Biography of Srinivasa Ramanujan:

Srinivasa Ramanujan (1887–1920) was an Indian mathematician known for his substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Despite having little formal training in mathematics, Ramanujan independently discovered a vast array of theorems and formulas that had a significant impact on the field. 
Here is a brief biography of Srinivasa Ramanujan:

Early Life:

1. Birth and Early Education:
Srinivasa Ramanujan was born on December 22, 1887, in Erode, Madras Presidency (now in Tamil Nadu, India).
His aptitude for mathematics became evident at an early age, and he began exploring mathematical concepts on his own.
Early Life - Contributions to Mathematics - Association with G.H. Hardy - Health and Later Years of Ramanujan
Biography of Srinivasa Ramanujan
2. Limited Formal Education:
Ramanujan had limited formal education due to financial constraints but continued to pursue mathematics independently.

Contributions to Mathematics:

1. Land of Pi Formulas:
Ramanujan made significant contributions to the field of infinite series, including formulas related to the mathematical constant pi (π). He discovered novel and rapidly converging series for pi.

2. Ramanujan Prime and Ramanujan-Hardy Number:
He introduced the concept of Ramanujan primes and the Ramanujan-Hardy number, both of which are significant in number theory.
3. Modular Forms:
Ramanujan’s work on modular forms laid the groundwork for further developments in the theory of elliptic functions and modular forms.
4. Partition Function:
His work on the partition function, denoted as p(n), provided groundbreaking insights into the number of ways an integer can be partitioned into summands.
5. Mock Theta Functions:
Ramanujan developed mock theta functions, a class of mathematical functions that have applications in various areas of mathematics and physics.

Ramanujan’s Association with G.H. Hardy:

1. Correspondence with Hardy:
Ramanujan’s work came to the attention of the English mathematician G.H. Hardy. Impressed by the depth and originality of Ramanujan’s results, Hardy invited him to Cambridge University in 1914.
2. Cambridge Years:
Ramanujan spent several years at Cambridge collaborating with Hardy and other mathematicians. He published numerous papers during this time.

Health and Later Years:

1. Health Issues:
Ramanujan faced health challenges, including periods of illness. His health deteriorated during his time in England.
2. Return to India:
In 1919, Ramanujan returned to India due to health reasons.
3. Death:
Srinivasa Ramanujan passed away on April 26, 1920, at the age of 32, in Kumbakonam, Tamil Nadu.

Legacy of Ramanujan:

1. Unsolved Problems:
Many of Ramanujan’s formulas and theorems remain the subject of ongoing mathematical research, and some of his conjectures have been proven long after his death.
2. Ramanujan-Hardy Number:
The number 1729 is known as the “Ramanujan-Hardy number” and is famous for an incident in which Hardy visited Ramanujan in the hospital and mentioned taking a particularly dull taxi numbered 1729. Ramanujan immediately responded that 1729 is an interesting number, being the smallest positive integer that can be expressed as the sum of two cubes in two different ways.
3. Recognition:
Ramanujan’s life and contributions have been celebrated in various ways, including through biographies, films, and annual events like National Mathematics Day in India (on Ramanujan’s birthday).
Srinivasa Ramanujan’s extraordinary mathematical abilities and discoveries have left an enduring impact on the field of mathematics. His story is one of exceptional talent, perseverance, and the pursuit of knowledge against challenging circumstances.