26th of April, 2020 marks the 100th death anniversary of the mathematician who brought India on the World Mathematics Map, Srinivasa Ramanujan is regarded as one of the greatest mathematicians of the modern world without any formal education in Mathematics.
Ramanujan was one of the greatest mathematical prodigies ever to emerge from India. Srinivasa Iyengar Ramanujan, commonly known as Ramanujan was born at Erode in the Madras Presidency on 22nd December 1887 to a Sri Vaishnava Brahmin Family. Ramanujan in his early life showed a strong inclination toward mathematics and his extraordinary powers appear to have amazed many. His quiet, meditative nature and an extraordinary memory would easily astonish his friends and teachers by mental calculations of many decimal places of π, e, and other mathematical constants. Ramanujan showed early signs of his intelligence in maths, he would always ask puzzling questions on concepts like, “zeros and imaginary quantities,” the “distances of stars” and the value of zero divided by zero.
By the age of 13 he completely mastered the book on advanced trigonometry written by S. L. Loney. He found his own method of solving cubic equations at the age of 15. In elementary school he won numerous awards for his calculating skills. Upon graduation in 1904, he won a scholarship for higher studies in Govt. College, Kumbakonam. In 1903 when he was 16, Ramanujan borrowed a copy of a book by G. S. Carr, titled ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’, it was this book that awakened his genius. He set himself to establish the formulae given therein. Consumed by his passion for mathematics, Ramanujan neglected all other subjects. As a result, he failed the entrance exam for the University of Madras. However, he continued his mathematical research with intensity and, by his early twenties, had become known to the leading mathematicians in the region.
On 14 July 1909, Ramanujan was married to a nine-year-old bride, Janaki Ammal, after marriage he searched for a job, for the next three years he held no serious job; he went door to door around the city of Madras looking for a clerical position. Despite his poverty, Ramanujan continued to immerse himself in mathematics. He scribbled his formulas, expressed in irregular and non–standard notation, in a series of scruffy notebooks.
Ramanujan was an ardent follower of the Hindu goddess Namagiri Devi. After receiving visions from the goddess in the form of blood droplets, Ramanujan saw scrolls that contained very complicated mathematics like Elliptic integrals, Hyper-geometric series, etc. It was a remarkable fact that frequently, on rising from bed, he would note down results and rapidly verify them, though he was not always able to supply a rigorous proof.
Ramanujan managed to secure a clerical job at the Madras Port Trust office in the accounts department. Ramanujan published his first research paper titled ‘Some properties of Bernoulli Numbers’ in the Journal of the Indian Mathematical Society in the December issue of Volume 3 in 1911. Along with the paper Ramanujan proposed some intricate questions.
At that time, since there were no mathematicians in India capable of understanding his extraordinary talent, Ramanujan, In January 1913 wrote a 10-page letter containing 120 theorems to another renowned British mathematician Prof. G. H. Hardy of Trinity College (Fellow of the Royal Society), Cambridge. He was amazed and intrigued by the theorems that Ramanujan had included in the letter. Hardy, himself a man of extraordinary ability, reviewed Ramanujan’s strange looking theorems and concluded, “A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they were not true, no one would have had the imagination to invent them.”
Hardy took a keen interest in Ramanujan’s work and decided to bring Ramanujan to Cambridge for pursuing some serious research. Furthermore, a special research scholarship of Rs.75/- per month was awarded him for two years by the University of Madras. Ramanujan thus became a professional mathematician and remained so for the rest of his life. Ramanujan was very pleased to receive an invitation from Hardy to work with him at Cambridge but his journey to England was delayed by a religious prohibition against foreign travel. During that time Ramanujan’s mother had a vivid dream in which the family Goddess Namagiri commanded her “to stand no longer between her son and the fulfillment of his life’s purpose” also Ramanujan had a vision from the Goddess granting him permission to go to Cambridge. Thus, on 17th March 1914 Ramanujan sailed to England.
At Cambridge, Ramanujan started working with Hardy and Littlewood, for the first time in his life, he was in a really comfortable position and could devote himself entirely to his mathematical research. Ramanujan and Hardy shared their unique mathematical perspectives, which led to some startling discoveries especially in Analytic number theory and Modular forms. They jointly found an astonishing formula to count the number of partitions of an integer (Partition function) which currently serves as an important application in modern physics.
Ramanujan independently developed several unusual formulas that enable modern computers to calculate virtually limitless values of π with incredible speed and accuracy. In 1917, he was elected to the London Mathematical Society and was inducted into the Royal Society as a Fellow
(FRS) in 1918 at the age of 30, an extremely young age.
Ramanujan returned to India in fragile health, he was believed to be tubercular, but with deteriorating health conditions he suffered a severe vitamin deficiency (Amebiasis). His sickness was not curable and on 26th April 1920, at the mere age of 32, the World of Mathematics lost a gem. However, Ramanujan’s deep dive into the field of mathematics knew no limits, even at the last stage of his life, he produced some of the most profound theorems including Mock Theta functions, q-series, Diophantine equations, Reciprocal functions, Mordell integrals, Continued fractions, and Modular forms.
Ramanujan’s life was tragically short. However his mathematical discoveries are still alive and flourishing. The work of Ramanujan was so unparalleled, unprecedented & rich that just the side comments on his work are enough to keep seasoned mathematicians busy even now. A century later, the legacy of this genius continues to influence mathematics, physics and computation fields.
Surprisingly in 2012 scientists found a profound and precise relationship between Ramanujan’s cryptic mock theta functions and hottest items in theoretical physics – string theory and black holes.
Great people live short lives, sometimes. May the young be inspired by such beautiful minds!