Srinivasa Ramanujan – A Mathematical Genius

India is celebrating 136th birth anniversary of Srinivasa Ramanujan, a mathematical prodigy who can stand comparison with world’s celebrated mathematicians like Euler, Lagrange, Jacobi and others, on 22nd December 2023.  As a tribute to the memory of the great mathematician, the Indian government declared 22nd December to be celebrated as National Mathematics Day every year to mark the birth anniversary of Srinivasa Ramanujan.  The announcement was made by Sri Manmohan Singh, the then Hon’ble Prime Minister on 26th December 2011.

Srinivasa Ramanujan is considered as one of the greatest mathematicians of all times, who lived for a very short period of 32 years between 1887 and 1920. The striking feature of his research is that he made substantial and seminal contributions to mathematical analysis, number theory, continued fractions, infinite series etc without a formal training in pure mathematics. It is said that “Every positive integer was a personal friend of Srinivasa Ramanujan”.  This article is a tribute to the memory of this great son of India. 

Ramanujan was born on 22nd December 1887 at Erode, located in the present state of Tamilnadu.  His father was Sri Srinivasa Iyengar and mother   Smt. Komalathammal.  His father was a clerk in a private cloth shop drawing a meagre salary of Rs. 20/- per month.  Ramanujan was born in a poor but traditional family and experienced the travails of abject poverty. He was admitted to Payal School at Kumbakonam in 1892. Later, he continued his education at Kangayan Primary School. His teachers and classmates were astonished at the unusual memory of Srinivasa Ramanujan. He demonstrated exceptional proficiency in mathematics thus impressing his teachers.  At the age of ten in 1897, he completed his primary school education by scoring highest marks for the district in English, Tamil, Geography and Arithmetic. He was admitted to Town Higher Secondary School.  Even as a child, he developed keen interest in mathematics.  It is recorded that at a very young age (when he was in primary class), he was able to give square root of ‘2’ and the value of ‘e’ to several decimal places. He was given fifty percent concession in fee considering the marks that he had scored at the primary school examination.

As Ramanujan’s father was busy at work most of the day, young Ramanujan used to spend most of his time with his mother who was a homemaker.  But,she had profound knowledge of puranas, and also a good singer of religious songs.   Ramanujan learnt puranas, to sing religious songs and perform pujas at temples under the guidance of his parents.

Ramanujan was a child prodigy.   At the age of twelve, he had solved all the problems in Loney’s book on “Advanced Trigonometry”. He had mastered trigonometry at the age of 13 by discovering several theorems on his own, without anyone’s assistance.  He proved Euler’s theorem for sine and cosine ratios.   When his interest in mathematics was expanding, he obtained a copy of “A Synopsis of Elementary Results in Pure and Applied Mathematics” authored by G.S. Carr.  It is a collection of about five thousand theorems which included integral calculus and power series calculations.  Ramanujan studied the content of the book in detail. It is said that these theorems motivated Ramanujan and laid the foundation for his future research in mathematics. He proved some of the theorems in his own way using his knowledge of mathematics and ingenuity. He wrote, solved and recorded hundreds of theorems in folded sheets.  The collection of these folded sheets is popularly known today as Ramanujan’s “note book”.

He passed his matriculation in 1903 securing first class. He joined Government Arts College, Kumbakonam for his F.A. Class.   In F.A class, subjects of study were English, Mathematics, Physiology, Greek and Roman History and Sanskrit.  Ramanujan’s obsession with mathematics was so intense that he devoted most of his time to the study of mathematics. As a consequence, except mathematics, he miserably failed in all the subjects and lost the scholarship. He could not pass F.A. examination and hence discontinued his college studies. Despite failure in F.A. examination, unemployment, poverty and other personal problems, Ramanujan continued his research in mathematics without any slackening in his pursuits.

He married Smt. Janaki Devi at the age of 22. In 1910, Ramanujan met Prof. V. Ramaswamy Iyer, Founder of Indian Mathematical Society and sought his help.  Prof. V. Ramaswamy Iyer, went through Ramanujan’s “note book” and was flabbergasted at Ramanujan’s mathematical ingeniousness. Prof. Ramaswamy through his friend Sri. Seshu Iyer, arranged for a meeting with Sri. Ramachandra Rao, the then collector of Nellore district.  After a long discussion with Ramanujan, Sri Ramachandra Rao realised that Ramanujan wan indeed a mathematical genius and he was eager to get a job for livelihood so that he could continue his research.  On the recommendation of Sri Ramachandra Rao, Ramanujan got a clerical post at Madras port on a salary of Rs. 30/- per month.  Even after getting the job, Ramanujan’s interest in mathematics did not get dampened.  He continued his research much more vigorously. He had already invented many theorems.  Due to poverty and paucity of funds, he used to work on a slate.  Whenever he invented new ideas, he used to record them in his note book.  He published new theorems invented by him in the Journal of Indian Mathematical Society.  These publications attracted the attention of several great mathematicians across the globe. His genius gradually gained recognition and earned appreciation from different quarters.

Based on the suggestions made by his well-wishers Sri Seshu Iyer and others, he began a correspondence with Cambridge University Professor and British mathematician Godfrey H. Hardy. It is often said that Prof. G. H. Hardy is the real discoverer of Ramanujan. In his very first letter, which he wrote in 1913, Ramanujan had described, and gave solutions for 120 theorems invented by him. Though Prof. G.H. Hardy was amazed with Ramanujan’s mathematical prowess, he did not believe Ramanujan at first instance. On the same day, after dinner, G. H. Hardy discussed with his friend Prof. Littlehood for almost three hours on Ramanujan’s inventions. After the discussion, they came to the conclusion that Ramanujan was an extraordinary person, mathematician of highest quality, a man of exceptional originality and a genius. Prof G. H. Hardy has said that Ramanujan could be compared to mathematical giants: Euler, Lagrange and Jacobi.

With the intention of providing an academic ambience conducive for nurturing the extra ordinary talents and mathematical abilities of Ramanujan, Prof. G. H. Hardy invited Ramanujan to England.  Hardy wrote to Ramanujan a letter expressing his interest in his work and also to work with him. As Ramanujan hailed from an orthodox brahmin family, his mother did not give her consent for Ramanujan to travel abroad.  Prof G. H. Hardy brought pressure through her friends and well-wishers. Seemingly, Komalathammal, Ramanujan’s mother had a dream in which the family God the deity of Namakkal asked her not to stand in between her son and the fulfilment of his life’s purpose. She finally agreed to the proposal. Ramanujan started his journey on 17th March, 1914 and reached England on 14th of April. He collaborated with G. H. Hardy for four years and carried out his research work at Cambridge.  He published 27 research papers during this period. Ramanujan’s work on Theory of Partitions is regarded as seminal work in the field.  He carried out an outstanding research work on several topics: continued fractions, hyper geometric series, theory of numbers, elliptic integrals etc., He earned international recognition as a mathematician of highest order.

The Cambridge university honoured him by awarding B.A. degree in 1916.  He was elected Fellow of Royal Society of London in 1918 in recognition of his exemplary research. He was the first Indian to earn this distinction.  We, Indians must feel proud of the accomplishments of Srinivasa Ramanujan.  He was only 30 years old when he achieved this international recognition. His achievements were exceptional and unparalleled.

The cold weather of England, western food, culture and traditions, separation from his family, total involvement in research and negligence on his personal wellbeing had tremendous negative impact on his health. But his brilliance and love for the numbers never faded.  He contracted tuberculosis. He was hospitalised.  Prof G.H. Hardy went to the hospital at Putney to meet ailing Ramanujan. Prof. G. H. Hardy said, I Quote “I travelled now by a taxi bearing registration number 1729. This number has no special characteristics”.  Immediately, Ramanujan replied that number was a special one.  He said it was the smallest number that could be expressed as a sum of cubes of two numbers in two different ways: 1³+ 12³ = 9³ + 10³ = 1729. 

He returned to India in 1919.  He was given the best medical treatment available at that time.  But it was in vain. In spite of his poor health, he invented “Mock Theta Functions”.

Besides Mathematics, he evinced interest in Palmistry. It is said that he had a premonition of his death. Looking at the lines on his palm, he used to tell his friends and relatives that he would live for about 35 years. Unfortunately, his prophecy proved true.  Srinivasa Ramanujan left for his heavenly abode on April 20, 1920 at the young age of 32 years.  With his untimely death, India lost a great mathematician of international repute.   Had he lived for several more years, he would have contributed much more to mathematics and in the process, he would have brought more laurels to his motherland.

Srinivasa Ramanujan who brought fame to his motherland with his exceptional research in mathematics, came to the earth like a meteor and then disappeared.  It is often remarked that three hundred years are required to comprehend mathematical inventions of Ramanujan carried out in his life span of 32 years.

In 1921, a year after his death, Nature listed Ramanujan among world’s distinguished scientists and mathematicians on a “Calender of Scientific Pioneers” who had achieved eminence. The Government of India issued stamps in honour of Ramanujan in 1962,2011,2012 and 2016. Ramanujan IT city was built in Chennai in 2011.

We fondly hope that the determination and unremitting commitment demonstrated by Ramanujan, and his accomplishments will motivate younger generation to take up research in pure science in a bigger way in the years to come.