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Srinivasa Ramanujan (1887-1920)
Srinivasa Ramanujan, an mathematician, was born in 1887 in the Southern region of India. Ramanujan was born in the quaint village of Erode, nestled approximately 400 kilometers southwest of Madras, now known as Chennai. His journey into the world of mathematics began in his formative years when he was just a year old. His mother relocated to Kumbakonam, a town about 160 kilometers closer to Madras, where his father worked as a clerk in a cloth merchant's shop. However, destiny had other plans for young Ramanujan. In December 1889, he contracted smallpox, which marked the first twist in his remarkable life.
Srinivasa Ramanujan Educational Journey -
Ramanujan's early education unfolded in Madras, where he attended a local school. His affinity for mathematics began to bloom at a young age, largely through self-study. Displaying immense promise, he garnered several academic accolades during his high school years. Ramanujan passion for mathematics presented challenges when he transitioned to college. Excelling predominantly in this field, he struggled in other subjects, ultimately leading to his decision to discontinue his college education. Despite this setback, Ramanujan's devotion to mathematics remained steadfast. He continued to cultivate his collection of mathematical theorems, concepts, and ideas. This dedication persisted until he experienced his groundbreaking breakthrough, propelling him into the realm of mathematical excellence.
Ramanujan's life journey and remarkable achievements shed profound light on his enduring struggles and unwavering dedication to advancing his field of expertise. These aspects serve as a pivotal illustration of his commitment and influence on the subject. It's noteworthy that Ramanujan biography and achievements hold significant weight in educational contexts, forming an integral part of the syllabus for aspirants preparing for upcoming challenges. The legacy of Ramanujan serves as a source of inspiration for those seeking to emulate his dedication and make their mark in the realm of mathematics.
The Scholar Emerges
As he approached the age of five, Ramanujan embarked on his academic journey, starting at a primary school in Kumbakonam. His brilliance shone brightly across all subjects, establishing him as an exceptional scholar. In the year 1900, he initiated his independent exploration of mathematics, delving into the realms of geometric and arithmetic series.
Self-Taught Prodigy
In 1902, Ramanujan was introduced to the world of cubic equations, and soon, he discovered his own method to tackle quartic equations. The following year, he dared to tackle the quintic, unaware that it could not be solved by radicals. His insatiable thirst for knowledge and unique problem-solving skills set him on an unparalleled trajectory.
A Fateful Encounter
It was during his tenure at the Town High School in Kumbakonam that Ramanujan stumbled upon a pivotal mathematics book, "Synopsis of Elementary Results in Pure Mathematics" by G.S. Carr. This book, though outdated by contemporary standards (published in 1886), became his gateway to mastering mathematics. Carr's book offered theorems, formulae, and concise proofs, setting the template for Ramanujan's future mathematical expressions
Into the Depths of Research
By 1904, Ramanujan had ventured into deep research. He embarked on a journey to comprehend the series ∑(1/n!) and remarkably calculated Euler's constant to 15 decimal places. Simultaneously, he explored the intricate world of Bernoulli numbers, charting his own path of mathematical discovery.
The Scholarship Lost
Ramanujan's remarkable schoolwork earned him a scholarship to Government College in Kumbakonam in 1904. However, the subsequent year brought a bitter twist of fate as his scholarship was not renewed due to his unwavering dedication to mathematics, at the expense of his other subjects. Financial hardships loomed large, prompting Ramanujan to make a daring decision.
The Escape to Pursue Passion
Without disclosing his intentions to his parents, Ramanujan left for the town of Vizagapatnam, approximately 650 kilometers north of Madras. Here, he continued his relentless pursuit of mathematics. During this period, he delved into hypergeometric series and explored the intricate connections between integrals and series, unknowingly edging closer to the study of elliptic functions
College and Illness
In 1906, Ramanujan arrived in Madras, enrolling at Pachaiyappa's College with the aspiration to pass the First Arts examination, a gateway to the University of Madras. He attended college lectures, but his health took a severe hit after three months of study. Despite leaving the course, he took the First Arts examination and excelled in mathematics, though he faced failure in all other subjects, consequently missing the opportunity to join the University of Madras.
A Self-Made Mathematical Genius
Undeterred by academic setbacks, Ramanujan continued his mathematical voyage, developing his ideas independently, with minimal guidance on contemporary research topics. His journey led him to explore continued fractions and divergent series in 1908, and during this time, he was battling severe health issues.
Marriage and Recognition
In a peculiar twist of fate, Ramanujan married a ten-year-old girl named S. Janaki Ammal when he was 14. However, they did not live together until she turned twelve. Despite his unconventional personal life, his mathematical prowess was gaining recognition. In 1911, he authored a groundbreaking research paper on Bernoulli numbers, which was published in the Journal of the Indian Mathematical Society, catapulting him to fame in the Madras region.
In 1912, Ramanujan took a significant step by applying for the position of clerk in the accounts section of the Madras Port Trust. His application letter revealed his limited formal education but also showcased his unwavering dedication to mathematics, a subject he had been diligently pursuing.
What sets Ramanujan apart was his innate mathematical talent, which was evident even to university mathematicians in Madras. E.W. Middlemast, the Professor of Mathematics at The Presidency College in Madras, provided a glowing reference for Ramanujan, highlighting his exceptional capacity for mathematics and rapid computational skills.
Based on Middlemast's recommendation, Ramanujan secured the clerk position at the Madras Port Trust, commencing his duties on March 1, 1912. This was a fortunate turn of events for Ramanujan, as several individuals in his vicinity were also passionate about mathematics. Notably, S.N. Aiyar, the Chief Accountant for the Madras Port Trust, published a paper on Ramanujan's work in 1913.
Another influential figure, C.L.T. Griffith, the professor of civil engineering at the Madras Engineering College, recognized Ramanujan's exceptional abilities and sought help from M.J.M. Hill, a professor of mathematics at University College London, to promote Ramanujan's work.
However, despite these connections, Ramanujan faced challenges in gaining recognition for his unconventional mathematical findings. His attempts to engage mathematicians like E.W. Hobson and H.F. Baker yielded no response.
In a moment of destiny, Ramanujan discovered G.H. Hardy's 1910 book "Orders of Infinity" and decided to write to him in January 1913. In his letter, Ramanujan introduced himself and his groundbreaking work, particularly his investigations into divergent series.
Hardy, along with his colleague Littlewood, was intrigued by Ramanujan's letter and the extensive list of unproved theorems he included. In February 1913, Hardy responded to Ramanujan, expressing keen interest in his work but requesting proofs to assess its validity.
Ramanujan was elated by Hardy's response and considered him a sympathetic friend. Despite facing dire financial circumstances and health challenges, Ramanujan continued his correspondence with Hardy, seeking support to obtain a scholarship either from the university or the government.
The University of Madras granted Ramanujan a scholarship in May 1913, offering a lifeline to his mathematical pursuits. In 1914, G.H. Hardy played a pivotal role in bringing Ramanujan to Trinity College, Cambridge, initiating a remarkable collaboration.
This transition to England was not without difficulties, including Ramanujan's strict vegetarianism and health issues exacerbated by the outbreak of World War I. Nevertheless, Ramanujan's collaboration with Hardy bore fruit from the outset, leading to groundbreaking results in mathematics.
One significant challenge was Ramanujan's lack of formal education, which prompted Hardy to enlist the help of other mathematicians, such as Littlewood, to teach him rigorous mathematical methods. However, Ramanujan's flood of original ideas made this task exceedingly challenging.
Despite facing numerous obstacles, Ramanujan's work in England began to gain momentum. He graduated from Cambridge in 1916 with a Bachelor of Arts by Research, and his dissertation focused on highly composite numbers, comprising seven papers published in England.
Unfortunately, Ramanujan's health deteriorated in 1917, leading to concerns for his life. His doctors initially speculated various illnesses, but eventually, it was believed to be tuberculosis. His condition improved slightly, and he continued to produce mathematics.
In 1918, Ramanujan received numerous honors, including election as a fellow of the Cambridge Philosophical Society and, most notably, his election as a fellow of the Royal Society of London. This recognition provided a boost to his health and renewed his mathematical endeavors.
By the end of 1918, Ramanujan's health had significantly improved, and he continued to produce exceptional mathematics. His journey, from the streets of India to the hallowed halls of Cambridge, was an extraordinary testament to the power of innate talent and unwavering dedication to the pursuit of knowledge.
Srinivasa Ramanujan Contributions:
During his stay in England between 1914 and 1919, Ramanujan, in collaboration with Hardy, authored over a dozen research papers. Over a span of three years, he astonishingly produced around 30 research papers, showcasing his prolific mathematical output. The collaboration between Hardy and Ramanujan led to the creation of a pioneering technique, now renowned as the circle method. This method was instrumental in deriving an asymptotic formula for a specific mathematical function. Rumanian’s inaugural publication, a 17-page treatise on Bernoulli numbers, was featured in the Journal of the Indian Mathematical Society in 1911. An especially notable achievement stemming from the partnership of Hardy and Ramanujan was the formulation of a ground-breaking formula for the count of partitions of a number 'n', a result of immense significance.
Srinivasa Ramanujan Death—
By 1919, Ramanujan's health began to decline, prompting his decision to return to India. Upon his arrival in 1920, his health continued to deteriorate, leading to his untimely demise at the tender age of 32.
Top questions about Srinivasa Ramanujan:
1. Why did Ramanujan die so early?
Ramanujan’s early demise at the age of 32 in 1920 has been attributed to various factors. Health issues, including severe vitamin deficiencies due to his vegetarian diet, may have contributed to conditions such as liver problems and tuberculosis. Living in poverty and inadequate access to proper medical care during his time likely exacerbated his health struggles, leading to his premature death.
2. Where was Srinivasa Ramanujan educated?
Srinivasa Ramanujan was largely self-taught and had no formal education in mathematics beyond basic school education. He attended local schools in Kumbakonam, his hometown in Tamil Nadu, India. However, his true mathematical genius emerged independently through his persistent self-study and research.
3. What were Srinivasa Ramanujan’s contributions?
Srinivasa Ramanujan made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Some of his most notable contributions include the Ramanujan Prime and the Ramanujan theta function, as well as groundbreaking discoveries in the theory of partitions and mock theta functions. His work has had a profound impact on various fields of mathematics, including the theory of numbers, continued fractions, and infinite series.
4. What is Srinivasa Ramanujan remembered for?
Srinivasa Ramanujan is remembered for his unparalleled mathematical genius and his extraordinary contributions to various areas of mathematics, particularly number theory. Despite his humble beginnings and lack of formal training, Ramanujan’s work has inspired countless mathematicians and continues to be studied and admired for its depth, complexity, and elegance. His story serves as a testament to the power of innate talent and the limitless potential of the human mind.
5. Why is 1729 called the Ramanujan number?
The term “Ramanujan number” stems from an intriguing incident involving the renowned mathematician Srinivasa Ramanujan and G. H. Hardy. During a hospital visit, Ramanujan remarked that the number of the taxi that brought Hardy, 1729, appeared uninteresting. In response, Hardy revealed that 1729 was, in fact, a unique number. It is the smallest positive number expressible as the sum of two cubes in two different ways: 1729=13+123=93+103. This episode forever associated the number 1729 with Ramanujan’s legacy, hence the moniker “Ramanujan number.”