Srinivasa Ramanujan was a self-taught mathematician whose genius and contributions to mathematics are celebrated worldwide. Born in 1887 in Erode, India, Ramanujan’s passion for mathematics began at an early age. Despite limited formal education, he demonstrated extraordinary abilities in mathematical reasoning, often creating original theorems while still a teenager. He became enamored with the subject to such an extent that he neglected other subjects, resulting in his failure in school exams. Nevertheless, Ramanujan continued to pursue mathematics with a relentless fervor, developing his theories without guidance from formal academic systems. His work was largely unknown outside of India until he sent a letter filled with his discoveries to G.H. Hardy, a prominent mathematician at Cambridge University in England. Hardy, initially skeptical, quickly recognized Ramanujan’s exceptional talent and invited him to Cambridge, where the two forged a deep intellectual partnership.
Ramanujan’s Life and Struggles
Srinivasa Ramanujan was born on December 22, 1887, in Erode, a small town in Tamil Nadu, India. His early life was marked by a natural affinity for numbers and mathematical concepts. His father, K. S. Narayan Iyengar, was a clerk in the British Indian government, while his mother, Komalatammal, was a devout woman who nurtured Ramanujan’s spiritual and intellectual curiosity. Growing up in a family with little exposure to advanced mathematics, Ramanujan was largely self-taught. His early exposure to mathematics came through a book on trigonometry, which he found at the age of 11. The book, A Synopsis of Elementary Results in Pure and Applied Mathematics by G.S. Carr, became his constant companion and sparked his passion for mathematics.
Ramanujan’s mathematical brilliance emerged at an early age, but his formal education was inconsistent. He attended various schools in his childhood, but his academic journey was disrupted by his intense focus on mathematics, which led him to neglect other subjects like English and history. As a result, he failed his school exams and was labeled as an underperforming student. His obsession with mathematics further alienated him from conventional schooling, and by the time he was 15, he had mastered many advanced mathematical concepts. However, his obsession came at a cost: his studies in other subjects suffered, and he was unable to finish his formal schooling. Despite this, he continued to develop his mathematical theories independently, writing extensive notebooks filled with new ideas and problems that would later challenge the world’s leading mathematicians.
Ramanujan’s early mathematical work was entirely self-developed and focused primarily on number theory, including properties of numbers and their divisors. His deep interest in these areas led him to develop a series of original, albeit unverified, results. At the age of 16, Ramanujan began to experiment with the theory of partitions, a branch of mathematics concerned with the ways in which integers can be broken down into sums of smaller integers. His work was impressive but remained largely unnoticed, as it was not aligned with the academic standards of the time. He was isolated in his pursuit of mathematical knowledge, without access to the kind of mathematical community or mentorship that would have helped him refine and validate his ideas.
Despite his isolation, Ramanujan’s abilities eventually attracted attention. In 1903, at the age of 16, he began to share his results with a few mathematicians in India, who were initially amazed by his extraordinary insights. However, his work was largely ignored by mainstream academic circles, and his lack of formal credentials continued to hinder his recognition. Ramanujan’s intense focus on mathematics, coupled with his rejection of other subjects, caused him to struggle in his career. In 1904, Ramanujan took a job as a clerk in the PWD (Public Works Department) in Madras (now Chennai), but his professional life did not bring him the fulfillment he sought. While working at the PWD, Ramanujan continued to produce notebooks filled with his mathematical ideas. At this stage, he was essentially living in a world of his own, consumed by his passion for mathematics, even as he struggled to make a living.
In 1910, Ramanujan’s life took a pivotal turn when he sent a letter to G.H. Hardy, a prominent mathematician at Cambridge University in England. This letter contained a collection of Ramanujan’s results, including several original theorems in number theory. Hardy, who was initially skeptical, was soon astounded by the depth and originality of Ramanujan’s work. Recognizing the genius behind the letter, Hardy invited Ramanujan to come to Cambridge, marking the beginning of one of the most remarkable collaborations in mathematical history. Hardy was later quoted as saying that Ramanujan was “the most remarkable mathematical genius” he had ever come across. This letter was the catalyst that would propel Ramanujan’s mathematical career, leading him to international recognition.
However, despite this breakthrough, Ramanujan’s problems were far from over. Ramanujan faced numerous challenges upon moving to England in 1914. The cold, damp climate of Cambridge was a harsh contrast to the warm, tropical environment of India, and Ramanujan’s health, already fragile, began to deteriorate rapidly. He suffered from a variety of illnesses, including a recurring fever and gastrointestinal problems, which led to frequent hospitalizations. The harsh academic environment at Cambridge, which valued rigorous proofs and formalism, also posed difficulties for Ramanujan. His methods were intuitive, and he had little formal training in mathematical proofs, which sometimes led to tension with the academic community. Despite these challenges, Hardy and his colleague J.E. Littlewood were supportive of Ramanujan, working closely with him to help refine his ideas.
Ramanujan’s initial struggles with formal mathematics and his difficulties in adjusting to life in England were compounded by his health issues. However, his time at Cambridge also marked the peak of his mathematical achievements. During this period, Ramanujan produced some of his most profound work, including the famous Ramanujan-Hardy number (1729), the partition formula, and his continued exploration of infinite series. These results would leave an indelible mark on the field of mathematics. Nevertheless, the physical and emotional toll of living in a foreign country eventually proved too much for Ramanujan. In 1919, after a period of declining health, he returned to India, but his time in England had already cemented his place as one of the greatest mathematicians of all time. His health, however, continued to deteriorate, and he passed away on April 26, 1920, at the age of 32.
Ramanujan’s early life and struggles reflect a story of perseverance in the face of adversity. Despite facing numerous personal and academic challenges, he triumphed through his sheer brilliance and passion for mathematics. His journey, from an isolated young man in colonial India to an internationally recognized genius, continues to inspire generations of mathematicians and scholars around the world.
Ramanujan’s magic square
Srinivasa Ramanujan is often associated with various remarkable mathematical discoveries, including his work on magic squares, though his contributions in this area are less widely known than his work in number theory. A magic square is a square grid filled with distinct numbers such that the sums of the numbers in each row, column, and diagonal are all equal. This constant sum is known as the “magic constant.”
One of Ramanujan’s most famous contributions to the world of magic squares is the Ramanujan’s Magic Square, a 4×4 square that is sometimes referred to as the “most famous magic square” linked to him. This magic square is especially notable because it was not only a typical magic square, but it also contains a set of numbers that are personally meaningful to Ramanujan.
Ramanujan’s magic square is as follows,
In this square, the sum of every row, column, and diagonal is 34, which is the magic constant for this 4×4 square.
What makes Ramanujan’s magic square particularly intriguing is the fact that it was linked to his personal life and his mystical beliefs. Ramanujan’s magic square is often considered as a manifestation of his connection to the divine, as he believed that his mathematical abilities were guided by the goddess Namagiri. This square was discovered during his time in England, where he was in poor health, and some even consider it as a symbol of Ramanujan’s enduring mathematical genius despite his struggles.
Interestingly, Ramanujan was fascinated with numbers that had special properties, and many of the numbers in his magic square, such as 1, 15, 14, and 4, are linked to his other work in number theory, particularly his research on highly composite numbers and number partitions. The magic square is thus not just a random arrangement of numbers but a subtle reflection of his mathematical insights and his deep spiritual connection.
Ramanujan’s magic square, along with his other mathematical discoveries, highlights his genius and his ability to find beauty and harmony in numbers in ways that were both scientifically groundbreaking and spiritually meaningful. The square remains an example of his unique approach to mathematics, blending rigorous intellectual pursuit with his personal beliefs and intuition.
Ramanujan’s belief in the Goddess Namagiri
Srinivasa Ramanujan’s belief in the goddess Namagiri, a form of the Hindu goddess Lakshmi, was a profound and integral aspect of his life. Ramanujan was deeply religious, and his faith influenced both his mathematical work and his worldview. Growing up in a devout Brahmin family, he believed that his mathematical abilities were a divine gift from the goddess Namagiri, to whom he attributed the source of his insights. In Ramanujan’s view, the goddess would appear in his dreams and provide him with mathematical formulas and solutions, which he would then transcribe into his notebooks. This mystical connection to the divine was central to his identity, and he often expressed that his mathematical intuition was guided by spiritual visions and revelations.
Ramanujan’s strong religious beliefs were evident in his daily life and work. He adhered strictly to his religious practices, observing rituals and reciting prayers regularly. Even when living in England, Ramanujan continued to maintain his devotional practices, despite the cultural differences and the academic demands of his new environment. He would often write about his spiritual experiences and the role of the goddess in his mathematical discoveries. Ramanujan famously claimed that his theorems came from the goddess and that he was merely a medium for her divine wisdom. This belief, however, was sometimes seen as unconventional by his peers in the mathematical community, who often approached mathematics with a strictly logical and formal mindset. Nonetheless, Ramanujan’s spirituality and his unwavering faith in the goddess Namagiri were intrinsic to his sense of purpose and to his exceptional ability to unlock the mysteries of mathematics.
This unique blend of spirituality and mathematics made Ramanujan’s work distinct. His intuitive, almost mystical approach to problem-solving stood in stark contrast to the rigorous methods of formal mathematical reasoning employed by his contemporaries. Despite this, his results were undeniably groundbreaking, and his contributions to number theory, continued fractions, and infinite series continue to inspire mathematicians to this day. Ramanujan’s belief in the goddess Namagiri, therefore, not only defined his personal life but also influenced the way he approached and understood the universe, making him one of the most remarkable and unconventional mathematicians in history.
In conclusion, Srinivasa Ramanujan’s life and work stand as a testament to the extraordinary intersection of divine belief and mathematical genius. His deep faith in the goddess Namagiri, which guided his mathematical insights, provided him with a unique and intuitive approach to problem-solving that defied conventional academic methods. Despite facing immense personal, academic, and cultural challenges, Ramanujan’s contributions to mathematics remain foundational, illustrating the power of innate talent, relentless dedication, and a profound spiritual connection. His legacy continues to inspire generations of mathematicians, proving that genius can emerge from the most unexpected sources, whether through rigorous logic or divine inspiration.
