Ramanujan - The Indian genius who changed the world of mathematics
New Post has been published on https://startupupdates.info/ramanujan-the-indian-genius-who-changed-the-world-of-mathematics/
Ramanujan - The Indian genius who changed the world of mathematics
In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. So think how genius Ramanujan was , When one of greatest mathematician of 20th century unhesitatingly replied that his greatest contribution was not any mathematics discovery but discovery of one Indian genius.
Srinivasa Ramanujan was born on December 22, 1887 and was predetermined to gotten to be a brilliant mathematician. Over the course of his life, he went on to create thousands of his own formulas, numerous of which have kept on be utilized in mathematics and science. In fact his Formula are indeed utilized to understand dark holes. He initially made a few of his theories while in India , in spite of the fact that when he travelled to Cambridge in Britain to talk about his scientific equations with the brightest minds of the time, he made numerous there as well. It was in Britain that Ramanujan started an inspirational partnership with the Cambridge teacher Godfrey Harold Hardy. Professor Hardy figured it out that Ramanujan had found certain mathematical formulas by himself that were really as of now known to the mathematical elite. However, what was more striking was that he created his own formulas, which warranted further understanding. Most of his theories have been proven correct over time and have provided mathematicians since then with the basis from which to create formulas that continue to shape science today.
Srinivasa Ramanujan was born in Erode, a city which is presently in the Indian state of Tamil Nadu. His father, K. Srinivasa Iyengar, was a receptionist in a sari shop whereas his mother, Komalatammal, was a housewife who frequently sang religious hymns at the local Hindu temple. When he was just two years old, Ramanujan contracted smallpox and later recovered from the disease. As a child, he did not like attending school and his family even enlisted the help of a local constable to ensure that he actually attended. Paradoxically, it was at Kangayan Primary School that he really flourished. He performed very well academically. In November 1897, at nine years old, Ramanujan completed his primary school education and scored the highest marks in his local district. He then enrolled at Town Higher Secondary School. It was there that his love and fascination with mathematics began.
Ramanujan’s thirst for mathematical knowledge was unquenchable. By the age of 13, he had mastered a textbook by Professor Sidney Luxton Loney on advanced trigonometry, or the study of relationships involving the lengths and angles of triangles. Within a couple of years he was discovering complex mathematical theories on his own, creating his own formulas and even completed mathematical examinations in less than half the allocated time.
Ramanujan received a copy of A Synopsis of Elementary Results in Pure and Applied Mathematics by the mathematician George Shoobridge Carr from a friend. This contained a staggering 5,000 of Carr’s own theories. It is generally believed that by studying this book Ramanujan’s mathematical prowess was awakened. In 1904, he was awarded the K. Ranganatha Rao prize by his school’s headmaster, after which he received a scholarship at Government Arts College in Kumbakonam. While there he was so enamoured with mathematics that he neglected all other subjects, and subsequently lost his scholarship. Ramanujan would later enroll at Pachaiyappa’s College in Madras, now known as Chennai. He failed in his Fellow of Arts degree as he again did not perform well in subjects other than mathematics. He sat for the examinations again a year later but also failed. Since he lacked a degree, he left formal education to pursue his work independently and because he lacked formal qualifications, he concentrated on his theories alone, living in utter poverty and was often on the brink of starvation.
In 1909, at the age of 22, Ramanujan was married to Srimathi Janaki, also known as Janakiammal. At this time in history, it was not unusual for marriages to be arranged with girls who were much younger than the husband. This was the case for Ramanujan’s marriage to Srimathi Janaki who was only 10 years old at the time.
Following this, Ramanujan spent time looking for work in Chennai, while living in his friend’s house. At the same time, to earn some money, he gave tuition to students from Presidency College, one of the oldest government arts colleges in India and one of the two Presidency colleges established by the British. At that time the Indian Mathematical Society of India was formed by V. Ramaswamy Aiyer, whom Ramanujan met with when he was looking for a job. Later, Aiyer recalled looking through Ramanujan’s notebooks upon meeting him.
“I was struck by the extraordinary mathematical results contained in it [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.”
This meeting was to be fortunate for Ramanujan, as he was soon sent to Chennai with letters of introduction from Aiyer. There he met with Aiyer’s mathematical peers, who again gave him letters of introduction and sent him to Raghunatha Ramachandra Rao, an Indian civil servant, mathematician and social and political activist and the secretary of the Indian Mathematical Society. Upon first meeting Ramanujan, Rao was unconvinced regarding his mathematical formulas and thought him a fraud. However upon talking and discussing various complicated mathematical theories with Ramanujan, he was won over by the young man’s mathematical genius. Ramanujan requested Rao’s help for financial aid while he continued his research and Rao happily obliged. This eventually led to Ramanujan having his work published in the Journal of the Indian Mathematical Society.
In 1912, Ramanujan applied for a temporary job in the Madras Accountant General’s office. There he was supposed to earn 20 Indian rupees a month, but he was only in this position for a couple of weeks. During this time, he applied for a job under the Chief Accountant of the Madras Port Trust. His application was accompanied by a letter of recommendation from Edgar William Middlemast, a professor of mathematics at Presidency College. This application landed Ramanujan a job as a Class III, Grade IV accounting clerk on March 1, 1912 with a monthly salary of 30 rupees. Ramanujan was adept at the work, finishing his assignments quickly, allowing him ample time to continue his research. His boss, Sir Francis Spring and his colleague, S. Narayana Iyer encouraged Ramanujan in his research.
In 1913, Diwan Bahadur Rao, Professor Middlemast and S. Narayana Iyer attempted to present Ramanujan’s work to various British mathematicians. Many of them ridiculed Ramanujan’s work, labelling him uneducated and a fraud. It was then that Ramanujan wrote to the mathematical elite at Cambridge University in England. Though he received the same negative reception from two professors, he received a warmer response from Professor Godfrey Harold Hardy. Though initially sceptical of Ramanujan’s work, upon analysing his manuscript further he was very impressed with some of his theories. Professor Hardy even stated that Ramanujan’s theories.
“defeated me completely; I had never seen anything in the least like them before”
“must be true, because, if they were not true, no one would have the imagination to invent them.”
After conferring with his colleague, Professor John Edensor Littlewood, who was equally impressed with Ramanujan’s work, Professor Hardy described him as a mathematician of the highest quality, a man whose work was original and powerful.
Professor Hardy wrote back to Ramanujan asking for more proof of his theories and began to arrange for Ramanujan to travel to Cambridge, contacting the Indian Office. Secretary Arthur Davies from the Advisory Committee for Indian Studies met with Ramanujan to discuss his trip to England, but Ramanujan refused to travel overseas to a foreign land, in observance of his strict Brahmin (priestly-caste) upbringing.
Despite this, Ramanujan felt very fortunate to have found such a friend. Professor Hardy even arranged, through his peers, for Ramanujan to receive a two-year research scholarship of 75 rupees a month from the University of Madras. While there he continued to submit papers containing his theories to the Journal of the Indian Mathematical Society.
There was a notable instance during which Ramanujan had pre-empted the work of another mathematician. Professor Edward Ross of Madras Christian College, who Ramanujan had met before, stormed into class one day. Flustered, he asked his students if Ramanujan knew Polish. It turned out that Ramanujan had written theories pre-empting the work of a Polish mathematician that had just arrived in the day’s mail.
Though dismayed at Ramanujan’s refusal to travel to Cambridge, Professor Hardy did not give up and enlisted the help of his colleague E. H. Neville. Over time, when Neville questioned Ramanujan regarding his refusal, it turned out that he no longer held reservations about traveling. Ramanujan promptly left for England, leaving his parents and wife behind in India.
Traveling to England and Life in Cambridge
Ramanujan’s journey from India to England took almost a whole month by sea. Traveling from Madras on March 17, 1914, he arrived in the ports of London on April 14. When he arrived, Ramanujan was whisked away to Cambridge after a couple of days stay in London. In Cambridge, Ramanujan was housed a short distance away from Professor Hardy’s own room. There he began working with Professor Hardy and Professor Littlewood almost immediately.
Studying his notebooks, they found many theories. Some had already been discovered by other mathematicians of the past, some they concluded were wrong and others they decided were complete breakthroughs. They were absolutely stunned by his brilliance, even comparing him to two of history’s most well-known mathematicians – Leonhard Euler and Carl Gustav Jacob Jacobi. Throughout Ramanujan’s time in England, Professor Hardy tried to provide Ramanujan with an education in the areas that he was not familiar with.
His five years spent in Cambridge was not without its difficulties. There was a clash of cultures between Ramanujan who came from a traditional Indian background and the two Cambridge professors. They had differences not only in the ways they worked together, but also in their beliefs. Ramanujan was a devout Hindu who relied on his intuition, whereas his colleague Professor Hardy was a stout atheist who only believed in what could be proven and in mathematics.
In March 1916, Ramanujan was awarded a PhD (then known as a Bachelor of Science) degree for his mathematical work, part of which was published as an academic paper in the journal Proceedings of the London Mathematical Society. This began a period of acceptance for Ramanujan and his work. He was elected to the London Mathematical Society in 1917, and then as Fellow of the Royal Society in 1918, the oldest scientific academy that still exists. He was only 31 years old at the time, making him one of the youngest Fellows since the Royal Society began in 1660. This award is only granted to those who have made a ‘substantial contribution to the improvement of natural knowledge, including mathematics, engineering science and medical science’. Other notable Fellows of the Royal Society include the likes of Sir Isaac Newton, Charles Darwin, Michael Faraday, Albert Einstein and Alan Turing. In 1918, Ramanuja made history by becoming the first ever Indian to be elected a Fellow of Trinity College, Cambridge.
Ramanujan was born into a deeply religious Hindu family. Since his father spent most of the day at work, he was especially close to his mother. It was from her that he learned of the ancient Hindu tradition, learned to sing religious hymns, was encouraged to attend religious services at the local temples and learned the ways of the Brahmin (priestly) caste.
Ramanujan’s original refusal of Professor Hardy’s invitation to travel to England came about from his strict orthodox Hindu lifestyle, which prohibited him from travelling overseas. His parents also objected to this invitation, in accordance with their Brahmin upbringing.
However, his mother’s opposition was withdrawn after she received a dream from the family goddess, Namagiri, who told her not to stand in the way of her son and the fulfilment of his life’s purpose. Once he received her permission he promptly embarked on his journey that would bring him acclaim and establish his works among those of the world’s leading mathematical elite.
Following his deeply held beliefs, Ramanujan actually attributed his mathematical genius to this very same goddess, Namagiri. In fact he is known to have said,
“an equation for me has no meaning, unless it expresses a thought of God.”
Ramanujan was never a very healthy person and suffered from illness and health issues throughout his life. This was exacerbated while in England, since he was not used to the foreign environment. He spent time at a sanatorium, or hospital for long-term illness after he was diagnosed with tuberculosis and a severe vitamin deficiency. Following this, he returned to India in 1919 but sadly, he passed away just a year later in 1920. He was 32 years old at the time of his passing. Ramanujan was survived by his wife Srimathi Janaki. Following an examination of his medical records, some experts have argued that his tuberculosis diagnosis was mistaken. They claim that he actually suffered from hepatic amoebiasis, a disease that could have been treated and even cured at the time.
Given his legacy as a great mathematician whose formulas still form the basis of many advanced equations and theories, his life and work have been celebrated in many ways. In 1962, the 75th anniversary of his birth, the Government of India released a memorial postal stamp in remembrance of his life and deeds. A new design of the stamp was released in 2011.
Learning institutions such as Government Arts College in Kumbakonam and IIT Madras in Chennai celebrate his achievements annually on what is referred to as Ramanujan Day. Various prizes for young mathematicians have also been started in his name, for example by the International Centre for Theoretical Physics, the SASTRA University and the Vasavi College of Engineering.
On December 22, 2011, the 125th anniversary of his birth, the Government of India declared that December 22 would be celebrated as ‘National Mathematics Day’ every year in honour of Srinivasa Ramanujan.
