanujan struggled to find recognition for his work. He sent letters to various Indian mathematicians, but it was his correspondence with G.H. Hardy, a leading British mathematician at Trinity College, Cambridge, that changed his life. In 1913, Hardy received a letter from Ramanujan containing about 120 theorems, which he described as "the one romantic incident in my life." Recognizing the genius in Ramanujan's work, Hardy, along with J.E. Littlewood, arranged for Ramanujan to come to England.

Years at Cambridge (1914-1919)

Ramanujan arrived in England in 1914, an era of profound cultural and scientific change. However, adapting to life in Britain was challenging for Ramanujan. He was a strict vegetarian, struggled with the cold English weather, and faced cultural isolation. Nevertheless, his collaboration with Hardy was exceptionally fruitful:

• Number Theory: Together, they published papers on the partition function, exploring how numbers can be broken down into the sum of smaller numbers. The Hardy-Ramanujan asymptotic formula for partitions is a testament to this work.
• Mock Theta Functions: Ramanujan introduced this concept in his later years in Cambridge, which remained a mystery until much later when mathematicians like George Andrews began to unravel its significance.
• Ramanujan's Master Theorem: A powerful tool for deriving series representations, which has found applications in various mathematical contexts.

Despite his academic success, Ramanujan's health deteriorated. He was diagnosed with tuberculosis and suffered from vitamin deficiencies, possibly exacerbated by his dietary restrictions and the British climate.

Return to India and Death

In 1919, Ramanujan returned to India, still very ill. His health continued to decline, and he passed away on April 26, 1920, in Kumbakonam. Even on his deathbed, Ramanujan continued to work on mathematics, sending theorems to Hardy, indicating his undying passion for the subject.

Posthumous Discoveries and Legacy

After his death, Ramanujan's notebooks became the subject of intense study. His "lost notebook," found years later in Trinity College's library, contained additional theorems, many of which were still unexplored. His work has since influenced:

• Number Theory and Analysis: His contributions to the theory of partitions, modular forms, and mock theta functions continue to be pivotal.
• Physics: His mathematical insights have found applications in string theory, quantum mechanics, and other areas of theoretical physics.
• Cultural Impact: Ramanujan's life story has inspired numerous works, including Robert Kanigel's biography "The Man Who Knew Infinity," which later became a film. The narrative of a self-taught genius from a remote part of India resonates globally.
• Awards and Tributes: The Ramanujan Prize, National Mathematics Day in India, and various educational initiatives bear his name, celebrating his contributions.

Ramanujan's Mathematical Style

Ramanujan's approach to mathematics was intuitive rather than rigorous in the classical sense. He often presented results without proof, relying on an almost mystical insight into numbers. His work was characterized by:

• Intuition Over Proof: Ramanujan's theorems often came to him in visions, which he would then verify mathematically.
• Originality: Many of his findings were novel or rediscovered independently from Western mathematics.
• Beauty in Mathematics: He had a deep aesthetic sense of mathematical beauty, often describing theorems as "beautiful" or "elegant."

Conclusion

Srinivasa Ramanujan's life and work encapsulate the essence of mathematical genius — a mind so attuned to the patterns of numbers that it could transcend formal education and cultural barriers to leave an everlasting legacy. His story is one of human triumph over adversity, a reminder that profound contributions can come from the most unassuming beginnings. Ramanujan's mathematics continues to challenge, inspire, and push the boundaries of what we understand about numbers, making him not just a mathematician but a symbol of the human spirit's quest for knowledge.