Introduction:
In the world of mathematics, many luminaries have made significant contributions to the field. Among them, Srinivasa Ramanujan stands out as a truly remarkable figure.
Born in humble surroundings in southern India, Ramanujan would go on to become one of the greatest mathematical minds of the 20th century.
Srinivasa Ramanujan, born on on December 22, 1887, and passed away on April 26, 1920 was an Indian mathematician who, despite lacking formal training in pure mathematics, made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions, solving problems that were previously thought to be unsolvable.
Ramanujan pursued his mathematical research independently and faced challenges in gaining recognition from professional mathematicians due to the novelty and unfamiliarity of his work. In 1913, he initiated a postal correspondence with G. H. Hardy, a prominent English mathematician at the University of Cambridge. Recognizing the extraordinary nature of Ramanujan’s work, Hardy facilitated his journey to Cambridge.
Life Death and Theorem
During his brief life, Ramanujan produced nearly 3,900 results, many of which were groundbreaking and unconventional.
His contributions, such as the Ramanujan prime, the Ramanujan theta function, partition formulae, and mock theta functions, opened new areas of mathematical exploration and inspired extensive research. Most of his results have since been proven correct, with only a few exceptions.
Ramanujan’s impact on mathematics led to the establishment of The Ramanujan Journal, dedicated to publishing work influenced by his ideas. His notebooks, containing summaries of both published and unpublished results, have been a source of inspiration for mathematicians. Even years after his death, researchers have uncovered profound number theory results hidden in his writings.
Despite facing ill health, likely due to hepatic amoebiasis, Ramanujan returned to India in 1919 and passed away at the age of 32 in 1920. His last letters to Hardy revealed that he continued to generate new mathematical ideas and theorems. The discovery of his “lost notebook” in 1976, containing findings from the last year of his life, generated excitement among mathematicians, highlighting the enduring legacy of this mathematical genius.
His unparalleled insights and extraordinary mathematical prowess continue to astonish and inspire mathematicians even today. In this article, we will delve into the life of Srinivasa Ramanujan, exploring both the chronological details of his life and the fascinating moments that shaped his extraordinary journey.
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Early Life and Sublime Intuition
From a young age, Ramanujan exhibited an extraordinary talent for numbers. His passion for mathematics was nurtured by his mother and a few mentors who recognized his prodigious abilities.
Ramanujan’s birthplace in Kumbakonam, TN
By the age of 11, he had surpassed the mathematical knowledge of two college students residing in his home. Introduced to advanced trigonometry through a book by S. L. Loney (a famous book used by JEE advance aspirants), Ramanujan mastered it by 13, discovering sophisticated theorems independently. At 14, he earned merit certificates and academic awards, showcasing his exceptional abilities in mathematics.
Ramanujan was so engrossed in mathematics that he hardly paid attention to other subjects. As a result, during his graduation from Pachaiyappa’s college in Madras, he performed poorly in other subjects, such as English, physiology, and Sanskrit. Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without an FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation.
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Self-Taught Genius
Ramanujan was largely self-taught in mathematics. He learned from a book called “A Synopsis of Elementary Results in Pure and Applied Mathematics” by George S. Carr. This book, which was essentially a compilation of mathematical theorems, sparked Ramanujan’s interest in the subject. He spent countless hours poring over the book, solving problems, and developing his own mathematical ideas. His insatiable curiosity and relentless determination led him to discover new theorems and formulas that were far beyond his years.
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Nature Conspires to help the true seeker (1910)
At 23, Ramanujan’s life transformed when he met Deputy Collector V. Ramaswamy Aiyer. Aiyer recognized Ramanujan’s brilliance, refusing to stifle it with a low-ranking job. With Aiyer’s introductions, Ramanujan gained support from R. Ramachandra Rao, enabling him to publish in the Journal of the Indian Mathematical Society.
Ramaswamy Aiyer, who saw a mathematician in Ramanujan
One of the first problems he posed in the journal was to find the value of:
He waited for a solution to be offered in three issues, over six months, but failed to receive any. At the end, Ramanujan supplied an incomplete solution to the problem himself.
Using this equation, the answer to the question posed in the Journal was simply 3, obtained by setting x = 2, n = 1, and a = 0
Acquaintance with British Mathematicians
With the help of friends, Ramanujan drafted letters to leading mathematicians at Cambridge University. The first two professors, H. F. Baker and E. W. Hobson, returned Ramanujan’s papers without comment. On 16 January 1913, Ramanujan wrote to G. H. Hardy. Coming from an unknown mathematician, the nine pages of mathematics made Hardy initially view Ramanujan’s manuscripts as a possible fraud. But with discussions with other professor friends, he concluded that the letters were “certainly the most remarkable I have received” and that Ramanujan was “a mathematician of the highest quality, a man of altogether exceptional originality and power”
Brahmins are forbidden to cross the seas
Hardy contacted the Indian Office to plan for Ramanujan’s trip to Cambridge. In accordance with his Brahmin upbringing, Ramanujan refused to leave his country to “go to a foreign land”. Meanwhile, he sent Hardy a letter packed with theorems, writing, “I have found a friend in you who views my labour sympathetically.”
Hardy’s correspondence with Ramanujan soured after Ramanujan refused to come to England. After few exchanges of mathematical proofs between them. Hardy enlisted a colleague lecturing in Madras, E. H. Neville, to mentor and bring Ramanujan to England.
Cambridge and Life in England
In came Ramanujan’s journey to Cambridge in 1913 was both exciting and challenging. Adjusting to the new cultural and academic environment posed initial difficulties, but Ramanujan soon found his place alongside other acclaimed mathematicians. Under Hardy’s guidance, Ramanujan’s mathematical insights flourished, leading to groundbreaking discoveries.
Ramanujan and Hardy’s collaboration resulted in significant contributions to number theory, infinite series, and continued fractions. Their work was published in renowned mathematical journals, and their methods challenged conventional mathematical thinking. One of their most remarkable achievements was Ramanujan’s formula for the partition function, revolutionizing the understanding of integers and partitions.
Ramanujan was awarded a Bachelor of Arts by Research degree (the predecessor of the PhD degree) in March 1916 for his work on highly composite numbers.
On 6 December 1917, Ramanujan was elected to the London Mathematical Society. On 2 May 1918, he was elected a Fellow of the Royal Society, the second Indian admitted, after Ardaseer Cursetjee in 1841. At age 31, Ramanujan was one of the youngest Fellows in the Royal Society’s history. He was elected “for his investigation in elliptic functions and the Theory of Numbers.” On 13 October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.
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Return to India and Tragic Legacy (1919-1920):
Although he excelled in mathematics there but his health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion there and because of wartime rationing in 1914–18. He was diagnosed with tuberculosis and a severe vitamin deficiency. In 1919, Ramanujan’s declining health and longing for his homeland led him to return to India. Despite his severe illness & pain, he continued to produce an astonishing amount of mathematical work with his inspiration from his family Goddess. Tragically, Ramanujan’s brilliance was cut short as he passed away on April 26, 1920, at the age of 32.
Famous anecdotes in Ramanujan’s life:
Taxicab number
The number 1729 is known as the Hardy–Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital. In Hardy’s words
“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 unfavourable 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.”
Immediately before this anecdote, Hardy quoted Littlewood as saying, “Every positive integer was one of [Ramanujan’s] personal friends.”
The two different ways are:
1729 = 13+123 = 93 +103
Generalisations of this idea have created the notion of “taxicab numbers”. In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729.
Unexplained Intuitions from Goddess
One of the most captivating aspects of Ramanujan’s work was his unexplained intuitions and extraordinary ability to arrive at solutions without detailed proofs. His notebooks comprise thousands of equations, theorems, and conjectures, many of which are yet to be fully understood by mathematicians.
He credited his acumen to his family goddess, Namagiri Thayar (Goddess Mahalakshmi). He looked to her for inspiration in his work and said he dreamed of blood drops that symbolised her consort, Narasimha. Later he had visions of scrolls of complex mathematical content unfolding before his eyes. He often said, “An equation for me has no meaning unless it expresses a thought of God.”
Ramanujan’s “Lost notebook”
This book is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries in the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Library at Trinity College.
Bruce C. Berndt says of the notebook’s discovery: “The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.
“An equation for me has no meaning unless it expresses a thought of God”
Several articles and biopics will come and go, but what lingers in the mind is this quote in the book from Ramanujan. One might contextualize this in terms of Ramanujan’s religious devotion to the family goddess in Namakkal. Alternatively, one could interpret it as a belief that genuine inspiration for work arises only when there is at least a suggestion of deeper meaning, when the mind engages with, or exists within, something larger.
Perhaps Ramanujan tapped into a spiritual well from which numbers flowed forth – what else could explain the fact that a man with no formal training in high mathematics produced such complex and significant work?
What we conclude from this line is that when Ramanujan started solving mathematics he got into the ‘State of flow’ (explained beautifully in the book Ikigai). This state of flow leads a person into the zone. A zone is state where no though exists. The person does work completely based on intuitive inspiration from a higher alter of belief.
Commemorative postal stamps by Government of India
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Conclusion
Although Ramanujan was a prodigy, his life would not have found completion without the intervention of two people, Ramaswamy Aiyer and Godfrey Hardy. They were Ramanujan Guru’s in disguise who connected him with opportunities at the right time. The role of such people often serves like a point in our life. We are sure you must have encountered such people in your life. Who are they? Let’s take a moment to express gratitude towards them.
