Srinivasa Ramanujan, one of the most extraordinary minds in the history of mathematics, remains an enigmatic figure whose contributions continue to inspire awe even a century after his death. Born into poverty in southern India in 1887, Ramanujan’s genius was so profound that he formulated complex theorems and equations with little formal training in mathematics. His story is a testament to the mysterious workings of the human mind and a reminder of the vast, untapped potential that lies within individuals who may be far removed from traditional academic systems.
Ramanujan’s work on infinite series, continued fractions, modular forms, and number theory remains relevant in both pure mathematics and modern physics. Despite his short life—he died at the age of 32—his legacy is monumental. This article explores Ramanujan’s life, his groundbreaking contributions to mathematics, and the mystery surrounding some of his most famous equations, many of which he claimed were divinely inspired.
Early Life and Background
Srinivasa Ramanujan was born on December 22, 1887, in Erode, in what is now the state of Tamil Nadu, India. His family was poor but deeply religious, and from a young age, Ramanujan showed a prodigious aptitude for mathematics. By the age of 11, he had mastered advanced trigonometry, and by the time he was 16, he had independently derived many results that were already established in mathematics, despite having no formal higher education.
Ramanujan’s fascination with mathematics was sparked when he encountered a book called “A Synopsis of Elementary Results in Pure and Applied Mathematics” by G. S. Carr. The book, though outdated and covering 5,000 theorems without proofs, provided Ramanujan with the foundation upon which he built his own groundbreaking discoveries. He quickly moved beyond the material in the book, developing new theories and equations entirely on his own.
However, his early obsession with mathematics came at a cost. Ramanujan neglected other subjects, which led to his academic failure and inability to secure a university degree. Despite this, he continued to pursue mathematics passionately, working in isolation in his small village.
The Turning Point: Collaboration with G. H. Hardy
Ramanujan’s life took a dramatic turn in 1913 when he sent a letter to the renowned British mathematician G. H. Hardy at the University of Cambridge. The letter contained pages filled with startlingly original mathematical results, many of which had never been seen before. Hardy was initially skeptical, suspecting that Ramanujan might be a fraud, but upon closer examination, he realized that Ramanujan was a true genius, possibly on par with greats like Euler and Gauss.
Hardy arranged for Ramanujan to come to Cambridge, and in 1914, Ramanujan made the journey to England, where he began collaborating with Hardy. Their partnership is one of the most famous in the history of mathematics. Over the next five years, Ramanujan made significant contributions to number theory, continued fractions, and infinite series, among other areas. His work was so original that many of his results opened up entirely new fields of mathematical research.
Ramanujan’s Contributions to Mathematics
Ramanujan’s contributions to mathematics were vast, and many of his discoveries were well ahead of his time. Some of his most famous contributions include:
1. Ramanujan’s Infinite Series for Pi
One of Ramanujan’s most famous results is his infinite series for calculating π (pi). His series converges so rapidly that it is incredibly useful for calculating pi to millions of decimal places with a relatively small number of terms. This formula was rediscovered and used by computer scientists in the 20th century to calculate pi with extraordinary precision.
2. Partition Function and Number Theory
Ramanujan made groundbreaking contributions to the study of partition functions. The partition of a number refers to the ways it can be expressed as the sum of other numbers. For example, the number 5 can be partitioned as 5, 4+1, 3+2, 3+1+1, 2+2+1, etc. Ramanujan’s work in this area led to the famous Ramanujan conjecture and laid the groundwork for the Hardy-Ramanujan asymptotic formula, which provides an approximation for the partition function.
3. Modular Forms
Ramanujan’s work on modular forms is one of his most profound contributions. His discovery of the Ramanujan tau function led to deep insights into the properties of modular forms and opened the door to new research in number theory and the theory of elliptic curves. These results are now foundational to modern string theory and quantum physics.
4. Mock Theta Functions
In his final years, Ramanujan introduced a new class of functions that he called mock theta functions. These functions have puzzled mathematicians for decades, and it wasn’t until the late 20th century that researchers began to understand their full significance. Mock theta functions have applications in modern mathematical fields, such as black hole entropy in physics.
Ramanujan’s Mysterious Equations: Divine Inspiration?
One of the most intriguing aspects of Ramanujan’s work is the mystical or divine nature he attributed to his equations. Ramanujan, a devout follower of the Hindu goddess Namagiri, often claimed that his mathematical insights came to him in visions or dreams. He would describe how Namagiri would appear to him, providing him with mathematical formulas and insights that he would later prove or develop further.
This spiritual connection to mathematics is part of what makes Ramanujan such a fascinating figure. His work often seemed to come out of nowhere—without formal proofs, background, or derivation—but they were almost always correct. The mathematical community has spent decades analyzing and proving results that Ramanujan intuitively knew but didn’t formally prove during his lifetime.
Many of his notebooks, filled with these “mystical” equations, were only published posthumously and are still being studied. The richness and depth of his mathematical intuition have led some to call his work “otherworldly” or beyond the grasp of normal human understanding.
Struggles with Health and Tragic Death
Ramanujan’s time in England was not easy. He struggled with the cold, the unfamiliar diet, and the isolation from his family and culture. His health deteriorated significantly while in Cambridge, and by 1919, he was seriously ill, likely suffering from tuberculosis and malnutrition.
He returned to India in 1919, hoping to recover, but his health continued to decline. Tragically, on April 26, 1920, at the age of 32, Ramanujan passed away, leaving behind a wealth of mathematical discoveries that would take decades for the world to fully understand.
Ramanujan’s Legacy
Ramanujan’s legacy is immense. His contributions to mathematics continue to influence a wide array of fields, from number theory to theoretical physics. His life story, marked by his profound genius, humble beginnings, and his untimely death, remains an inspiration to mathematicians, scientists, and thinkers around the world.
In recognition of his extraordinary contributions, Ramanujan was posthumously made a Fellow of the Royal Society in 1918, becoming one of the youngest Fellows ever. His life has been the subject of numerous books and films, including the acclaimed 2015 movie “The Man Who Knew Infinity,” based on the biography of the same name by Robert Kanigel.
In 2012, the Ramanujan Prize was established to recognize outstanding contributions by young mathematicians from developing countries, continuing the legacy of Ramanujan’s brilliance and perseverance.
Conclusion: A Genius Beyond Boundaries
Srinivasa Ramanujan’s life and work represent one of the most remarkable stories in the history of mathematics. His ability to intuit complex mathematical truths without formal training, combined with his deep spiritual connection to his work, make him a singular figure in both the mathematical world and human history.
Although he lived a tragically short life, his contributions have had an enduring impact, influencing everything from pure mathematics to modern physics. Ramanujan’s story reminds us that genius can emerge in the most unexpected places and that the mysteries of the universe are often unlocked by those with the boldness to think beyond the known.