Srinivasa Ramanujan : The Man Who Knew Infinity

 

      Srinivasa   Ramanujan : The Man Who Knew Infinity

 

 

Srinivasa Ramanujan: Childhood, and Early Life

 He was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu, India) at his maternal grandparent's residence. His father was K. Srinivasa Iyengar, an accounting clerk for a clothing merchant, and his mother was Komalatammal, a housewife and sang at a local temple. 

 

The family was of high caste and was very poor. Srinivasa Ramanujan's parents moved around a lot, and so he attended a variety of different elementary schools. 

Education

In November 1897, he passed his primary examinations in English, Tamil, geography, and arithmetic, and gained vest scores in the district. He entered Town Higher Secondary School in the same year and encountered formal mathematics for the first time.

Srinivasa Ramanujan: Discovery as a Mathematician of Genius

·         At the age of 11, he had taken the mathematics knowledge of two college students who were lodgers at his home. Later, he lent a book written by S. L. Loney on advanced trigonometry. By the age of 13, he had mastered it and discovered his theorems on his own. 

·         At 14 years of age, he received merit certificates and academic awards that continued all through his school career. Also, he completed an exam in mathematics in half of the allotted time and showed familiarity with geometry and infinite series. 

·         In 1902, he showed how to solve cubic equations. He also developed his own methods.

·         At the age of 15, he obtained a copy of George Shoobridge Car's

 

 

 

Ramanujan’s major contributions to mathematics:

Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions.

Infinite series for pi : In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics.

 

Game theory: Ramanujan discovered a long list of new ideas for solving many challenging mathematical problems that have given great impetus to the development of 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: Theta function 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 by extensively Ramanujan who came up with the Ramanujan theta function, that generalizes the form of Jacobi theta functions and also captures general properties. Ramanujan theta function is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory.

 

 Srinivasa Ramanujan: Illness and Death

He contracted tuberculosis in 1917. His condition improved so that he could return to India in 1919. He died the following year. He left behind three notebooks and some pages, also known as the "lost notebook" that contained various unpublished results. Mathematicians continued to verify these results after his death.