From Zero to Infinity
Biography of Srinivasa Ramanujan
The arithmetic class was in progress. The
teacher was solving questions on division. On the blackboard were drawn three
“We have three bananas,” the teacher said, “and
we have three boys. Can you tell me how many each will get?”
A smart boy in the front row replied, “Each
will get one.”
“Right,” the teacher said. “Now, similarly, if
1,000 bananas are distributed among 1,000 boys, each will get one, isn’t that
While the teacher was explaining, a boy sitting
in one corner raised his hand and stood up. The teacher stopped and waited for
the boy to speak.
“Sir,” the boy asked, “If no banana is
distributed among no one, will everyone still get one banana?” There was a roar
of laughter in the class. What a silly question to ask!
“Quiet!” the teacher said loudly and thumped
the desk. “There’s nothing to laugh at. I will just explain what he means to
say. For the division of bananas, we divided three by three, saying that each
boy will get one banana. Similarly, we divided 1,000 by 1,000 to get one. What
he is asking is that if zero banana is divided among zero, will each one get
one? The answer is ‘no’. Mathematically, each will get an infinite number of
Everyone laughed again. The boys understood the
trick, arithmetic had played upon them. What they could not understand was why
the teacher later complimented the boy who had asked that absurd question.
The boy had asked a question that had taken
mathematicians several centuries to answer. Some mathematicians claimed that
zero divided by zero was zero. Others claimed it to be unity. It was the Indian
mathematician Bhaskara who proved that it is infinity.
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.
* What was the reaction
of the classmates to Ramanujan’s
classmates laughed at Ramanujan's questions
* What did the Indian
mathematician Bhaskara prove?
Indian mathematician Bhaskara proved that zero divided by zero is infinity.
Ramanujan was born in Erode in Tamil Nadu on
December 22, 1887. His father was a petty clerk in a cloth shop. From early
childhood it was evident that he was a prodigy.
Senior students used to go to his dingy
house to get their difficulties in mathematics solved. At the age of 13,
Ramanujan was lent a book on advanced trigonometry written by S.L. Loney. Not
only did he master this rather difficult book but also began his own research.
He came forth with many mathematical theorems and formulae not given in the
book, though they had been discovered much earlier by great mathematicians.
The most significant turn came two years later
when one of his senior friends showed him 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. For a boy of 16 the title itself must be frightening, but Ramanujan was
delighted. He took the book home and began to work on the problems given in it.
This book triggered the mathematical genius in him.
Mathematical ideas began to come in such a flood
to his mind that he was not able to write all of them down. He used to do
problems on loose sheets of paper or on a slate and jot the results down in
notebooks. Before he went abroad he had filled three notebooks, which later
became famous as Ramanujan’s Frayed
* Where did Ramanujan get S.L.
Loney’s book on Trigonometry?
got "Loney's Trignometry" book from a college library.
* Where did Ramanujan do his
used to do problems on loose sheets of paper or on a slate.
Although Ramanujan secured a first class in
Mathematics in the matriculation examination and was awarded the Subramanyan Scholarship,
he failed twice in his first-year arts examination in college, as he neglected
other subjects such as History, English and Physiology.
This disappointed his father. When he found the boy always scribbling numbers
and not doing much else, he thought Ramanujan had gone mad.
Ramanujan began to look for a job. He had to
find money not only for food but for papers as well to do his calculations. He
needed about 2,000 sheets of paper every month. Ramanujan started using even
scraps of paper he found lying on the streets. Sometimes he used a red pen to
write over what was written in blue ink on the piece of paper he had picked up.
Unkempt and uncouth, he would visit offices, showing everyone his frayed notebooks and telling
them that he knew mathematics and could do a clerical job. But no one could
understand what was written in the notebooks and his applications for jobs were
Luckily for him, he at last found someone who
was impressed by his notebooks. He was the Director of Madras Port Trust,
Francis Spring, and he gave Ramanujan a clerical job on a monthly salary of ₹25. 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.
* What were the
subjects neglected by Ramanujan in college?
subjects neglected by Ramanujan in college were History, English and
* Which University granted him a
fellowship of ₹75 a month?
university of Madras granted him a fellowship ₹75 of a month.
A few months earlier, 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. But Ramanujan was ignorant of the work of the German
mathematician, George F. Riemann, who had earlier arrived at the series, a rare
achievement. Also included was Ramanujan’s conjecture
about the kind of equations called “modular”. Pierre Deligne subsequently
proved this conjecture to be correct.
It did not take long for Hardy and his
colleague, J.E. Littlewood, to realise that they had discovered a rare
mathematical genius. They made arrangements for Ramanujan’s passage and stay at
Cambridge University. On March 17, 1914, he sailed for Britain.
* What did
Ramanujan send to G.H. Hardy?
sent a letter to G.H. Hardy in which he set out 120 theorems and formulae.
* Who discovered a rare mathematical genius in Ramanujan?
H. Hardy and his colleague, J.E. Littlewood discovered a rare mathematical
genius in Ramanujan.
Ramanujan found himself a stranger at
Cambridge. The cold was hard to bear and being a vegetarian, he had to cook his
own food. However, he continued his research in Mathematics with determination.
In the company of Hardy and Littlewood, he could forget much of the hardship he
had to endure.
In Ramanujan, Hardy found an unsystematic
mathematician, similar to one who knows the Pythagorus theorem but does not
know what a congruent triangle means. Several discrepancies
in his research could be attributed to his lack of formal education. Ramanujan
played with numbers, as a child would with a toy. It was sheer genius that led
him to mathematical “truths”. The task of proving them, so important in
Science, he left to lesser mortals.
Ramanujan was elected, Fellow of the Royal
Society on February 28, 1918. He was the youngest Indian to receive this distinguished fellowship. In October that year he
became the first Indian to be elected Fellow of Trinity College, Cambridge. His
achievements at Cambridge include the Hardy-Ramanujan-Littlewood circle method
in number theory, Roger-Ramanujan’s identities in partition of integers, a long
list of the highest composite numbers, besides work on the number theory and
the algebra of inequalities. In algebra his work on continued fractions is
considered to be equal in importance to that of great mathematicians like
Leonard Euler and Jacobi.
While Ramanujan continued his research work,
Tuberculosis, then an incurable disease, was devouring
him. Ramanujan was sent back to India and when he disembarked,
his friends found him pale, exhausted and emaciated.
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”.