Childhood
Srinivasa Ramanujan was born on December 22, 1887, in Erode, a town in the Indian state of Tamil Nadu. His father, K. Srinivasa Iyengar, was a clerk in a cloth merchant’s shop, and his mother, Komalatammal, was a housewife.
Ramanujan’s childhood was marked by poverty and illness. As a child, he was prone to frequent bouts of illness, which often kept him from attending school regularly. Despite his absences, he showed a remarkable aptitude for mathematics from a young age.
At the age of 13, Ramanujan discovered a book on advanced trigonometry, which he devoured. He quickly mastered the contents of the book and began to explore other branches of mathematics, such as number theory and infinite series.
Ramanujan’s passion for mathematics soon became evident to his family and teachers. However, his lack of formal education and training made it difficult for him to advance in the field. He failed his matriculation exam twice, which prevented him from pursuing higher education in mathematics.
Despite these setbacks, Ramanujan continued to study and work on mathematics on his own. He started to compile his own notebooks, where he recorded his findings and discoveries. These notebooks would later become a valuable resource for mathematicians around the world.
Ramanujan’s talent and dedication eventually caught the attention of mathematicians in India, and he was introduced to the British mathematician G. H. Hardy. With Hardy’s help, Ramanujan was able to publish several papers on number theory and continued fractions, which quickly gained him recognition in the mathematical community.
Education
He grew up in poverty and did not have access to formal education until he was 10 years old. Even after he joined school, he often skipped classes to pursue his interest in mathematics.
Ramanujan demonstrated a remarkable ability in mathematics from a young age, and by the time he was 13, he had already independently discovered many theorems and formulas in mathematics, including the sum of a geometric series.
In 1909, Ramanujan sent a letter to the famous mathematician G. H. Hardy, who was a fellow of Trinity College, Cambridge. The letter contained a list of theorems and formulas, which immediately impressed Hardy. Hardy invited Ramanujan to study at Cambridge, and Ramanujan arrived in England in 1914.
At Cambridge, Ramanujan worked closely with Hardy and other mathematicians, and he made significant contributions to number theory, including the discovery of Ramanujan’s prime and the Ramanujan conjecture.
Despite his lack of formal education, Ramanujan was elected as a fellow of the Royal Society of London in 1918, one of the highest honors in the field of mathematics. However, his health began to decline, and he returned to India in 1919, where he died on April 26, 1920, at the age of 32.
Spiritual Life
Srinivasa Ramanujan had a strong spiritual inclination throughout his life. He grew up in a deeply religious environment. His mother was a devout follower of the Hindu goddess Namagiri, and Ramanujan was deeply influenced by her faith.
Throughout his life, Ramanujan believed that his mathematical discoveries were a result of divine inspiration. He often spoke about how he received his ideas through dreams and visions, and believed that his mathematical insights came from a supernatural source.
Ramanujan was particularly drawn to the concept of infinity, which he saw as a reflection of the infinite nature of the divine. He saw mathematics as a way to understand and connect with the divine, and his spiritual beliefs were a driving force behind his work.
In his later years, Ramanujan became more deeply involved in religious practice, spending long hours in prayer and meditation. He was also deeply interested in the philosophical and spiritual teachings of Hinduism, and read extensively on topics such as yoga, Vedanta, and the Upanishads.
Overall, Ramanujan’s spiritual life was an integral part of his identity and work as a mathematician. He saw his mathematical insights as a way to connect with the divine, and his faith was a guiding force in his search for knowledge and understanding.
What is Ramanujan famous for
Srinivasa Ramanujan is famous for his contributions to number theory, mathematical analysis, and continued fractions. He made numerous groundbreaking discoveries, many of which were years ahead of their time and have had a lasting impact on mathematics.
Some of Ramanujan’s most significant contributions include:
- Ramanujan’s conjecture: He made a conjecture about the size of certain mathematical functions, which was later proved by other mathematicians.
- Partition function: Ramanujan made significant contributions to the study of partitions, which are ways of breaking up a number into smaller parts. His work on the partition function led to the development of new techniques in number theory.
- Modular forms: Ramanujan worked on modular forms, which are complex functions that have symmetry properties under certain transformations. His work on modular forms has applications in many areas of mathematics, including string theory and cryptography.
- Continued fractions: Ramanujan developed new techniques for calculating continued fractions, which are expressions that involve infinitely many fractions. His work on continued fractions has applications in approximation theory and mathematical physics.
Contribution to Mathematics
Here are some of his most notable contributions:
- Partition function: Ramanujan introduced the concept of the partition function, which counts the number of ways that a positive integer can be expressed as a sum of smaller positive integers. His work in this area led to the development of the famous Rogers-Ramanujan identities, which are still studied today.
- Ramanujan’s theta functions: Ramanujan defined a class of functions called theta functions, which have applications in many areas of mathematics, including number theory, analysis, and combinatorics.
- Infinite series: Ramanujan is known for his work on infinite series, particularly his formula for the sum of an infinite series of reciprocals of factorials. This formula has applications in physics, particularly in quantum mechanics.
- Hardy-Ramanujan-Littlewood circle method: Ramanujan collaborated with British mathematicians G.H. Hardy and J.E. Littlewood to develop a method for estimating the number of prime numbers in a given range. This method, now known as the Hardy-Ramanujan-Littlewood circle method, is still used today in number theory.
- Mock theta functions: Ramanujan introduced a class of functions called mock theta functions, which have applications in several areas of mathematics, including combinatorics and representation theory.
Ramanujan’s contributions to mathematics were recognized during his lifetime, and he was elected as a Fellow of the Royal Society in 1918. Today, his work continues to inspire and influence mathematicians around the world.
Ramanujan’s Theorem
The theorem provides an asymptotic formula for the partition function, which counts the number of ways a positive integer can be expressed as a sum of positive integers, ignoring the order of the terms.
The partition function is denoted by p(n), where n is a positive integer. Ramanujan’s Theorem states that:
p(n) ~ (1/4n√3) * exp(π√(2n/3))
Here, the symbol “~” means “is asymptotic to,” which indicates that the formula on the right-hand side of the equation gives an approximate value for p(n) that becomes more accurate as n becomes large.
Ramanujan’s Theorem is a remarkable result in number theory because it provides a simple and elegant formula for the partition function, which has been a subject of study for many mathematicians over the centuries. The formula has important applications in the analysis of algorithms, statistical mechanics, and the theory of modular forms.
Ramanujan’s Life in England
He spent five years in England, from 1914 to 1919, working with some of the leading mathematicians of his time. His time in England was a period of great intellectual growth for him, but it was also a time of personal and professional challenges.
Ramanujan arrived in England in 1914, at the invitation of the English mathematician G.H. Hardy, who recognized Ramanujan’s talent and potential. Ramanujan’s mathematical ideas were highly original and often difficult to understand, but Hardy worked closely with him to help him develop his ideas and express them in a more formal mathematical language.
During his time in England, Ramanujan made significant contributions to the field of mathematics, particularly in the areas of number theory and infinite series. His work on partitions and the Riemann zeta function, for example, has had a profound impact on modern mathematics.
Despite his mathematical successes, Ramanujan’s time in England was not without its challenges. He struggled with poor health, homesickness, and the cultural differences between India and England. Additionally, as an Indian man working in a predominantly white and male academic community, he faced discrimination and racism.
Married Life
Ramanujan married his wife Janaki Ammal on July 14, 1909, in the traditional Indian style arranged marriage. Janaki Ammal was a ten-year-old girl at the time of their marriage, and Ramanujan was twenty-two years old. They had no children.
According to various biographies of Ramanujan, their marriage was not an easy one. Ramanujan’s devotion to mathematics often led him to neglect his responsibilities as a husband and a father. He would spend long hours working on his mathematical theories and equations, often forgetting to eat or sleep.
Furthermore, Ramanujan’s poor health and financial struggles added to the difficulties in their married life. He suffered from various illnesses, including tuberculosis and dysentery, which affected his ability to work and earn a living.
Despite these challenges, Janaki Ammal remained a supportive and devoted wife to Ramanujan. She took care of him during his illnesses, managed their household finances, and even learned some mathematics to better understand her husband’s work.
Sadly, Ramanujan’s marriage was cut short when he passed away on April 26, 1920, at the age of 32 due to complications from tuberculosis. Janaki Ammal was left to raise their families and continue to preserve her husband’s mathematical legacy.
Ramanujan’s Death
He died at a relatively young age due to health complications. Ramanujan had been suffering from health problems for several years, which had initially been misdiagnosed as tuberculosis. In 1917, he traveled to England to work with the famous mathematician G. H. Hardy at the University of Cambridge.
However, his health continued to deteriorate, and he was diagnosed with severe vitamin deficiencies, which had weakened his immune system and made him vulnerable to infections.
Despite receiving medical treatment, Ramanujan’s health did not improve, and he was eventually forced to return to India in 1919. He died there on April 26, 1920, at the age of 32. The exact cause of his death remains unclear, but it is believed to have been related to the health problems he had been experiencing for several years.
Ramanujan’s death was a significant loss to the field of mathematics, as he had the potential to make even more groundbreaking contributions if he had lived longer. His legacy lives on, however, through his mathematical discoveries, which continue to inspire and fascinate mathematicians to this day.