|
A smart boy in the front row replied, "Each will
get one."
"Right, " the teacher said. "Now, similarly, if 1,000
i bananas are distributed among 1,000 boys, each will get one, Isn't that
so?"
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 bananas!"
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.
Ramanujan was born at 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 able to get Loney's Trigonometry from a college library. 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 Synopsis of Elementary Results in Pure and Applied
Mathematics by George Shoobridge Carr. For a boy of 15 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 to jot the results down in notebooks. Before
he went abroad he had filled three notebooks, which later became famous
as Ramanujan's Frayed Notebooks. Even today mathematicians are
studying them to prove or disprove the results given in them.
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. "To set him right", he forced
his son to marry. The girl chosen was eight-year-old Janaki.
Ramanujan began to look for a job. He had to find money not only for bread
but for paper 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 in 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 turned down.
Luckily for him, he at last found someone who was impressed by his notebooks.
He was the Director of the Madras Port Trust, Francis Spring, and he gave
Ramanujan a clerical job on a monthly salary of Rs. 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 Rs. 75 a month, though he had no qualifying
degree.
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, atopic 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. He also gave a key formula in the
hypergeometric series,which came to be named after him.
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.
Ramanujan found himself a stranger at Cambridge.The cold
was hard to bear and, being a Brahmin and 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 second 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 deathbed.
On April 26, 1920, he died at Chetpet in Madras.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". |
