As a child, I was always scared by mathematics and now I am relatively good at it but fear is still in my heart. I think, most of you also have fear of mathematics. But here, I am going to tell you about a gentleman who is considered a wizard of mathematics, a person who has immense love for numbers and mathematical calculations. This person had opened new doors for the future mathematics and results which he had given a long time back are still helping us to understand our nature in a very precise manner. Now, you all will be thinking that who was that person who had such love for the scariest subject like mathematics. Mathematics is the root mother of all science and what we have achieved as human beings in the last many centuries was not possible without mathematics. Without boring you, I am going to tell you about the wizard of mathematics Mr. Srinivasa Ramanujan.
On 22nd December 1887, a boy was born in village Kumbakonam of district Erode, Tamil Nadu. He belonged to the Tamil brahmin family, because of that he had deep faith in God and he used to worship God daily. His father Kuppuswami Srinivasa Iyengar was a clerk in the local sari shop and had money only to feed his family. From childhood, Ramanujan had a great obsession with mathematics and numbers.
Once the teacher was teaching students about numbers and arithmetic and asking some simple questions in arithmetic. The class was learning about the simple operation of division. When did the teacher ask students that how many bananas will each of the 3 boys get from a stack of 3 bananas? All boys answered one. Then again teacher asked the how many bananas will each of the 1000 boys get from a stack of 1000 bananas? Students answered one. But at that time there was a boy who had a question in his mind that what will happen if none of the banana was distributed among one boy or no boys? When he asked this question in the class, the whole class burst into laughter. But the teacher seemed to have impressed by the question asked by the student. Then teacher explained to the class that the question asked by the student was not a silly question but rather a profound one. The teacher told the class that this student was asking about the concept of infinity or indefinite. The teacher explained to the class that this concept had baffled mathematicians for centuries until an Indian mathematician Bhaskara had thrown light on it. He had proved that zero divided by zero was neither zero nor one, but infinity. This student who asked this question was none other than Ramanujan.
From childhood, Ramanujan had a deep interest in mathematics, at the early age of thirteen he has mastered the book “Advanced Trigonometry” by S.L. Loney. He was so good at this subject that his many seniors from school and college came to him to understand the subject. He was so taken by the subject that he started to solve all the unsolved and solved problems of the book in his own book. By the age of fifteen, he had developed his own way of solving quadratic and cubic equations.
The real turning point came into his life when a friend of his introduced him to the library copy of the book “Synopsis of Elementary Results in Pure and Applied Mathematics” by George Shoobridge Carr. Ramanujan was only sixteen when he started reading this book, where any other person at this age may be recoiled by this book, Ramanujan became delighted by this. This book had a collection of 5000 theorems and Ramanujan studied this from the first word to the last word. The book is generally acknowledged as a key element in awakening his genius. Ramanujan was so impressed by this book that he solved each problem from this book in his own way. The next year Ramanujan independently developed and found the Bernoulli numbers and calculated the Euler-Maschroni constant up to 15 decimal places. His peers at the time said they “rarely understood him” and “stood in respectful awe” of him. Do you imagine that how many sheets he used per month? Two thousand! He scribbled his own work in loose sheets and notebooks. In fact, when he combined all his results he filled three notebooks. Later these notebooks are known as Ramanujan’s Frayed Notebooks.
Ramanujan’s father was a clerk but he never fathoms Ramanujan’s obsession for mathematics. Although the boy had secured the first rank in the matriculation examination among his classmates and had also been awarded the K. Ranganatha Rao prize for mathematics by the school’s headmaster, Krishnaswami Iyer. Iyer was so impressed by Ramanujan that he introduced him as an outstanding student who deserved scores higher than the maximum. He received a Subramanyan scholarship to study at Government Arts College, Kumbakonam, but he was so intent on mathematics that failed in almost all subjects except mathematics and lost his scholarship. Desiring to bring his “mad” son back on the course of “normalcy”, the worried father got him married to Janaki a young girl of eight who was selected by his mother Komaltammal.
Marriage put Ramanujan in a real dilemma. He needed to find money to support his family and himself. Oh yes, but his marriage did not distract him from his real love and magnificent obsession. To cut down his expenses he reused his mathematics paper and rewrite those with different ink so that he can differentiate among the ideas which he had written on those papers. To made his family survive, he approached several offices and applied for many clerical jobs, despite being good in mathematics he found no job. Luckily, he came across Francis Spring who was a civil engineer and chairman at Port Trust madras. Francis Spring was the person responsible for the British railway line project in the madras region. Since he was an engineer so he had a decent grasp of mathematics, so when Ramanujan came across to him he was impressed by Ramanujan’s mathematics, and he had given him a clerk job in Port Trust. At Port Trust, Ramanujan met with the deputy collector of Madras V. Ramaswamy Aiyer, who had founded the Indian Mathematical Society. Then Francis introduced Aiyer to Ramanujan’s mathematical work and Aiyer seemed to have been impressed. Then Aiyer along with other educationists seemed to impressed by Ramanujan’s work. As a result, the University of Madras awarded him a fellowship although he had no formal degree.
In the meantime, Ramanujan had approached the great mathematician G.H. Hardy, a professor at Cambridge University. Ramanujan sent him a notebook that had a hundred and twenty theorems and formulae formulated by Ramanujan in his own way. A part of the notebook was the Reimann series, a topic in definite integral in calculus. Ignorant of Reimann’s original work, Ramanujan had formulated the work all over again.
Then, Ramanujan sent another collection of the theorems to G.H. Hardy which had Ramanujan’s interpretation about the equations called “modular”. Many of the work which Ramanujan had sent to Hardy consisted only of the results of the problems, not the formulations, which was later proved that Ramanujan’s conjectures were indeed correct. The collection also included a formula in hypergeometric series, which later came to be named after him.
Hardy and his colleague, J.E. Littlewood, recognized the genius in Ramanujan and made all arrangements for him to travel to Cambridge University to study. Hardy was so impressed and amused to find that Ramanujan was an unsystematic mathematician, who played with math like a kid play with toys. Most of Ramanujan’s work was just problem statements and results without formulations, so at Cambridge, Hardy and Ramanujan worked together and proved some of those problems and left many to other mathematicians to prove. All Ramanujan’s formulae notebooks are preserved in Cambridge University and many of great brains across the globe are trying to prove his work.
Left Side Person: G.H. Hardy and Right Side Person: S. Ramanujan
Ramanujan was elected fellow of the Royal Society in February 1918. He was the second Indian to be honored with this fellowship and the first Indian to be elected fellow of Trinity College, Cambridge University. His contributions to the field of mathematics included the Ramanujan’s Sum, Ramanujan’s Series, Hardy-Ramanujan-Littlewood circle method in number theory, Rogers-Ramanujan’s identities in the partition of integers, list of highest composite numbers, Ramanujan’s master theorem, and some work on the algebra of inequalities and number theory. Unfortunately, Ramanujan fell victim to tuberculosis which at that time was a big hazard because of no cure so Ramanujan had to be sent back to India. Fighting pain and death, Ramanujan kept himself preoccupied with playing with mathematics. He succumbed to the illness at the younger age of thirty-two. Within the short life span, Ramanujan has earned repute as a mathematician and an orator too.
The people like Ramanujan never die, they always remain immortal through their work. He is an inspiration to the world, future generations. His work is helping us to understand our nature in a more precise manner. May his body has left us but his legacy remains immortal.