Up to which extent a human can think? Quite a lot…? Right…? We have so many examples like Isaac Newton, Albert Einstein and many more. They have given so much to the mankind. Fortunately, they had a long time to provide their knowledge and experience but the man, Srinivasa Ramanujan hadn’t much time in their life but the knowledge he shared is remarkable and unmatched. He can play with numbers in his own. So without any further ado, let’s get started.
Srinivasa Ramanujan was born on December 22, 1887, in a town called Erode, in Tamil Nadu, India. His father K. Srinivasa Iyengar, was an accounting clerk. His mother Komalatammal was a singer at the local temple. Although his family was a high caste of Brahmins, yet they were very poor.
Due to this fact, Ramanujan’s family moved around a lot, and he attended a variety of different elementary schools. He was the top student at the age of 10, not just in his school, but in his district. He was very bright in Maths but not in others.
In 1903 he secured a scholarship to the University of Madras. But he failed in his non-mathematical exams and lost his scholarship. In 1905 he traveled to Madras and enrolled at Pachaiyappa’s College, but again failed his non-mathematical exams.
At 15, he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880–86). This collection of thousands of theorems, many presented with only the briefest of proofs and with no material newer than 1860, aroused his genius. Having verified the results in Carr’s book, he went beyond it, developing his own theorems and ideas.
He continued his work, without employment and living in the poorest circumstances. He was married to 9-year-old Janaki Ammal in 1909. Then he began a search for permanent employment. During an interview with a government official, Ramachandra Rao. He impressed by his mathematical prowess. He supported his research a lot.
Journey to Cambridge, England
In 1911 Ramanujan published his first paper in the Journal of the Indian Mathematical Society. His genius slowly gained attention and recognition, and in 1913 he began a correspondence with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.
He traveled to England in 1914, where Hardy tutored him and collaborated with him in some research. During their subsequent five-year mentorship, Hardy provided him the formal framework to prosper his knowledge of numbers.
He published more than 20 papers on his own and more in collaboration with Hardy. He was awarded a Bachelor of Sciences for research from Cambridge in 1916 and in 1918 became a member of the Royal Society of London.
Note: Since the Royal Society’s foundation in 1660, about 8,000 Fellows have been elected, with persons of Indian origin numbering about 60. Srinivasa Ramanujan was the second Indian to be inducted, in 1918, the first being Ardaseer Cursetjee, an engineer, in 1841.
A natural genius
His knowledge of mathematics was something out of the box. Although he was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician.
He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series.
On the other hand, he knew nothing of doubly periodic functions, the classical theory of quadratic forms, or Cauchy’s theorem, and he had only the most nebulous idea of what constitutes a mathematical proof. Though brilliant, many of his theorems on the theory of prime numbers were wrong.
He used to say that all these ideas come up in his mind in the dreams. The God put all these ideas in his mind, and he wrote down it in his notebook. It’s hard to believe but on seeing his whole work, it can’t be ignored completely because most of his theorems were without proofs yet proved right later. Whatever the logic, but the fact is we have founded so much by his courtesy.
In 1917 he diagnosed of tuberculosis. He returned to India in 1919. He died the following year, generally unknown to the world at large but recognized by mathematicians as a phenomenal genius.
He left behind three notebooks and a sheaf of pages (also called the “lost notebook”) containing approximately 4000 claims, all without proofs. Most of the claims have now been proved. Many unpublished results that mathematicians continued to verify long after his death.
1729 is the natural number known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Ramanujan in hospital. He related their conversation:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”
The two different ways are: 1729 = 1³ + 12³ = 9³ + 10³
Some amazing and interesting facts about him
- His house in Kumbakonam is now maintained as the Srinivasa Ramanujan International Monument.
- He is recognized as one of the greatest mathematicians of his time, but he had almost no formal training in math.
- He was the second Indian to be inducted as a Fellow of the Royal Society. A group of eminent scientists.
- He compiled 3,900 results (mostly identities and equations). His infinite series for pi was one of his most celebrated findings.
- There is also a museum dedicated to telling Ramanujan’s life story. It is located in Chennai.
- His birth anniversary, December 22, is celebrated as the National Mathematics Day every year.
- 1729 is known as the Hardy-Ramanujan number.
The man who knew infinity
He died on April 26, 1920, at the early age of 32. And even on his deathbed, he wrote down a group of theorems that he said had come to him in a dream. These and many of his earlier theorems are so complex that the full scope of his legacy has yet to be completely revealed and his work remains the focus of much mathematical research. His collected papers were published by Cambridge University Press in 1927.
A biography of Ramanujan titled “The Man Who Knew Infinity” was published in 1991 and a movie of the same name premiered in September 2015 at the Toronto Film Festival.
“It was his insight into algebraical formulae, transformations of infinite series, and so forth that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi.”
“I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.”
G. H. Hardy, 1877 – 1947 (Mathematician)
“Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.”
Paul Erdos, 1913 – 1996 (Mathematician)
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