When Instinct Works Lesson Summary in English


The chapter introduces the great mathematician Srinivasa Ramanujan and narrates his journey from a young boy with an absurd question to becoming one of the greatest mathematicians. 

Three Bananas

In a class, a teacher was explaining the concept of division in mathematics. He used the example of three bananas and how they would be divided among three boys. While the teacher was explaining, a boy sitting in one corner raised his hand and stood up. The boy asked a rather unusual question that made his fellow mates laugh, but the teacher praised him for his question and gave him the answer.

The boy asked that if no banana was distributed among no one, would everyone still get one banana? The answer is ‘no’. Mathematically, each will get an infinite number of bananas. The boy had asked a question that had taken mathematicians several centuries to answer.  The boy who asked the intriguing question was Srinivasa Ramanujan.

Throughout his life, whether in his native Kumbakonam or Cambridge, he was always ahead of his mathematics teachers. Ramanujan was born in Erode in Tamil Nadu on December 22, 1887. He was the smartest guy in school and even his seniors would seek his help to solve sums.

When he was 13, he received a book on trigonometry, he mastered this rather tough book and came up with theorems and formulae that were not in the book. Two years later he received the book A Synopsis of Elementary Results in Pure Applied Mathematics, a collection of 4,865 formulas and theorems without proof by G.S. Carr. This book triggered the mathematical genius in him. He had so many ideas and solutions, that he would write them on loose sheets. Before he went abroad, he had filled three notebooks, which later became famous as Ramanujan’s Frayed Notebooks.

Ramanujan had secured the first class in mathematics in the matriculation examination and was awarded the Subramanian scholarship however he failed twice in his first-year arts examination in college. He started looking for a job but no one could understand what was written in the notebooks and his applications for jobs were turned down.

From Kumbakonam to Cambridge

Francis Spring the director of Madras Port Trust gave Ramanujan his first job as a clerk with a monthly salary of 25 rupees. Later some teachers and educationists interested in Mathematics initiated a move to provide Ramanujan with a research fellowship. On May 1, 1913, the University of Madras granted him a fellowship of ?75 a month, though he had no qualifying degree.

Ramanujan had sent a letter to the great mathematician G. H. Hardy, of Cambridge University, in which he set out 120 theorems and formulae. Among them was what is known as the Reimann Series, a topic in the definite integral of Calculus. Hardy and his colleague J.E Littlewood realised that Ramanujan was a rare mathematical genius and arranged for him to come to Cambridge University. On March 17, 1914, he sailed for Britain.

Ramanujan faced difficulties in adjusting in Cambridge but he overcame those with Hardy and Littlewood’s companionship. Hardy found Ramanujan to be an unsystematic mathematician. Several loopholes in his research were results of his lack of formal education. It was sheer genius that led him to mathematical “truths”.

Ramanujan was elected, Fellow of the Royal Society on February 28, 1918. He was the youngest Indian to receive this fellowship. In October that year he became the first Indian to be elected Fellow of Trinity College, Cambridge. He has significantly contributed to research in algebra and number theory.

Ramanujan fell ill with tuberculosis and at that time it had no cure. He returned to India tired and pale. To forget the agonising pain, he continued to play with numbers even on his death bed. Besides being a mathematician, Ramanujan was an astrologer of repute and a good speaker. He used to give lectures on subjects like “God, Zero and Infinity”.