National Mathematics Day: Remembering the legacy of Srinivasa Ramanujan

Context: Every year, on December 22nd, the birth anniversary of legendary mathematician Srinivasa Ramanujan (1887-1920), is celebrated as National Mathematics Day.

• In 2012, then Prime Minister Manmohan Singh declared December 22 as National Mathematics Day in honor of the great man.

About Srinivasa Ramanujan

• Birth: He was born on 22nd December, 1887 in the town of Erode in Madras Presidency (now Tamil Nadu), to a Brahmin Iyengar family.
• Excelled in Mathematical Aptitude: By the age of 14, he was completing mathematics examinations in half the allotted time, and exploring complex topics way beyond the capability of an average 14-year old.

Srinivasa Ramanujan: A Chronology of his Achievements

• In 1904: After finishing secondary school, he received a scholarship at the Government Arts College, Kumbakonam. 
• By 1910: He was gaining popularity in Madras’ mathematical circles. 
• In 1911: He published the first of his papers in the Journal of the Indian Mathematical Society. 
• In 1912: V Ramaswamy Iyer, founder of the Indian Mathematical Society, helped him get a clerical position at the Madras Port Trust. 
• In 1913: Impressed with his’s theorems and work related to infinite series, the Cambridge-based GH Hardy called him to London.
• In 1914: He traveled to England and with Hardy’s help, got enrolled in Trinity College, Cambridge, where Hardy tutored him and collaborated with him in some research.
• In 1917: He was elected to be a member of the London Mathematical Society. 
• In 1918: He was elected to the prestigious Royal Society for his research on Elliptic Functions and theory of numbers, becoming one of the youngest to ever achieve the feat.
  • He was also the first Indian to be elected a Fellow of the Trinity College.

Ramanujan: His Major Contributions to Mathematics

• Infinite Series for pi: In 1914, Ramanujan found a formula for infinite series for pi. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics.
• Game Theory: His contribution to game theory is purely based on intuition and natural talent and is unmatched to this day.
• Mock Theta Function: He elaborated on the mock theta function, a concept in the field of modular forms of mathematics.
• Ramanujan Number: 1729 is known as the Ramanujan number which is the sum of the cubes of two numbers 10 and 9.
• Circle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. 
  • This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring’s conjecture and other additional questions.
• Theta Function: It is a special function of several complex variables. 
  • German mathematician Carl Gustav Jacob Jacobi invented several closely related theta functions known as Jacobi theta functions. 
  • Theta function was studied extensively by Ramanujan who came up with the Ramanujan theta function, which is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory.
• His Significant Contributions: Mathematical fields such as complex analysis, number theory, infinite series, continued fractions, Riemann series, elliptic integrals, hypergeometric series, and the functional equations of the zeta function.
  • He discovered his own theorems and independently compiled 3,900 results.

His Later Stage

• In 1919: Ramanujan returned to India from England. 
  • He spent his last year producing some of his most profound mathematics. 
• In 1920: At just 32 years of age, he breathed his last owing to deteriorating health. 
  • After his death, Ramanujan left behind three notebooks and some pages containing unpublished results, on which mathematicians continued to work for many years.

News Source: The Indian Express