Srinivasa Ramanujan: The Self-Taught Mathematical Genius
Early Life:
Srinivasa Ramanujan was born on December 22, 1887, in Erode, a small town in Tamil Nadu, India. His parents were K. Srinivasa Iyengar, a clerk in a cloth merchant’s shop, and Komalatammal. From an early age, Ramanujan showed an extraordinary talent for mathematics, and his interest in the subject became evident during his school years.
Despite excelling in mathematics, Ramanujan faced financial challenges that threatened to disrupt his education. However, his maternal uncle, S. Narayana Iyer, recognized his nephew’s mathematical abilities and provided support for his education.
Self-Taught Mathematician:
Ramanujan’s mathematical journey began with the study of a book titled “A Synopsis of Elementary Results in Pure and Applied Mathematics.” This book, published by George Shoobridge Carr, contained a compilation of mathematical results without proofs. Ramanujan, with little formal training, immersed himself in solving the problems presented in the book.
His self-taught exploration of mathematics led him to make significant discoveries and develop his unique mathematical style. By the age of 16, Ramanujan had compiled a notebook containing results and theorems that showcased his extraordinary talent.
College Education and Struggles:
In 1903, Ramanujan entered the Government College in Kumbakonam, where his mathematical prowess continued to shine. However, his unorthodox approach and focus on self-discovered results sometimes led to conflicts with his professors.
Financial difficulties persisted, and Ramanujan had to drop out of college. Undeterred, he continued his independent mathematical pursuits while supporting himself with various jobs. During this period, he worked on developing his mathematical ideas, unaware that he was laying the groundwork for groundbreaking contributions to the field.
Correspondence with G.H. Hardy:
In 1913, Ramanujan wrote a letter to the distinguished British mathematician G.H. Hardy, enclosing a sample of his work. Hardy, initially skeptical about the claims made by an unknown Indian mathematician, soon recognized the brilliance of Ramanujan’s results.
Impressed by Ramanujan’s work, Hardy invited him to visit Cambridge in 1914. This marked the beginning of a fruitful collaboration between the two mathematicians. Ramanujan’s unproven results were rigorously examined and verified by Hardy and other mathematicians at Cambridge.
Contributions to Number Theory:
Ramanujan’s contributions to number theory were particularly profound. His work encompassed areas such as infinite series, partitions of numbers, modular forms, and mock theta functions. Some of his most famous results include the Ramanujan-Hardy number, the Ramanujan prime, and the Rogers-Ramanujan identities.
Despite facing health challenges and adapting to the English climate, Ramanujan continued to produce mathematical gems. His collaboration with Hardy resulted in numerous joint publications.
Return to India and Legacy:
Ramanujan returned to India in 1919 due to deteriorating health. He passed away on April 26, 1920, at the young age of 32. The exact cause of his death remains uncertain, with some speculating tuberculosis or malnutrition.
Srinivasa Ramanujan’s legacy is immeasurable. His work has had a profound impact on various branches of mathematics, inspiring generations of mathematicians. The Ramanujan-Hardy number (1729), famously known as the “Hardy-Ramanujan number,” is named after an incident where Hardy visited Ramanujan in the hospital and remarked that the number of his taxi, 1729, seemed uninteresting. Ramanujan quickly corrected him, stating that it was, in fact, a very interesting number—it is the smallest positive integer expressible as the sum of two cubes in two different ways (1729 = 1³ + 12³ = 9³ + 10³).
Ramanujan’s life and work continue to be celebrated, and his story serves as an inspiration for aspiring mathematicians worldwide. In 2011, a biographical film titled “The Man Who Knew Infinity” was released, depicting Ramanujan’s life and his contributions to mathematics.
