DR. RAJ SHREE DHAR
From the whole, the whole arises, take away the whole from the whole, the whole remains Om Shanti Shanti Shanti.
A short, uncouth figure, stout, unshaven, with one conspicuous feature- shining eyes walked with a frayed note- book under his arm – Ramachander Rao, a Professor of Mathematics on describing the personality of a great mathematician Ramanujan.
Rightly regarded as ‘natural genius’ by the English mathematician G.H Hardy, Srinivasa Ramanujan displayed an amazing talent in mathematics, even though he did not receive formal training in that subject. He contributed to several areas of mathematics such as the number theory, mathematical analysis, infinite series and continued fractions. This great mathematician of the 20th century added much to the field of advance mathematics with his fascinating theories and proofs, which are in use even today. Also, in 1997, ‘The Ramanujan Journal’ was published by an American mathematician Bruce .C. Berndt, which showed Ramanujan’s areas of study. He formulated many formulas to solve problems, but his untimely death put an end to his great exploration to the unseen beauty and enormity of this subject. Within a short-life, he independently compiled about 3,900 results involving identities and equations. Ramanujan used to jot down some of the proofs and theorems in his notebooks that had been studied by many mathematicians, after his death.
Early Life
Srinivasa Ramanujan was born at his grandmother’s house in Erode, a small town located about 400 km towards southwest Madras. His father was a clerk in a textile shop in Kumbakonam. Young Ramanujan contracted small pox in December, 1889. However, unlike many other people in that town, Ramanujan overcame the epidemic invasion even though his father’s income was barely sufficient to meet extra medical expenses. When he was five, he was sent to a Primary School in Kumbakonam. Before he entered the Town High School in Kumbakonam in 1898 January, he went to several other private schools. Towards 1900, he began to work towards developing his mathematical ability, dealing with geometrics and arithmetic series. His talent was exposed to the world very early in 1902, when he showed how to solve cubic equations. While in Town High School, he read a book ‘Synopsis of elementary results in mathematics’, which was very concise that he could teach himself without taking help from any tutor. In this book, various theorems were mentioned in the book, along with shortcuts and formulas to solve them. During this time, Ramanujan engaged himself in deep research in 1904 and during this time he investigated the series ‘sigma 1/n’ and also extended Euler’s constant to 15 decimal points. Because of his great work in school studies, he was awarded a scholarship to attend Government College in Kumbakonam, in 1904. Due to his lack of interest in other subjects, he could not utilise this opportunity properly. He kept up his mathematical works and studied in depth about hyper geometric series and the relationship between series and integrals.
Career
Ramanujan was focused to pass the First Arts examination, which would be his ticket to the University of Madras. Hence, he went to Pachaiyappa’s College in Madras in 1906 and put all his efforts in studying and attended all the lectures. Unfortunately, after three months of his dedicated study, he became ill. He appeared for the Fine Arts examination and cleared in mathematics, but failed in all the other subjects. This stopped him from pursuing his dream of getting into the University of Madras. He left college without a degree and pursued independent research in Mathematics. In 1908, he studied fractions and divergent series. His health deteriorated and this time, it became worse and he had to undergo an operation in 1909. It took considerable time for him to recover. Ramanujan spent more time and effort in developing his mathematical ability and solved problems in the Journal of the Indian Mathematical Society, developing relations between elliptic modular equations. His brilliant work on the Bernoulli numbers in 1911, in the Journal of the Indian Mathematical Society, grabbed the recognition for all his hard work over the years. Though he did not have a university qualification, he became quite famous in Madras as a mathematical genius. He required means of income and so, he approached the founder of the Indian Mathematical Society in 1911. Hence, he was appointed in a temporary post at the Accountant General Office in Madras. Afterwards, he also approached Ramachandra Rao, the Collector at Nellore, for a job. In 1912, Ramanujan applied at the Madras Port Trust in the section of accounts for the clerical post. Recommendations from the university mathematicians helped him to get through the selection process. Hence, he joined the office on 1st March 1912. In the office, he was surrounded with great mathematicians who enhanced Ramanujan’s knowledge in the subject.
Life in England and Return to India
Ramanujan sent a copy of his works to some of the greatest mathematicians of this time, but that didn’t help him find his way further. After having read ‘Orders of Infinity’ by G.H Hardy in 1913, he also wrote to him. Hardy, along with Littlewood, went through his works and to Ramanujan’s delight, Hardy replied to him. In May 1913, The Board of Studies in Mathematics bestowed Ramanujan with a scholarship of Rs.75 per month for his two-year study in University of Madras. The following year Ramanujan went to Trinity College, Cambridge, with the help of Hardy. This gave way to extra ordinary collaboration. Ramanujan left India on 17th March 1914 and arrived in London on 14th April 1914. Along with Hardy, Ramanujan was able to prove some important results. Ramanujan had some health issues in the early winter season in March 1915, which stopped him from publishing anything for five months. Hence, on 16th March 1916, he graduated from Cambridge and acquired a Bachelor of Science degree by research. It is during this time that his health deteriorated and doctors were not confident. In 1919, 27th February, he went back to India and by this time his health was completely destroyed. With regard to his great recognition, he received a generous scholarship from the Madras University and every possible measure was arranged for his further research in the field of Mathematics.
Ramanujan-Hardy Number (1729)
When Ramanujan fell ill, Hardy came to his residence to visit Ramanujan in a cab with a number 1729. That day, he made a comment to Ramanujan saying that the number appeared to be very dull number. Ramanujan corrected him instantly saying that is an interesting number and explained that it is the smallest natural number that could be expressed as the sum of two positive cubes, in two different ways (i.e., 13 + 123 and 93 + 103.)
Personal Life and Death
In July, 14, 1909, Ramanujan married a ten year old girl, S. Janaki Ammal. However, he did not live with her until she was twelve years old. He succumbed to tuberculosis (T.B) in 1920 and was eventually admitted in the hospital. All the efforts went in vain and he passed away at the age of 32, on 26th April 1920.
On the 125th Anniversary of his Birth, India declared the Birthday of Ramanujan, December 22nd, as ‘National Mathematics Day.’ The declaration was made by Dr. Manmohan Singh in Chennai on 26th December , 2011.
(The author is Nodal Officer, J & K Institute of Mathematical Sciences, Jammu.)
