From Zero To Infinity (Prose)

Unit 6 – Prose

From Zero to Infinity

Biography of Srinivasa Ramanujan

Warm up

• Did you enjoy solving this?
• Was it easy or hard to solve?
• Do you like Mathematics? Give reasons.

The arithmetic class was in progress.
The teacher was solving questions on division. On the blackboard were drawn three bananas.

“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 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.

Early Life

Ramanujan was born in Erode, 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.

Two years later, one of his senior friends showed him the book A Synopsis of Elementary Results in Pure Applied Mathematics, a collection of 4,865 formulae 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 Notebooks.

College Years & Struggles

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 turned down.

Turning Point

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.

Cambridge & Hardy

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 Riemann 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.

Life at Cambridge

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 Pythagoras 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.

Achievements

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
- 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.

Final Days

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”.

Glossary

Word	Meaning
absurd	stupid and unreasonable, silly in a humorous way
infinity	unlimited space, time, amount; a number large beyond any limit
intriguing	very interesting because of being unusual or mysterious
prodigy	a child who shows a great ability at a young age
dingy	a dark and dirty place
Physiology	the branch of biology that deals with the normal functions of living organisms and their parts
unkempt	not neat or cared for
uncouth	behaving in an unpleasant way
conjecture	an opinion or conclusion formed on the basis of incomplete information
discrepancy	an illogical or surprising lack of compatibility or similarity between two or more facts
distinguished	used to describe a person respected and admired for excellence
devouring	destructively consuming
disembark	to leave a ship, aircraft, etc. after a journey
emaciated	very thin and weak, usually because of illness or extreme hunger
agonising	causing extreme physical or mental pain

Section A – Answer in a sentence or two

1. Why did the students laugh at Ramanujan?
2. Why did the teacher compliment Ramanujan?
3. What did Ramanujan do after reading the book on Trigonometry?
4. What disappointed Ramanujan’s father?
5. How did Ramanujan manage his paper crisis?
6. Why were Ramanujan’s applications for jobs rejected?
7. Why was Ramanujan sent back to India?

Section B – Answer in 80–100 words

1. Describe the life of Srinivasa Ramanujan in India.
2. Narrate the association of Ramanujan with G.H. Hardy.

Section C – Vocabulary

Match the words with correct Synonym and Antonym.

S.No	Word	Synonym	Antonym
1	distribute	circulate	collect
2	infinite	boundless	measurable
3	significant	important	trivial
4	delight	joy	sorrow
5	unkempt	messy	clean
6	initiate	commence	conclude
7	conjecture	guess	fact

Section F – Reading Comprehension (ATM Passage)

1. What made John Shepherd-Barron come up with the idea of ATM?
2. When and where was the first ATM installed?
3. Who was the first person to withdraw cash from the ATM?
4. Why did Shepherd-Barron reduce the PIN number from six digits to four?
5. Which theory of Ramanujan helps the ATMs to dispense cash?

Writing

Paragraph Writing – Model

Topic Sentence → Supporting Details → Concluding Sentence

1. Write a paragraph of 100–120 words about a memorable anecdote/incident of your life.
2. Write a paragraph of 100–120 words about your favourite personality.

Grammar

Connectors

Complete the sentences using appropriate connectors from the box:
moreover, although, meanwhile, therefore, because, as long as, thus, above all, for instance, except

1. Irine felt cold although she was wearing a winter coat.
2. This restaurant has some of the best chefs in the town. Moreover, their service is excellent.
3. I’m not going to the party tonight because I didn’t get an invitation.
4. You can set the table. Meanwhile, I’ll start making dinner.
5. I can play quite a few instruments. For instance, the flute, the guitar and the piano.
6. The store was out of chocolate chips; therefore they would need to make a different type of cookies.
7. The stores are open daily except Sundays.
8. I’ll stay as long as you need me.
9. This detergent is highly concentrated and thus you will need to dilute it.
10. It was the thing he prized above all.

Active & Passive Voice

Convert the following active sentences into passive:

1. She will not recognize us.
   → We will not be recognized by her.

2. They didn’t invite me, but I went anyway.
   → I wasn’t invited, but I went anyway.

3. They broke up the table for firewood.
   → The table was broken up for firewood.

4. She has won the first prize.
   → The first prize has been won by her.

5. A friend of mine is repairing the car.
   → The car is being repaired by a friend of mine.

6. Begin the work tomorrow.
   → Let the work be begun tomorrow.

7. They speak English in New Zealand.
   → English is spoken in New Zealand.

8. His attitude shocked me.
   → I was shocked by his attitude.

9. She had already sent the parcel.
   → The parcel had already been sent by her.

10. Her silence worries me.
    → I am worried by her silence.

Imperatives in Passive

Change the following into passive voice:

1. Stanley will inform you later.
   → You will be informed by Stanley later.

2. People speak Portuguese in Brazil.
   → Portuguese is spoken in Brazil.

3. My grandfather built this house in 1943.
   → This house was built by my grandfather in 1943.

4. Do not hurt the animals.
   → Let the animals not be hurt.

5. You must not drop litter in the streets.
   → Litter must not be dropped in the streets.

6. Carry it home.
   → Let it be carried home.

7. They are decorating the wall.
   → The wall is being decorated.

8. He has already mended the TV set.
   → The TV set has already been mended.

Project

Make a scrapbook of ‘Famous Biographies’ by collecting at least five biographies of famous scientists, mathematicians, inventors, artists etc., of your choice. You may also collect pictures related to their achievements, inventions etc.

Suggested Names:
- Marie Curie
- Jonas Salk
- M.S. Subbalakshmi
- Stephen Hawking

Practice Practice Exercises

1. She will not recognize us. or. We by her.

a. will not recognize. b. will not being recognized. c. will not be recognized

2. They didn’t invite me, but I went anyway. Or. I but I went anyway.

a. wasn't invited. b. wasn't being invited. c. wasn't inviting

3. They broke up the table for firewood. Or. The table up for firewood.

a. broke. b. had broken. c. was broken

4. She has won the first prize. Or. The first prize by her.

a. has won. b. has been won. c. had been won

5. A friend of mine is repairing the car. Or. The car by a friend of mine.

a. is repairing. b. is repaired. c. is being repaired

6. Begin the work tomorrow. Or. Let the work tomorrow.

a. be begun. b. begin. c. is beginning

7. They speak English in New Zealand. Or. English in New Zealand.

a. is speaking. b. is spoken. c. is being spoken

8. His attitude shocked me. Or. I by his attitude.

a. had shocked. b. had been shocked. c. was shocked

9. She had already sent the parcel. Or. The parcel by her.

a. has already been sent. b. had already been sent. c. was already sent

10. Her silence worries me. Or. I her silence.

a. am worrying by. b. am worried by. c. have worried by

1. Stanley will inform you later.

2. People speak Portuguese in Brazil.

3. My grandfather built this house in 1943.

4. Do not hurt the animals.

5. You must not drop litter in the streets.

6. Carry it home.

7. They are decorating the wall.

8. He has already mended the TV set.

1. Why did the students laugh at Ramanujan?

2. Why did the teacher compliment Ramanujan?

3. What did Ramanujan do after reading the book on Trigonometry?

4. What disappointed Ramanujan’s father?

5. How did Ramanujan manage his paper crisis?

6. Why were Ramanujan’s application for jobs rejected?

7. Why was Ramanujan sent back to India?

1. Describe the life of Srinivasa Ramanujan in India.

2. Narrate the association of Ramanujan with G.H. Hardy.

1. What made John Shepherd-Barron to come up with the idea of ATM?

2. When and where was the first ATM installed?

3. Who was the first person to withdraw cash from the ATM?

4. Why did Shepherd-Barron reduce the PIN number from six digits to four?

5. Which theory of Ramanujan helps the ATMs to dispense cash?

Topic Sentence Supporting Detail #1 Supporting Detail #2 Concluding Sentence

G. 1. Write a paragraph of 100 – 120 words about a memorable anecdote or Incident of your life.

2. Write a paragraph of 100 – 120 words about your favourite personality.

1. Irine felt cold she was wearing a winter coat.

2. This restaurant has some of the best chefs in the town their service is excellent.

3. I’m not going to the party tonight I didn’t get an invitation.

4. You can set the table. I’ll start making dinner.

5. I can play quite a few instruments. the flute, the guitar and the piano.

6. The store was out of chocolate chips; they would need to make a different type of cookies.

7. The stores are open daily Sundays.

8. I’will stay you need me.

9. This detergent is highly concentrated and you will need to dilute it.

10. It was the thing he prized