Notes Class 8 Chapter 4.4 Balbharati English Maharashtra Board

Ramanujan

1. About the Chapter

• Biographical sketch of Srinivasa Ramanujan, a self-taught Indian mathematical genius.
• Focuses on his discovery by G.H. Hardy, his struggles, achievements, and contribution to mathematics.

2. Discovery by G.H. Hardy

• In 1913, Hardy received a letter with unusual mathematical theorems from India.
• The letter was untidy, written in broken English, with no proofs.
• Initially, Hardy thought it was boring, irritating, and possibly a fraud.
• The theorems kept bothering him due to their uniqueness.
• He discussed them with Littlewood that night.
• They realized the author was a genius.

3. Ramanujan’s Background

• A poor clerk in Madras (now Chennai).
• Lived with his wife and mother on £20 a year.
• Deeply religious and followed strict caste laws.
• His mother was strongly opposed to him crossing the sea.

4. Divine Intervention

• His mother had a dream of the goddess of Namakkal telling her not to stop Ramanujan.
• This convinced her to allow him to go to England.

5. Life in England

• Ramanujan reached England in 1914.
• Lived in Trinity College, Cambridge.
• Followed his religious rituals strictly.
• Cooked his own food in his room.
• Despite cultural and educational differences, he and Hardy had a touching friendship.

6. Challenges Faced

• Ramanujan was self-taught, unaware of modern proofs and mathematical rigor.
• Couldn’t enter Madras University due to failing English.
• Hardy had to teach him formal mathematics like a school student.
• Ramanujan’s work amazed even the most educated mathematicians.

7. Achievements in England

• Became a Fellow of the Royal Society at age 30 (a rare honour).
• Also elected Fellow of Trinity College.
• First Indian to receive both distinctions.
• Admired and respected by the academic community.

8. Decline in Health

• Fell seriously ill in England.
• Was later hospitalized at Putney.
• Hardy visited him regularly.

9. Famous 1729 Incident

• Hardy said the taxi number 1729 was dull.
• Ramanujan replied:
  • It is the smallest number that can be expressed as the sum of two cubes in two different ways:
    • 13+123=17291^3 + 12^3 = 172913+123=1729
    • 93+103=17299^3 + 10^3 = 172993+103=1729

10. Death

• Could not be moved to a warmer climate due to World War restrictions.
• Returned to India and died of tuberculosis in 1920, at the age of 33.

11. Hardy’s Reflection

• Hardy compared Ramanujan’s genius to Gauss and Euler.
• Called his teaching experience with Ramanujan the most singular in his life.
• Believed if Ramanujan had formal education, he could have achieved even more.