The great mathematician Ramanujan

Famous French mathematician Laplace wrote his book ‘Cosmological-kinetics’. When Napoleon met, Napoleon asked him, “How surprising that you wrote such a great book on the Universe and that the ‘Creator of the Universe’ is not mentioned even once?” Laplace replied simply, ‘Manyavar, the principles propounded in my text do not require that’ hypothesis’. “

But the matter was different for Ramanujan. There was no talk of any great divine power, Ramanujan also believed in village deities. But it was not just faith. He used to say that a village-goddess named Namagiri helps him in his dreams and extracts mathematical formulas. As far as I believe, Ramanujan could never make it clear how the ‘help’ of the Goddess was in the form, through which medium.

I do not want to get into the field of psychoanalysis, but this help of Deviji to Ramanujan is a puzzle to me and will probably remain. The problem is for the Tarun mathematicians who do not want to allow the gods and goddesses to enter the field of science. How nice it would be if these innumerable deities also help those who do not believe in them. I think they are also compassionate, otherwise all progress would stop.

Whatever Ramanujan’s own beliefs were, he was undoubtedly a great mathematician. He has a prominent place among the mathematicians of the twentieth century, not only in India but among the great mathematicians of the world. The difficulty with which Ramanujan has served Mathematics is an ideal for us. It will not be possible to discuss his mathematical principles in detail here, as he is also a ‘mathematician of mathematicians’.

Srinivasa Ramanujan Iyengar was born on 22 December 1887 in a poor Brahmin family. His father was an ordinary bookkeeper at a cloth merchant’s shop in Kumbakonam (Tanjore district, Madras). When they had no children for a long time after marriage, Ramanujan’s maternal grandmother accepted the nomination of a village-goddess named Namagiri. A few days later Ramanujan was born.

Ramanujan’s early education was in the high school of Kumbakonam. Always been first in primary classes. He was calm by nature and had a great memory. He used to entertain his peers with mathematics puzzles. In those days it was very difficult to get books of mathematics. When Ramanujan was studying in high school, one of his benefactors brought him a book titled ‘Synopsis of Pure Mathematics’ by Kar Mahashi. What was then Ramanujan forgot day and night. Through this book, he first discovered some formulas of arithmetic, then moved towards geometry. At the same time, he independently found the exact length of the equatorial circle of the earth. He then progressed to algebra. Because Ramanujan was the only book of higher accounting, there were some of the formulas he researched that were already known to mathematicians. But this does not reduce the importance of Ramanujan’s independent soj in any way.

In 1903, at the age of 16, Ramanujan passed the matriculation examination. They also started getting scholarships. He was weak in other subjects, as he used to devote all his time to mathematics. Therefore, Ramanujan failed the exam as a result and lost his scholarship. The condition of the house was already bad, so he moved to Madras. In 1907, he again sat for examination, but again failed. After this, he never sat the exam again. He continued to study mathematics independently.

Ramanujan married in 1909. Now it became necessary for him to do the job. Ramanujan was introduced to Dewan Bahadur Ramchandra Rao in connection with job search. Ramachandra Rao was the collector of Nellore and was a lover of mathematics. He describes his first meeting with Ramanujan in the following words: “A few years ago my nephew, who has no knowledge of mathematics, came to me and said, I know a man who always does mathematics. Discusses. I don’t understand anything. ‘ Due to my love for mathematics, I allowed Ramanujan to be present. A small, thin, somewhat filthy, but shining in the eyes and holding a notebook in his side, a statue appeared in front of me. It was clear That his condition was very pathetic. He had moved from Kumbakonam to Madras for the purpose of keeping his mathematical studies going. He had no more desires. Just, he wanted so much convenience. He should get the food, so that no obstacle to rum in your dreams.

“He opened his notebook and started explaining some of the formulas to me. I immediately understood that there was something special about them, but because of my little knowledge of mathematics, taking Ramanujan’s form was out of my grasp. Without making some decisions, I gave it again. Asked to come and he came too. But this time he took some easy work in front of me, because he had evaporated my math-related little knowledge. Gradually he gave me his hard work. Mle is also explained. Finally, she asked to keep the current study mathematics he only wants some insouciance. “

For some time, Ramchandra Rao took Ramanujan’s own car. Getting Diwati became difficult. But Ramanujan did not want to be a burden on anyone. In the end, he accepted a job of 30 rupees monthly in the office of Madras Port Trust. But there was no shortage of Ramanujan’s study of mathematics. His first article in 1911 was the mouthpiece of the Mathematical Society

Published in At this time Ramanujan was 23 years old. The following year he used two articles in Ini Patra. With the influence of Ramachandra Rao, the various head of Madras Engineering Palij and Chairman of Madras Port Trust, Sir Fasim Spring assisted Ramanjan greatly. At that time, Dr. Hockey was the talk of the emerging mathematicians of England. Ramanujan started correspondence in Sahari with the advice of the beneficiaries. His first letter to Nigam Harty on January 16, 1913 was as follows:

“greetings,

I am an ordinary-clerk in the Madras Port-office. Could not achieve in the high hill of the university, but had studied in the school. Since leaving school, he has given his free time to mathematics. Although I am not familiar with the mathematics in the university, I have independently discovered some principles in mathematics. I have discovered some new theories related to the divergent series. Local mathematicians believe that my research is ‘amazing’.

I am sending my research with this letter sincerely request you to see my articles. I am a poor Indian. If there is any novelty in my articles, then you will definitely help in their publication. You are the knower of that subject. Your inspiration will inspire me. I apologize for the pain.

                                     Respectful

                                     Ramanujan “

With this letter, Ramanujan wrote to Dr. Hardy sent 120 of his theorems. Some of these were already known to mathematicians. But some of these were also theorems, which could be the product of the wisdom of an extraordinary mathematician. Dr. Hardy was very impressed by these theorems and he arranged for their publication.

Finally, in May 1913, Ramanujan received a special scholarship with the help of friends and was also freed from the Madras Port-Trust. On the other hand, Hardy started trying to call Sir Ramanujan in England. But the caste people hindered them from going abroad. In the end, he got permission to go abroad in a strange way. One day in the morning his mother said that he had dreamed at night, in which he saw that his son is sitting among the white people in a very big hall and Namgiri Devi has also ordered that the son’s foreign trip hinders Do not be. Meanwhile, the University of Madras accepted a 250 pound annual scholarship for Ramanujan to go abroad. Ramanujan left for England on 17 March 1914, after obtaining mother’s permission and making some arrangements for him from his scholarship.

Ramanujan reached England, but a new problem arose in front of Dr. Hardy. How to guide this person? There were some appendices of Mathematics over which Ramanujan had full authority, but there were some preliminary things about which he had little knowledge. Teaching mathematics to a genius like Ramanujan was futile. So Hardy himself took responsibility for his guidance. Yet Dr. Hardy finally admitted – “I learned more from him than I taught Ramanujan.”

Even while living in England, Ramanujan remained an Indian by food and behavior. They used to make food with their own hands – vegetarian food used to do so much mental percolation that it was natural to have health effects in the end. In 1917, signs of tuberculosis started appearing. He was admitted to the hospital in Cambridge. Here, his reputation had increased considerably due to his articles being published in high-quality newspapers and magazines. Finally, the famous ‘Royal Society’ of England made Ramanujan as his Fellow on 28 February 1918. This gave him even more enthusiasm and taking care of his health, he started busy in research.

In 1919, Ramanujan returned home after the end of the First World War. For the sake of health, he was kept in Kodmandi village on the Kaveri coast, but there was no improvement in health. Finally, on 26 April 1920, at the young age of only 33, this great mathematician gave up his life.

Ramanujan was a pure mathematician. All his research is related to numerology. Just as mathematics itself has a prominent position in all the sciences, similarly numerology has a prominent place in mathematics. Well, since the beginning of civilization, man has been counting with natural numbers, but since the beginning of mathematicians, it has been the endeavor to know such rules related to numbers like 1, 2, 3, 4, 5 which are not one or two, To be equally applicable to all numbers.

In numerology, we are not only concerned with one or two numbers (eg 6 can be divided exactly by 2), but consider whole numbers together (eg all numbers can be exactly divided by 2). is) . You may find these decisions to be very easy, but when the question of proving them arises, mathematicians have to go very deep. For example, we can take the approximation given by Goldbach: Give every even number greater than 2. Akhand is the sum of numbers, thus 4 is the sum of two non-numeric numbers 2 and 2, 6 is the sum of two non-numeric numbers 3 and 3, 8 is the sum of two non-numeric numbers 3 and 5, and so on. Scrum will go on. But by giving many similar written examples it does not prove that all the numbers are the sum of two non-numeric numbers. However, no such example has been found so far that can prove the ‘Goldbach’s conjecture’ wrong.

Another question of numerology, which Ramanujan had to solve, is related to division of whole numbers. Take any whole number, such as 33; We can write it in three different forms – 3 + 0, 1 + 2, 1 + 1 + 1. You can easily know that you cannot reveal this number in any other division. Similarly, you can express 4 in 5 different forms – 4 + 0, 3 + 1, 2 + 2, 2 + 1 + 1, 1 + 1 + 1 + 1. There can be no other form other than this. But it is a matter of small numbers. What would you do if you had a huge number like 7,80,00,000 instead of 3? We have to find a well-known formula that can reveal different divisions of all numbers, big or small. In 1917, Ramanujan discovered a similar formula.

Ramanujan was in fact a member of the mathematics class that considers mathematics as a game. Just as a game has its own rules, similarly in mathematics, a type of game is played with symbols like 1, 3, +, -, =. He does not make sense of the utility of this mathematics.

Referring to Ramanujan’s mathematical research, Dr. Hardy wrote, “People have asked me many times whether Ramanujan had any magic? Did his methods differ from other mathematicians? Was his thinking system different from others Thi? I have no exact answer to all these questions. I believe that by going deep down, all mathematicians think the same way and Ramanujan is no exception to this. Sector. Those with scores that play like a professional player. ” I remember Dr. Littlewood once said – “He (Ramanujan) has a deep friendship with every issue.” Is a one-time event. Ramanujan was in the hospital at that time and I went to see him. The taxi number was 1729. On meeting Ramanujan, I said that this is an inauspicious number, (this number is a factor 13, and by tradition this number has been considered inauspicious. But Ramanujan quickly replied – ‘No, this is a wonderful Is a number. It is the smallest number that we can express in two different forms using the sum of two positive numbers.

1729 = 7 × 13 × 19

           = 12³ + 1³

           = 10³ + 9³

In 1926, Cambridge University Press edited Ramanujan’s essays from Dr. Hardy. Dr. Hardy wrote at one place in his life introduction:

“Ramanujan’s life seems to be full of contradictions and protests. Each other’s wisdom patterns fail in their relationship. The only thing we agree about him is that he was a great mathematician.

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