essay on great mathematician srinivasa ramanujan

Essay on Srinivasa Ramanujan

500 words essay on srinivasa ramanujan.

Srinivasa Ramanujan is one of the world’s greatest mathematicians of all time. Furthermore, this man, from a poor Indian family, rose to prominence in the field of mathematics. This essay on Srinivasa Ramanujan will throw more light on the life of this great personality.

                                                                                             Essay On Srinivasa Ramanujan

Early Life of Srinivasa Ramanujan

Ramanujan was born in Erode on December 22, 1887, in his grandmother’s house.  Furthermore, he went to primary school in Kumbakonamwas when he was five years old.  Moreover, he would attend several different primary schools before his entry took place to the Town High School in Kumbakonam in January 1898.

At the Town High School, Ramanujan proved himself as a talented student and did well in all of his school subjects. In 1900, he became involved with mathematics and began summing geometric and arithmetic series on his own.

In the Town High School, Ramanujan began reading a mathematics book called ‘Synopsis of Elementary Results in Pure Mathematics’. Furthermore, this book was by G. S. Carr.

With the help of this book, Ramanujan began to teach himself mathematics . Furthermore, the book contained theorems, formulas and short proofs. It also contained an index to papers on pure mathematics.

His Contribution to Mathematics

By 1904, Ramanujan’s focus was on deep research. Moreover, an investigation took place by him of the series (1/n). Moreover, calculation took place by him of Euler’s constant to 15 decimal places. This was entirely his own independent discovery.

Ramanujan gained a scholarship because of his outstanding performance in his studies. Consequently, he was a brilliant student at Kumbakonam’s Government College. Moreover, his fascination and passion for mathematics kept on growing.

In the spring of 1913, there was the presentation of Ramanujan’s work to British mathematicians by Narayana Iyer, Ramachandra Rao and E. W. Middlemast. Afterwards, M.J.M Hill did not made an offer to take Ramanujan on as a student, rather, he provided professional advice to him. With the help of friends, Ramanujan sent letters to leading mathematicians at Cambridge University and was ultimately selected.

Ramanujan spent a significant time period of five years at Cambridge. At Cambridge, collaboration took place of Ramanujan with Hardy and Littlewood. Most noteworthy, the publishing of his findings took place there.

Ramanujan received the honour of a Bachelor of Arts by Research degree in March 1916. This honour was due to his work on highly composite numbers, sections of the first part whose publishing had taken place the preceding year. Moreover, the paper’s size was more than fifty pages long.

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Conclusion of the Essay on Srinivasa Ramanujan

Srinivasa Ramanujan is a man whose contributions to the field of mathematics are unmatchable. Furthermore, experts in mathematics worldwide all recognize his tremendous worth. Most noteworthy, Srinivasa Ramanujan made his country proud at a time when India was still under British occupation.

FAQs For Essay on Srinivasa Ramanujan

Question 1: What is Srinivasa Ramanujan famous for?

Answer 1: Srinivas Ramanujan is famous for his discoveries that have influenced several areas of mathematics. Furthermore, he is famous for his contributions to number theory and infinite series. Moreover, he came up with fascinating formulas that facilitate in the calculation of the digits of pi in unusual ways.

Question 2: What is the special quality of number 1729 discovered by Srinivasa Ramanujan?

Answer 2:  Srinivas Ramanujan discovered that the number 1729 had a special characteristic.  Furthermore, this quality is that the number 1729 is the only number whose expression can take place as the sum of the cubes of two different sets of numbers. Consequently, people call 1729 the magic number.

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Essay on Srinivasa Ramanujan for Students | 500+ Words Essay

December 10, 2020 by Sandeep

Essay on Srinivasa Ramanujan: Srinivasa Ramanujan was a renowned mathematician of India. He was born on 22nd December 1887 in Madras during the British Raj. Since childhood, he was drawn towards maths and took a particular interest in learning the subject. He did not receive formal education in mathematics but had mastered maths in various sections. During his time in Cambridge, he grew close to the great mathematician named Hardy. Together they invented the Hardy-Ramanujan number 1729. He got married at the age of 22 to Janakiammal on 14th July 1904. Several books were written by him based on his theories and formulas. He even received the K. Ranganatha Rao prize for mathematics. On 26th April 1920, he departed at the age of 32.

Below we have provided an essay on Srinivasa Ramanujan in English, written in easy and simple words for class 4, 5, 6, 7, 8, 9 and 10 school students.

Essay on Srinivasa Ramanujan 500 Words in English

Below we have provided extended essay on Srinivasa Ramanujan, suitable for classes 7, 8, 9 and 10 students.

Ramanujan was the maths genius who said that “An equation for me has no meaning unless it expresses a thought of God.” He always had a vision of scrolls of complicated maths unfolding before him. He is referred to as an Indian Mathematician who lived during the British period and who contributed substantially to mathematics analysis, number theory, infinite series and continued fractions. He has been described by many as a simple person with pleasant manners.

Ramanujan was born on 22nd December 1887 into a Tamil Brahmin family in Erode, Madras. His father, Kuppuswamy Srinivasa Iyengar hailed from Thanjavur district and worked as a clerk in a saree shop. His mother, Komalatammal, was a housewife and used to sing at a local temple. They lived in a small traditional home. When Ramanujan was only a year and a half old, his mother was blessed with a son named Sadagopan but unfortunately died less than three months later.

In 1889, Ramanujan contracted smallpox but recovered, unlike many others who faced the death. Then, in 1891 and 1894, his mother again gave birth to two more children, but both of them died before their first birthdays. Since his father was at work most of the day, his mother took care of him, and their bond grew stronger. From his mother he learnt about the tradition and Puranas, to sing religious songs and to attend puja at a temple.

He became well versed with the Brahmin culture and followed particular eating habits. Just before turning ten, he passed his primary education in English, Tamil, geography and arithmetic. His scores were the best in the district. In the same year, he encountered formal mathematics for the first time. At the age of sixteen, he acquired a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics from a friend.

He studied the contents of the book thoroughly. The next year, he developed and investigated the Bernoulli numbers and calculate Euler’s constant up to 15 decimals. His peers could hardly understand his nature, and we’re always in awe because of his brilliance. Due to his extraordinary mind, he received a scholarship to study at Government Arts College, Kumbakonam. But he lost this scholarship because of his firm determination towards studying only maths and ignoring other subjects.

Later, too he failed in subjects like English, Sanskrit and physiology. In 1906, he flunked in his Fellow of Arts exam in December. Without a FA degree, he left college and decided to study independently in mathematics through research and referring books. Such a condition caused him extreme poverty, and he reached on the brink of starvation. He married Janakiammal on 14th July 1909 and took a job as a tutor at Presidency College.

Ramanujan met deputy collector V. Ramaswamy Aiyer in 1910, who was the founder of Mathematical society and wished to work in the revenue department. When Ramanujan showed his mathematics book to him, he stated that- “I was struck by the extraordinary mathematical results contained in Ramanujan’s books.” As he advanced further in maths, he even wrote his formal paper on the properties of Bernoulli numbers.

A journal editor M.T. Narayana Iyengar noted that Mr Ramanujan’s methods and presentation was terse and lacked precision and clearness. An ordinary person could hardly follow him. In England, he was awarded a Bachelor of Arts by Research degree. He was also elected to the London Mathematical Society. Ramanujan was the first Indian to be elected a Fellow of Trinity College, Cambridge.

In 1994, he died due to Tuberculosis and left the world. In the words of Hardy, Ramanujan had produced groundbreaking theorems and defeated him many times. He had never seen such theories in his life before. In his obituary, it was written that his insight into the subject was terrific and what he did was outstanding and remarkable.

The government of India in 2011, declared his birthday as National Mathematics Day to commemorate his valuable contribution and efforts. The former President even proclaimed that 2012 would be celebrated as National Mathematics Year.

Also Read – Republic Day Speech 2022 in English

Short Essay on Srinivasa Ramanujan in 250 Words

Below we have provided a short essay on Srinivasa Ramanujan, suitable for class 3, 4, 5 & 6 students.

Srinivasa Ramanujan was a well-known Indian Mathematician who was born on 22nd December 1887 during the British rule. He was born in a poor Indian village, Erode belonging to a Tamil family. His father’s name was Kuppuswamy Srinivas Aiyangar who worked as a clerk in a saree shop, and his mother was a religious housewife. They lived in Erode only for a year and then moved to Kumbakonam.

In this small town, Ramanujan attended many primary schools and achieved a distinction in his primary education. At the age of thirteen, he focused his attention on the sum of geometric an arithmetic series and in 1902, he created a method to solve quadratic equations and even explored Euler’s Constant. In the same year, he received a scholarship for his outstanding performance in his studies, and therefore he got admission at Kumbakonam’s Government college.

His passion for mathematics grew more robust, and hence he excelled in maths but failed in other subjects. The failure caused him depression, and he fled to Vizagapatnam without telling his parents. One year later, he returned to study and pass at First Art’s examination but again failed in all and passed in maths. Ramanujan got married to his old distant relative Janaki Ammal.

Furthermore, he published his first paper based on Bernoulli numbers in Journal of the Indian Mathematical Society and received recognition and achievement. His hard work got paid off, and he was appointed as a clerk at Madras Port Trust. At this time, he became famous throughout Madras and caught the attention of C.L.T Griffith who helped Ramanujan. Later, Ramanujan graduated from London and held a degree of Science for research on highly composite numbers.

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Srinivasa Ramanujan (1887-1920) was an Indian mathematician who made great and original contributions to many mathematical fields, including complex analysis , number theory , infinite series , and continued fractions . He was "discovered" by G. H. Hardy and J. E. Littlewood, two world-class mathematicians at Cambridge, and enjoyed an extremely fruitful period of collaboration with them from 1914 to 1919. Unfortunately, his mathematical career was curtailed by health problems; he returned to India and died when he was only 32 years old.

Hardy, who was a great mathematician in his own right, recognized Ramanujan's genius from a series of letters that Ramanujan sent to mathematicians at Cambridge in 1913. Like much of his writing, the letters contained a dizzying array of unique and difficult results, stated without much explanation or proof. The contrast between Hardy, who was above all concerned with mathematical rigor and purity, and Ramanujan, whose writing was difficult to read and peppered with mistakes but bespoke an almost supernatural insight, produced a rich partnership.

Since his death, Ramanujan's writings (many contained in his famous notebooks) have been studied extensively. Some of his conjectures and assertions have led to the creation of new fields of study. Some of his formulas are believed to be true but as yet unproven.

There are many existing biographies of Ramanujan. The Man Who Knew Infinity , by Robert Kanigel, is an accessible and well-researched historical account of his life. The rest of this wiki will give a brief and light summary of the mathematical life of Ramanujan. As an appetizer, here is an anecdote from Kanigel's book.

In 1914, Ramanujan's friend P. C. Mahalanobis gave him a problem he had read in the English magazine Strand . The problem was to determine the number \( x \) of a particular house on a street where the houses were numbered \( 1,2,3,\ldots,n \). The house with number \( x \) had the property that the sum of the house numbers to the left of it equaled the sum of the house numbers to the right of it. The problem specified that \( 50 < n < 500 \).

Ramanujan quickly dictated a continued fraction for Mahalanobis to write down. The numerators and denominators of the convergents to that continued fraction gave all solutions \( (n,x) \) to the problem \((\)not just the particular one where \( 50 < n < 500). \) Mahalanobis was astonished, and asked Ramanujan how he had found the solution.

Ramanujan responded, "...It was clear that the solution should obviously be a continued fraction; I then thought, which continued fraction? And the answer came to my mind."

This is not the most illuminating answer! If we cannot duplicate the genius of Ramanujan, let us at least find the solution to the original problem. What is \( x \)?

\(\) Bonus: Which continued fraction did Ramanujan give Mahalanobis?

This anecdote and problem is taken from The Man Who Knew Infinity , a biography of Ramanujan by Robert Kanigel.

Taxicab numbers, nested radicals and continued fractions, ramanujan primes, ramanujan sums, the ramanujan \( \tau \) function and ramanujan's conjecture.

Many of Ramanujan's mathematical formulas are difficult to understand, let alone prove. For instance, an identity such as

\[\frac1{\pi} = \frac{2\sqrt{2}}{9801}\sum_{k=0}^{\infty} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\]

is not particularly easy to get a handle on. Perhaps this is why the most famous mathematical fact about Ramanujan is trivial and uninteresting, compared to the many brilliant theorems he proved.

The story goes that Hardy was visiting Ramanujan in the hospital, and remarked offhandedly that the taxi he had taken had a "dull number," 1729. Instantly Ramanujan replied, "No, it is a very interesting number! It is the smallest positive integer expressible as the sum of two positive cubes in two different ways."

That is, \( 1729 = 1^3+12^3 = 9^3+10^3 \).

Hardy and Wright proved in 1938 that for every \( n \), there is a positive integer \( \text{Ta}(n) \) that is expressible as the sum of two positive cubes in \( n \) different ways. So \( \text{Ta}(2) = 1729 \). \((\)The value of \( \text{Ta}(2) \) had been known since the \(17^\text{th}\) century, which is in some sense characteristic of Ramanujan as well: as he was largely self-taught, he was often rediscovering theorems that were already well-known at the same time as he was constructing entirely new ones.\()\) The numbers \( \text{Ta}(n) \) are called taxicab numbers in honor of Hardy and Ramanujan.

Ramanujan developed several formulas that allowed him to evaluate nested radicals such as \[ 3 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}}. \] This is a special case of a result from his notebooks, which is proved in the wiki on nested functions .

He also contributed greatly to the theory of continued fractions . One of the identities in his letter to Hardy was \[ 1+\frac{e^{-2\pi}}{1+\frac{e^{-4\pi}}{1+\frac{e^{-6\pi}}{\cdots}}} = \left( \sqrt{\frac{5+\sqrt{5}}2} - \frac{1+\sqrt{5}}2 \right)e^{2\pi/5}. \] This and several others along these lines were among the results that convinced Hardy that Ramanujan was a brilliant mathematician. This result is in fact a special case of the Rogers-Ramanujan continued fraction , which is of the form \[ R(q) = \frac{q^{1/5}}{1+\frac{q}{1+\frac{q^2}{1+\frac{q^3}{\cdots}}}} \] and is related to the theory of modular forms, a deep branch of modern number theory.

Ramanujan's work with modular forms produced the following celebrated divisibility results involving the partition function \( p(n) \): \[ \begin{align} p(5k+4) &\equiv 0 \pmod 5 \\ p(7k+5) &\equiv 0 \pmod 7 \\ p(11k+6) &\equiv 0 \pmod{11}. \end{align} \] Ramanujan commented in the paper in which he proved these results that there did not appear to be any other simple results of the same type. But in fact there are similar congruences of the form \( p(ak+b) \equiv 0 \pmod n \) for any \( n \) relatively prime to \( 6\); this is due to Ken Ono (2000). (Even for small \( n\), the values of \( a \) and \( b \) in the congruences are quite large.) The topic remains the subject of much contemporary research.

Ramanujan proved a generalization of Bertrand's postulate , as follows: Let \( \pi(x) \) be the number of positive prime numbers \( \le x \); then for every positive integer \( n \), there exists a prime number \( R_n \) such that \[ \pi(x)-\pi(x/2) \ge n \text{ for all } x \ge R_n. \] \((\)The case \( n = 1 \), \( R_n = 2 \) is Bertrand's postulate.\()\)

The \( R_n \) are called Ramanujan primes .

The sum \( c_q(n) \) of the \(n^\text{th}\) powers of the primitive \( q^\text{th}\) roots of unity is called a Ramanujan sum . It can be shown that these are multiplicative arithmetic functions , and in fact that \[c_q(n) = \frac{\mu\left(\frac qd\right)\phi(q)}{\phi\left(\frac qd\right)},\] where \( d = \text{gcd}(q,n)\), and \( \mu \) and \( \phi \) are the Mobius function and Euler's totient function , respectively.

Let \(c_{2015}(n)\) be the sum of the \(n^\text{th}\) powers of all the primitive \(2015^\text{th}\) roots of unity, \(\omega.\) Find the minimal value of \(c_{2015}(n)\) for all positive integers \(n\).

This year's problem

Ramanujan found nice infinite sums of the form \( \sum a_n c_q(n) \) or \( \sum a_q c_q(n) \) representing the standard arithmetic functions that are important in number theory. For instance, \[ d(n) = -\frac1{2\gamma+\ln(n)} \sum_{q=1}^{\infty} \frac{\ln(q)^2}{q} c_q(n), \] where \( \gamma \) is the Euler-Mascheroni constant .

Another example: the identity \[ \sum_{q=1}^{\infty} \frac{c_q(n)}{q} = 0 \] turns out to be equivalent to the prime number theorem .

Sums involving \( c_q(n) \) are known as Ramanujan sums ; these were also used in applications including the proof of Vinogradov's theorem that every sufficiently large odd positive integer is the sum of three primes.

Ramanujan's \( \tau \) function is defined by the formula \[ \sum_{n=1}^{\infty} \tau(n) q^n = q\prod_{n=1}^{\infty} (1-q^n)^{24} \] and is related to the theory of modular forms.

Ramanujan conjectured several properties of the \( \tau \) function, including \[ |\tau(p)| \le 2p^{11/2} \text{ for all primes } p. \] This turned out to be an extremely important and deep result, which was proved in 1974 by Pierre Deligne in his Fields-medal-winning proofs of the Weil conjectures on points on algebraic varieties over finite fields.

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Srinivasa Ramanujan

Srinivasa Ramanujan was born on December 22, 1887 in Erode, a city in the Tamil Nadu state of India. His father, K. Srinivasa Iyengar was a clerk while his mother, Komalatammal performed as a singer, in a temple. Even though they belonged to the Brahmins who are known to be the highest caste of Hinduism, Ramanujan’s family was very poor.

At the age of 10, in 1897, Ramanujan attended the high school in Kumbakonam Town. There he discovered his intelligence in the field of mathematics and by his independent study of books from the school library; Ramanujan increased his knowledge and skills. At age of just 12 years, he had developed understanding of trigonometry and was able to solve cubic equations and arithmetic and geometric series as well.

Among all of the mathematical literature Ramanujan went through, a book by George Shoobridge Carr , titled as A Synopsis of Elementary Results in Pure and Applied Mathematics , written in 1886, proved to be the primary medium that laid him onto the path of becoming a great mathematician. He got access to its copy in 1902 and in a short time he not only went through all of its theorems but also verified their results. He also rediscovered the work done by many famous mathematicians including Carl Friedrich Gauss and Leonhard Euler . In addition to this, many new theorems were also formulated by him.

Ramanujan completed his high school by the age of 17, in 1904. Due to his outstanding results, he was awarded scholarship for higher studies in the Government Arts College in Kumbakonam. But his inclination towards mathematics led to his failure in non-mathematical subjects and ultimately discontinuation of his scholarship. Ramanujan had to face the same situation in Pachaiyappa’s College, an affiliation of the University of Madras by losing his scholarship there.

When Ramanujan got married at the age of 22, in 1909, he got worried for his financial instability, but was still strong-willed to continue with his passion. He started independent research work in mathematics by getting enrolled in a college. He was supported by a government official and secretary of the Indian Mathematical Society , Ramachandra Rao .

In 1911, Ramanujan got his first publication with the assistance of Ramaswamy Aiyer , the founder of the Indian Mathematical Society , in the society’s journal only. This research was on Bernoulli Numbers , done independently by him in 1904. After about a year, Ramanujan started working in Madras at the Port Trust Office as a clerk alongside his research work.

After applying for British Universities in 1913, Ramanujan’s work got acknowledged by a prominent mathematician of the Cambridge University , Godfrey Harold Hardy who funded him for research in the University of Madras. In 1914, Ramanujan went to England to utilize his scholarship at Trinity College, Cambridge and work in collaboration with G. H. Hardy and J. E. Littlewood . In 1916, Ramanujan got his Bachelors in Science degree and a year later he became a fellow of the British Royal Society .

Ramanujan has contributed a lot to mathematics in his short lifespan. This includes his independent works from India as well as the researches done under the mentorship of G. H. Hardy in England. Alongside his outstanding discoveries in continued fractions , divergent series , hypergeometric series , Reimann series and elliptic integrals , his advancements in partition of numbers are quite phenomenal. Ramanujan worked on properties of partition function and in collaboration with G. H. Hardy, developed the circular method to represent an integer in the form of its partitions. This led to many developments in analytic number theory by future mathematicians.

In 1917, Ramanujan got diagnosed with tuberculosis. He returned to India in 1919 and died in 1920, at the age of 32.

About three months before his death, Ramanujan wrote his last letter to Hardy, explaining his new discovery in mathematics; the Theta Function and its 17 identities. Later, many mathematicians worked on this function, proved the identities and found new ones too.

Even though Ramanujan had got many papers published in different journals during his life, much work remained unpublished. The notes that he left behind were studied by many mathematicians after him, who verified his discoveries, and found their potential applications.

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Srinivasa Ramanujan: The Eminent Mathematician

Last updated on December 23, 2022 by ClearIAS Team

Every year, Srinivasa Ramanujan’s birth anniversary on December 22 is commemorated as National Mathematics Day. Ramanujan made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. Read here to know more about his life.

National Mathematics Day is observed annually on December 22nd to mark the anniversary of the eminent mathematician Srinivasa Ramanujan’s birth.

Srinivasa Ramanujan was a self-taught mathematician and one of the most eminent scientists the country has seen.

Ramanujan spent most of his brief but significant life working on theorems that seemed difficult to answer.

His contributions to the fields of elliptic integrals, hypergeometric series, continuous fractions, Riemann series, and functional equations about the zeta function are well known.

Table of Contents

The early life of Srinivasa Ramanujan

Ramanujan was born in his grandmother’s house in Erode, a small village about 400 km southwest of Madras (now Chennai).

When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant’s shop.

When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898.

Before turning 10, he passed his primary examinations in English, Tamil, geography, and arithmetic with the best scores in the district. That year, Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time.

By age 11 he was recognized as a child prodigy as he had exhausted the mathematical knowledge of two college students who were lodgers at his home.

By age 13, he mastered advanced trigonometry and by age 14 he had started showing affinity to geometry and infinite series.

Ramanujan was shown how to solve cubic equations in 1902. He would later develop his method to solve the quartic. In 1903, he tried to solve the quintic, not knowing that it was impossible to solve with radicals.

He received a scholarship to study at Government Arts College, Kumbakonam. Still, he was so intent on mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process.

He then ran away from his house to Vishakapatnam where he continued his mathematical work, however, and at this time he worked on hypergeometric series and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions.

In 1906 Ramanujan went to Madras where he entered Pachaiyappa’s College. He aimed to pass the First Arts examination which would allow him to be admitted to the University of Madras. He attended lectures at Pachaiyappa’s College but became ill after three months of study. He took the First Arts examination after having left the course.

• He passed mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras.
• In the following years, he worked on mathematics developing his ideas without any help and without any real idea of the then-current research topics other than that provided by Carr’s book.

He became seriously ill again and underwent an operation in April 1909 after which it took him some considerable time to recover.

He married on 14 July 1909 when his mother arranged for him to marry a ten-year-old girl S Janaki Ammal.

The mathematical journey of Srinivasa Ramanujan

Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908.

Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society.

• He developed relations between elliptic modular equations in 1910.
• After the publication of a brilliant research paper on Bernoulli numbers in 1911 in the Journal of the Indian Mathematical Society he gained recognition for his work.

Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius.

Ramanujan was able to get a job as a clerk in the madras post trust on the recommendation of EW Middlemast, a professor of mathematics in the Presidency college madras.

In January 1913 Ramanujan wrote to G H Hardy having seen a copy of his 1910 book Orders of infinity.

Hardy and Littlewood were very impressed by Ramanujan’s work and helped him get a scholarship at the University of Madras in 1913.

In 1914, Hardy brought Ramanujan to Trinity College, Cambridge to begin an extraordinary collaboration.

Life in Cambridge, England

Right from the beginning, he had problems with his diet. The outbreak of World War I made obtaining special items of food (as he was a strict vegetarian) harder and it was not long before Ramanujan had health problems.

Ramanujan’s collaboration with Hardy led to important results. But his lack of formal education did cause some problems, hence Littlewood was asked to help teach Ramanujan rigorous mathematical methods.

• However, Hardy said- “ it was extremely difficult because every time some matter, which it was thought that Ramanujan needed to know, was mentioned, Ramanujan’s response was an avalanche of original ideas which made it almost impossible for Littlewood to persist in his original intention .”

On 16 March 1916 Srinivasa Ramanujan graduated from Cambridge with a Bachelor of Arts in Research (the degree was called a Ph.D. from 1920).

• He had been allowed to enroll in June 1914 despite not having the proper qualifications.
• Ramanujan’s dissertation was on Highly composite numbers and consisted of seven of his papers published in England.

From 1917 to 1918, he fell seriously ill and spent most of his time in various nursing homes.

On 18 February 1918 Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honor that he would receive, his name appeared on the list for election as a fellow of the Royal Society of London.

• He had been proposed by an impressive list of mathematicians, namely Hardy, MacMahon, Grace, Larmor, Bromwich, Hobson, Baker, Littlewood, Nicholson, Young, Whittaker, Forsyth, and Whitehead.
• His election as a fellow of the Royal Society was confirmed on 2 May 1918, then on 10 October 1918, he was elected a Fellow of Trinity College Cambridge, the fellowship to run for six years.

He returned to India in 1919.

He died in 1920 at the age of 32 due to ill health.

Ramanujan’s work in mathematics

The letters Ramanujan wrote to Hardy in 1913 contained many fascinating results.

• Ramanujan worked out the Riemann series, the elliptic integrals, the hypergeometric series, and the functional equations of the zeta function.
• On the other hand, he had only a vague idea of what constitutes mathematical proof.
• Despite many brilliant results, some of his theorems on prime numbers were completely wrong.

Ramanujan independently discovered the results of Gauss, Kummer, and others on hypergeometric series. Ramanujan’s work on partial sums and products of hypergeometric series has led to a major development in the topic.

Ramanujan left several unpublished notebooks filled with theorems that mathematicians have continued to study.

G N Watson, Mason Professor of Pure Mathematics at Birmingham from 1918 to 1951 published 14 papers under the general title Theorems stated by Ramanujan, and in all, he published nearly 30 papers that were inspired by Ramanujan’s work.

Hardy passed on to Watson a large number of manuscripts of Ramanujan that he had, both written before 1914 and some written in Ramanujan’s last year in India before his death.

The number 1729 is known as the Hardy–Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital.

• In Ramanujan’s words, “It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”

In his obituary of Ramanujan, written for Nature in 1920, Hardy observed that Ramanujan’s work primarily involved fields less known even among other pure mathematicians.

Legacy of Srinivasa Ramanujan

The year after his death, Nature listed Ramanujan among other distinguished scientists and mathematicians on a “Calendar of Scientific Pioneers” who had achieved eminence.

Ramanujan’s home state of Tamil Nadu celebrates 22 December (Ramanujan’s birthday) as ‘State IT Day’.

Stamps picturing Ramanujan were issued by the government of India in 1962, 2011, 2012, and 2016.

In 2012, former Prime Minister Dr. Manmohan Singh paid tribute to the mathematician during a ceremony in Chennai to commemorate Ramanujan’s birth anniversary and declared December 22 National Mathematics Day.

The Ramanujan Math Park located in Kuppam, Andhra Pradesh, was inaugurated on this day in 2017.

-Article written by Swathi Satish

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Essay on Srinivasa Ramanujan in 100 and 500 Words for School Students

• Updated on  
• Dec 21, 2023

Dr. S Ramanujan is recognized as one of the greatest Mathematicians in the world, owing to his contributions to this academic field. His most commendable works include “The Journal of the Indian Mathematical Society” and  “Ramanujan Summation” method. Also, his becoming a member of the “London Mathematical Society in Britain” is an achievement to be proud of. Acknowledging his dedication to the field of mathematics, in 2012, Dr. Manmohan Singh declared 22 December as “ National Mathematics Day ”. To learn more about this Math genius, let us explore the Essay on Srinivasa Ramanujan in 150 and 500 words. 

Also Read: 20 Most Famous Indian Mathematicians

Essay on Srinivasa Ramanujan in 150 words

Here is an Essay on Srinivasa Ramanujan in 150 words:

Also Read: Famous Mathematicians of All Times

Essay on Srinivasa Ramanujan in 500 words

Now, let us go through an Essay on Srinivasa Ramanujan in 500 words:

Also Read: Ramanujan Fellowship

Ans: National Mathematics Day is celebrated on 22 December each year as it is the birth date of Dr S Ramanujan.

Ans: “The Journal of the Indian Mathematical Society” was Ramanujan’s first published paper.

Ans: Dr Srinivasa Ramanujan lost his life to TB on 26 April 1920.

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Ankita Singh

Ankita is a history enthusiast with a few years of experience in academic writing. Her love for literature and history helps her curate engaging and informative content for education blog. When not writing, she finds peace in analysing historical and political anectodes.

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• Essay On Ramanujan

Essay on Ramanujan

500+ words essay on ramanujan.

Srinivasa Ramanujan Aiyangar, who is also known as Ramanujan, is one of the greatest mathematicians of all time. The genius mathematician made a significant contribution to several areas of mathematics though he had no formal training in pre-mathematics. His contributions to the theory of numbers, mathematical analysis, number theory, infinite series, and continued fractions are considered to be extraordinary. The Indian mathematician is also known for his ability to solve mathematical problems that were previously considered impossible to solve.

About Srinivasa Ramanujan

Srinivasa Ramanujan, who is often referred to as ‘The World’s Greatest Mathematician’, was born in Erode on 22nd December 1887. His parents were Kuppuswamy Srinivasa Iyengar and Komalatammal. As a young boy, Srinivasa Ramanujan did not like going to school, and his parents had to enlist a constable’s help to ensure he attended school. But by the age of 11, Ramanujan was a child prodigy who developed his own sophisticated theorems to master trigonometry.

By the age of 17, the young mathematical genius had received several awards and merit certificates. Upon graduating high school, S. Ramanujan was awarded a scholarship to study at Government Arts College, Kumbakonam. But since he was intent only on studying mathematics, he failed all other subjects. He later enrolled at Pachaiyappa’s College, Madras, where he failed all other subjects and passed only in mathematics. Ramanujan continued to pursue independent research in mathematics and was eventually included as a researcher at the University of Madras.

His work and intellect were recognized by British mathematicians too. He was elected to the London Mathematical Society in 1917, and in 1918, he was elected to the Royal Society of London. He was the second Indian to be elected to the Royal Society and one of the youngest fellows elected in the history of the society. In 1918, he became the first Indian to be elected to the Fellow of Trinity College, Cambridge.

Ramanujan was a deeply religious person who believed there was a link between mathematics and spirituality. He thought that zero represented absolute reality. He credited his mathematical genius and acumen to his family deity, Goddess Namagiri Thayar. He drew inspiration from her for his work and he claimed to have visions that gave him knowledge of complex mathematical content.

Ramanujan found theorems and formulae as the best manifestation of reality. He compiled around 4000 results, which included theorems, equations and identities in number theory, combinatorics and algebra. He focused on several areas, from hypergeometric and infinite series to highly composite numbers. However, the two central regions Ramanujan felt he had a relationship with are ‘number theory’ and ‘modular functions’. He wrote and published several papers of great mathematical significance with his mentor Professor Hardy during his stay at Cambridge University.

But the mathematical genius did not live a long life. Ramanujan fell sick in 1919, which compelled him to return to India from Cambridge. The genius mathematician died on 26th April 1920 after a brief illness at the young age of 32. His last letters to his mentor, English mathematician G. H. Hardy revealed that he continued working on mathematical ideas before his death. His work was so intricate that it opened up new directions for mathematical research.

Posthumous Awards and Recognition

Srinivasa Ramanujan’s mathematical genius, his work and his achievements were recognized posthumously. The Government of India 2011 declared his birthday National Mathematics Day to commemorate his valuable contribution. The former Prime Minister, Dr Manmohan Singh, proclaimed that 2012 would be celebrated as the National Mathematics Year.

Tamil Nadu, which is Ramanujan’s home state, recognizes his birthday (22nd December) as “State IT Day.” The Government of India also introduced several stamps picturing Ramanujan in 1962, 2011, 2012 and 2016. Several universities and institutions have introduced prizes and awards in his name to students making outstanding contributions to the field of mathematics.

In conclusion, Ramanujan has been compared to notable names, including some masters of mathematics like Euler and Jacobi. He has inspired a whole generation of mathematicians, and his legacy lives on. Ramanujan died at the young age of 37, leaving us a rich legacy of mathematical discoveries.

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• © 2013

The Mathematical Legacy of Srinivasa Ramanujan

• M. Ram Murty 0 ,
• V. Kumar Murty 1

Department of Mathematics, Queen's University, Kingston, Canada

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Department of Mathematics, University of Toronto, Toronto, Canada

• Gives a panoramic view of the main contributions of Srinivasa Ramanujan
• Presents a major theme of Ramanujan's work in non-technical language
• Provides an excellent introduction to Ramanujan's life and work
• Includes supplementary material: sn.pub/extras

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Table of contents (13 chapters)

Front matter, the legacy of srinivasa ramanujan.

• M. Ram Murty, V. Kumar Murty

The Ramanujan τ-Function

Ramanujan’s conjecture and ℓ-adic representations, the ramanujan conjecture from gl(2) to gl(n).

• The Circle Method

Ramanujan and Transcendence

Arithmetic of the partition function, some nonlinear identities for divisor functions, mock theta functions and mock modular forms, prime numbers and highly composite numbers.

• Probabilistic Number Theory

The Sato–Tate Conjecture for the Ramanujan τ-Function

Erratum to: the ramanujan τ-function, back matter.

• Mock Modular Forms
• Partition Function
• Ramanujan's Conjectures
• combinatorics

“This book is based on a number of talks the authors gave at various research institutes. Their aim is to survey some of Srinivasa Ramanujan’s most significant achievements and the developments they have led to over the last decades. … This volume is suitable as a first introduction to some of Ramanujan’s remarkable and deep ideas.” (C. Baxa, Monatshefte für Mathematik, Vo. 180, 2016)

“The authors introduce the reader to the topics through a historical account of the origin and later developments. … We warmly recommend this book for those who would like to have a glimpse on Ramanujan’s mathematics. Without being lost in the technicalities the reader will get a good look at the shape of many central questions.” (Péter Hajnal, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)

“The Murtys’ goal … is to present Ramanujan’s mathematical legacy to a broad audience, and the thrust of the book is a set of eleven chapters discussing exactly that. … the book will utterly charm you, given its accessibility, style, structure, and depth. It’s a great pleasure to read, and it’s fine scholarship.” (Michael Berg, MAA Reviews, December, 2013)

Srinivasa Ramanujan’s Contributions in Mathematics

Srinivasa Ramanujan is considered to be one of the geniuses in the field of mathematics. He was born on 22nd December 1887, in a small village of Tamil Nadu during British rule in India. His birthday is celebrated as national mathematics day. In high school, he used to do very well in all subjects. In 1990, he started working on his mathematics in geometry and arithmetic series. Although he had no official training in mathematics, even then, he was able to solve problems that were considered unsolvable. He published his first paper in 1911. In January 1913, Ramanujan began a postal conversation with an English mathematician, G.H. Hardy at the University of Cambridge, England and wrote a letter after having seen a copy of his book  Orders of infinity . He found Ramanujan’s work to be extraordinary and arranged for him to travel to Cambridge in 1914. As Ramanujan was an orthodox Brahmin, a vegetarian, his religion might have restricted him to travel. This difficulty of Ramanujan was solved partly by E H Neville, a colleague of Hardy. Hardy after analysing the works of Ramanujan, said,

Ramanujan had produced groundbreaking new theorems, including some that defeated me completely.I had never seen anything in the least like them before.’

At the age of 32, he died of Tuberculosis. In his short life span, he independently found 3900 results. He worked on real analysis, number theory, infinite series, and continued fractions. Some of his other works such as Ramanujan number, Ramanujan prime, Ramanujan theta function, partition formulae, mock theta function, and many more opened new areas for research in the field of mathematics. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his theory of divergent series, in which he found a value for the sum of such series, using a technique he invented, that came to be called Ramanujan summation. In England, Ramanujan made further researches, especially in the partition of numbers, i.e, the number of ways in which a positive integer can be expressed as the sum of positive integers. Some of his results are still under research. His journal, Ramanujan Journal, was established to keep a record of all his notebooks and results, both published and unpublished, in the field of mathematics. As late as 2012, researchers studied even the small comments in his book, as they do not want to miss any results or identities given by him, that remained unsuspected until a century after his death. From his last letters in 1920 that he wrote to Hardy, it was evident that he was still working on new ideas and theorems of mathematics. In 1976, mathematicians found the ‘lost notebook’, that contained the works of Ramanujan from the last year of his life. Ramanujan devoted all his mathematical intelligence to his family goddess Namagir Thayar. He once said, “An equation for me has no meaning unless it expresses a thought of God.” Now, we will discuss in detail all his contributions to mathematics.

1. Infinite series of π

William Shanks, a 19th-century British mathematician tried calculating the value of infinite series of π. In 1873, he calculated the value of π to 707 decimal places. Ramanujan, in 1914, published ‘Modular equations and approximations to π’, which contained not only one, but 17 different series, that will converge very fastly to π, after calculating just fewer terms of the series.

2. Ramanujan number

The number 1729 is known as the Ramanujan number or Hardy-Ramanujan number. It is the smallest natural number that can be expressed as the sum of two cubes, in two different ways, i.e., 1729 = 1 3  + 12 3  = 9 3  + 10 3 . There is a small story behind the discovery of this number. When Ramanujan was under treatment, G.H. Hardy once visited him in the hospital and had a conversation in which he mentioned,

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.’

This is how the Ramanujan number came into existence. Later on, more properties of this number were discovered.

3. Ramanujan Prime

Ramanujan published a two-page paper on the proof of Bertrand’s postulate. At the end of the last page, he mentioned a result, π(x) – π(x/2) ≥ 1, 2, 3, 4, 5,….., for all x≥ 2, 11, 17, 29, 41,…. respectively, where π(x) is the prime counting function, equals to the number of primes equal or less than x. The nth Ramanujan prime number is the least integer {R}_{n} , for which there are at least n primes between x and x/2, for all x ≥ {R}_{n} . The first five Ramanujan primes are 2, 11, 17, 29, 41

4. Ramanujan Theta Function

Ramanujan theta function is the generalised form of the Jacob theta function. In particular, Jacobi triple product can be beautifully represented by the Ramanujan theta function. The Ramanujan theta function is given below.

for |ab|<1.With the help of Ramanujan theta function, Jacobi triple product can be represented as,

5. Mock Theta Function

Ramanujan in his last letter to G.H. Hardy and in his ‘lost notebook’, gave the first example of mock theta function. A mock theta function is a mock modular form( the holomorphic part of a harmonic weak Maass form), of weight 1/2. His last letter to Hardy contained 17 examples of mock theta functions, and some more examples were mentioned in his ‘lost notebook.’ Ramanujan gave an order to his mock theta function. Before the attempts of Zwegers, the order of mock theta function was 3, 5, 6, 7, 8, 10.

6. Partition

Partition or integer partition of an integer ‘n’ is a way of writing ‘n’ as a sum of positive integers. Partitions that differ only in the order of summands are considered as the same partitions. Each summand in the partition is called a part. The number of partitions of an integer ‘n’ is denoted by p(n). For example, integer 4 has 5 partitions as given below.

Here partition 1+3 is the same as 3+1 and 1+2+1 is the same as 1+1+2 and p(4)=5. Partitions can also be visualised with the help of the Young diagram and Ferrers diagram.

7. Ramanujan Magic Squares

In his school days, he used to enjoy solving magic squares. Magic squares are the cells in 3 rows and 3 columns, filled with numbers starting from 1 to 9. The numbers in the cells are arranged in such a way that the sum of numbers in each row is equal to the sum of numbers in each column is equal to the sum of numbers in each diagonal. Ramanujan gave a general formula for solving the magic square of dimension 3×3,

where A, B, C and P, Q, R are in arithmetic progression. The following formula was also given by him.

8. Ramanujan Congruences

Ramanujan obtained three congruences when m is a whole number, p (5 m + 4) ≡ 0 (mod 5), p (7 m + 5) ≡ 0 (mod 7), p (11 m + 6) ≡ 0 (mod 11). Hardy and E.M. Wright wrote, 

he was first to led the conjecture and then to prove, three striking arithmetic properties associated with the moduli 5, 7 and 11.”

9. Highly composite numbers

Composite numbers are the numbers that have factors other than 1 and the number itself. Ramanujan raised an interesting question that if ‘n’ is a composite number then what properties make a number highly composite. Ramanujan’s definition of Highly composite numbers,

A natural number is a highly composite number if d ( m ) < d ( n ) for all m < n.”

He also published a paper on highly composite numbers in 1915. According to him, there were infinitely many highly composite numbers.

10. Symmetric Equation by Ramanujan

Ramanujan noticed symmetry in Diophantine’s equation, {x}^{y} = {y}^{x} . He proved that there exists only one integer solution to this equation, i.e., x=4, y=2, and an infinite number of rational solutions, for example, {(27/8)}^{(9/4)} = {(9/4)}^{(27/8)} .

11. Ramanujan-Nagell Equation

Ramanujan-Nagell Equation is the equation of type {2}^{n} – 7 = {x}^{2} . It is an example of Diophantine equation. In 1913, Ramanujan claimed that this equation had only 1²+7 = 2³, 3²+7 = {2}^{4} , 5²+7 = {2}^{5} , 11²+7 = {2}^{7} , 181²+7 = {2}^{15} integral solutions. This conjecture was later on proved by Trygve Navell and is widely used in coding theory.

12. On Certain Arithmetical Functions

Ramanujan published a paper “On certain arithmetic functions” in 1916, in which he discussed the properties of Fourier coefficients of modular forms. Though the concept of modular forms was not even developed then, he gave three fundamental conjectures. In 1936, after 20 years of his published paper, a Greman mathematician Erich Hecke developed the Hecke theory with the help of his first two conjectures. His last conjecture played a vital role in the Langlands program (a program that relates representation theory and algebraic number theory). “On certain arithmetical functions” by Ramanujan was very effective in creating a sensation in 2oth century mathematics.

13. On Fermat’s Last Theorem

In 2013, mathematicians found some evidence that revealed Ramanujan was working on Fermat’s last theorem. Pierre de Fermat mentioned that,

 if n is a whole number greater than 2, then there are no positive whole number triples x, y and z, such that x n  + y n  = z n .”

Ramanujan claimed that he had found an infinite family of whole numbers that will satisfy (approximately, not exactly) Fermat’s equation for n=3. He gave the example of the number 1729, which do not fits into the equation just by the mark of 1, for x=9, y=10, z=12. Ramanujan also worked on the equations of the form, y 2  = x 3  + ax + b. An elliptic curve is obtained, when the points (x,y) of this equation are plotted. These elliptic curves were of great significance and were used by Sir Andrew Wiles while he was proving Fermat’s last theorem in 1994.

14. Roger-Ramanujan Identities

In 1894, these identities were discovered and proved by Leonard James Rogers. Nearby 1913, Ramanujan rediscovered these identities. He had no proof but found Roger’s paper in 1917. Then they both united and gave a joint new proof.

15. Roger-Ramanujan Continued Fractions

Roger discovered continued fractions in 1894, which were later rediscovered by Ramanujan in 1912.

Ramanujan found various results concerning R(q), for example, R( {e}^{-2π} ) is given below in the picture and he also calculated R( {e}^{-2π√n} ) for n= 4, 9, 16, 64

16. Ramanujan’s Master Theorem

Ramanujan’s Master Theorem provides an analytic expression for the Mellin transform of an analytical function. This theorem is used by Ramanujan to calculate definite integrals and infinite series. The result of the theorem is given in the picture below.

17. Properties of Bernoulli Numbers

In 1904, Ramanujan independently studied and rediscovered Bernoulli numbers. In 1911, he wrote his first article on this topic. Bernoulli numbers {B}_{n} are the sequence of rational numbers, that appear in the Taylor series expansion of tangent and hyperbolic tangent functions. One of the properties that he discussed states that, the denominator of all Bernoulli numbers are divisible by six. Based on previous Bernoulli numbers, he also suggested a method to calculate Bernoulli numbers. According to the method proposed by him, if  n  is even but not equal to zero,

• B n  is a fraction and the numerator of  B n / n in its lowest terms is a prime number.
• The denominator of B n contains each of the factors 2 and 3 once and only once.
• 2 n (2 n  − 1) B n / n  is an integer and  2(2 n  − 1)B n  consequently is an odd integer.

18. Euler Mascheroni Constant

Ramanujan calculated the Euler Mascheroni constant also known as the Euler constant, up to 15 decimal places. It is the limiting difference between the harmonic series and the natural logarithm. Later on, a value up to 50 decimal places was calculated and is equal to, 0.57721566490153286060651209008240243104215933593992…..

γ denotes the Euler constant

19. Ramanujan Summation

Ramanujan, in one of his books, stated that, if we add up all natural numbers starting from 1 up to infinity, then the sum will be a finite number, i.e., 1+2+3+……….+∞= -1⁄12

20. Ramanujan Puzzles

• The first puzzle was to prove the equation of infinite nested radical. In 1911, Ramanujan sent the RHS of this equation to a mathematical journal as a puzzle. The puzzle and its solution are elaborated in the video below.

• The next puzzle is to find the value of the Golden ratio(Φ), which is equal to the infinite continued fraction given in the picture below.

The continued fraction in the black box is the same as that in the outer red box. Setting this equal to x, we get Φ   = 1 + 1/x, which yields x 2  – x – 1 = 0. The solutions of this quadratic equation are ( 1 +√5 )⁄2  and  ( 1 −√5 )⁄ 2. Neglecting the negative solution, the value of Φ is ( 1 +√5 )⁄2

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Read this Essay on Srinivasa Ramanujan  (1887 A.D. – 1920 A.D.) !

One of the greatest mathematicians of India, Ramanujan’s contribution to the theory of numbers has been profound. He was indeed a mathematical phenomenon of the twentieth century. This legendary genius of India ranks among the all time greats like Euler and Jacobi.

Ramanujan lived just for 32 years but during this short span he produced such theorems and formulae which even today remain unfathomable in the present age of super computers. He left behind him about 4000 formulae and theorems.

It is believed that these were the beginning of some great theory that he had at conceptual stage which failed to develop because of his premature and untimely demise. His personal life was as mysterious as his theorems and formulae.

It is believed that he was a great devotee of the Hindu goddess of creativity and that the goddess used to visit him in dreams and she wrote equations on his tongue. Ramanujan was the first Indian to be elected to the Royal Society of London.

Ramanujan was born to poor parents on December 22, 1887 at Erode in Tamil Nadu. His father was employed as a clerk in a cloth merchant’s shop. However, his mother had a sharp intellect and was known for making astrological predictions.

Not much is known about his early life and schooling except that he was a solitary child by nature. It is believed that he was born as a result of ardent prayers to the goddess Namgiri. Later Ramanujan attributed his mathematical power to this goddess of creation and wisdom. For him nothing was useful unless it expressed the essence of spirituality.

Ramanujan found mathematics as a profound manifestation of the Reality. He was such a great mathematician and genius as transcends all thoughts and imagination. He was an expert in the interpretation of dreams and astrology. These qualities he had inherited from his mother.

His interest and devotion to mathematics was to the point of obsession. He ignored everything else and would play with numbers day and night on a slate and in his mind. One day he came to possess G.S Carr’s “Synopsis of Pure Mathematics”, which contained over 6,000 formulae in Algebra, Trigonometry and Calculus but contained no proofs.

Ramanujan made it his constant companion and improved it further on his own. His obsession and preoccupation with mathematics did not allow him to pass his intermediate examination in spite of three attempts. He could not get even the minimum pass marks in other subjects.

Ramanujan was married to a nine year old girl called lauaki and it added more to his family responsibilities. With the recommendation of the Collector of Nellore, who was very much impressed by his mathematical genius, Ramanujan sound a clerk’s job at Madras Fort Trust. In 1913 he came across an article written by Professor Hardy.

Ramanujan stayed at Cambridge for four years and during this period he produced many papers of great mathematical significance in collaboration with his mentor Professor Hardy. His phenomenal and exceptional genius was recognized all over the academic world.

He was elected Fellow of the Royal Society, London in 1918. He was then 30 years of age. His mastery of certain areas of mathematics was really fantastic and unbelievable. But soon his hard work began to affect his health and he fell seriously ill in April, 1917.

Ramanujan had contracted tuberculosis. And it was decided to send him back to India for some time. He reached India on March 27, 1919. He breathed his last on April 26, 1920 at Kumbakonam at the age of 32 years. His death shocked Professor Hardy and others beyond words.

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