How did 12th pass Ramanujan, who knew 'infinite', baffled the world's greatest mathematician?

How did 12th pass Ramanujan, who knew ‘infinite’, baffled the world’s greatest mathematician?

Srinivasa Ramanujan: It is famous that Ramanujan could formulate a maths question in more than 100 ways. That’s why he got the status of the god of mathematics in the world. He was such an Indian who knew ‘Anant’. Let us study some important facts related to them in this article.

Srinivasa Ramanujan: Srinivasa Ramanujan was born on 22 December 1887 and was a great Indian mathematician. As we all know that Ramanujan did not get any special test in mathematics but still he contributed a lot in the areas of analysis and number theory. He is counted among the greatest mathematical thinkers of modern times. He proved with his hard work and constancy that nothing is impossible and made wonderful inventions in the field of mathematics.

National Mathematics Day is celebrated every year on 22 December to mark the birth anniversary of the great Indian mathematician, Srinivasa Ramanujan. At a very young age, Srinivasa Ramanujan emerged as an emerging genius and set an example, and contributed to mathematics in the fields of Faction, Infinite Series or Infinite Series, Number Theory, Mathematical Analysis, etc.

Mathematics is a big part of Ramanujan’s story. And mathematics has no language. In this, solving questions, doing previous, etc, have to be done.

Let’s look at an example: three plus three is six. We all know this, but if it is said that the former Tell me then. Now to do this, only maths It will take It can be told by giving examples, but this has to be done through mathematics. On the other hand, talking about Ramanujan, used to make equations without proofing. Let’s see.

How did Ramanujan make equations without proofing? Let’s know.

Ramanujan’s language was mathematics, mostly he used to invent equations and then tell them. But the veteran of modern mathematics needed proof. But Ramanujan did not take training in Modern Mathematics. When she first went to Cambridge, Hardy told him about the methods of modern maths. The Man Who Knew Infinity: A Life of the Genius Ramanujan is a biography of the Indian mathematician Srinivasa Ramanujan, written by Robert Kanigel.

This book is about his upbringing in India, his mathematical achievements and the mathematician gives a detailed account of his mathematical collaboration with G H. Hardy. The book also reviews Hardy’s life and the academic culture of the University of Cambridge during the early twentieth century.

About Srinivasa Ramanujan’s marriage and career in mathematics

In July 1909, he married Janakiammal. He became ill and had surgery around 1910. After his successful surgery, he looked for a job.

He also taught students at the Presidency College in Madras who were preparing for their Fellow of Arts examination. In 1910, he met V. Ramaswamy Iyer, who founded the Indian Mathematical Society.

His luck favored him and as a result, with Iyer’s help, his work was published in the Journal of the Indian Mathematical Society.

He got a job as an accounting clerk in the Madras Port Trust in 1912 and his financial situation improved. His intelligence and talent were slowly recognized And he began a correspondence with the British mathematician Godfrey H. Hardy in 1913, which led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.

Here is an interesting anecdote from January 1913. When G H Hardy arrived at Trinity College, Cambridge, he found some letters on his table. Hardy was a world-famous mathematician, so he used to get many letters every day. At the same time, a letter which he found on the table came from India. When he opened it, the theorem and mathematical symbols were filled one after the other. Some of these equations were such that Hardy had never seen before. In such a situation, Hardy felt that some fraud is sending something like this by writing, and then He put the letter aside. But that letter kept swirling in Hardy’s mind throughout the day.

Then coming back at night, Hardy looked at the letter again and called one of his friends, Littlewood. For a long time, both kept discussing the equations written in that letter. Both the professors kept trying to understand the theorem written in a notebook and then finally concluded that it could have been a genius to write these equations. Hardy was impressed by Ramanujan’s equations and then asked him to come to Cambridge.

Let us now know about his life in England.

He traveled to England in 1911, where Hardy tutored him. He collaborated with him on some research work. He brought his notebooks from India, which were filled with thousands of identities, equations, and theorems, which he wrote in 1903 In the years from 1914 had discovered for himself. Some were discovered by earlier mathematicians; Some were wrong due to inexperience, and many were completely new.

He had little formal training in mathematics. He spent about 5 years at Cambridge, together with Hardy and Littlewood, and published part or some of his findings there.

Major Works of Srinivasa Ramanujan

He worked in many areas, including the Riemann series, elliptical integrals, hypergeometric series, functional equations of zeta functions, and his theory of discrete series, using a technique in which he discovered a value for the sum of such series. And he came to be known as Ramanujan summation.

He also made several discoveries in England, mainly in the division of numbers into the various ways in which a positive integer can be expressed as the sum of positive integers. For example, 4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 = 1.

His papers were published in English and European journals. He was elected to the Royal Society of London in 1918 and became the second Indian. He was also selected “for his investigation of elliptical functions and the theory of numbers”.

In October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge. He is also known for Landau – Ramanujan constant, Mock theta functions, Ramanujan conjecture, Ramanujan prime, Ramanujan – Soldner constant, Ramanujan theta function, Ramanujan’s sum, Rogers – Ramanujan identities, Ramanujan’smaster theorem, and Ramanujan – Sato series.

1729 is known as the Hardy-Ramanujan number, and the generalization of this idea has led to the notion of “taxicab numbers”.

Illness and death of Srinivasa Ramanujan

In 1917, he was diagnosed with tuberculosis. His condition improved so that he could return to India in 1919. He died the following year i.e. April 1920. He left behind three notebooks and a few pages, also known as the “lost notebooks”, which contained various unpublished results. Mathematicians continued to confirm these results even after his death.

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