Srinivasa Ramanujan: Life and Mathematics

E. W. Barnes was Ramanujan's tutor at Cambridge who was both a mathematician and later became a bishop in the Anglican church. Barnes was a Fellow of the Royal Society and supported Ramanujan during his time at Trinity College, Cambridge.

The Ramanujan conjecture (also known as the tau conjecture) was a significant hypothesis about tau functions that kept mathematicians puzzled for decades. It was finally solved by Pierre Deligne in 1974, for which Deligne was awarded the Fields Medal.

Ramanujan's scholarship at Government College in Kumbakonam was withdrawn because he failed in his English examination. Ramanujan was so focused on mathematics that he neglected other subjects, and this led to the loss of his financial support.

Ramanujan's first paper presented to the London Mathematical Society in 1914 was titled 'Modular Equations and Approximations to π' (pi). This work focused on novel approximations of the value of pi using his theories of modular functions and elliptic functions. Hardy's theory and quantum theory are unrelated to Ramanujan's work, while Bernoulli's theorem was already well-established.

Srinivasa Ramanujan was elected as a Fellow of The Royal Society in 1918. This was a historic achievement as one of the youngest Fellows ever elected and the first Indian to receive this honor. He was proposed by Hardy and supported by other eminent mathematicians based on his groundbreaking work in number theory and mathematical analysis.

Ramanujan discovered and studied mock theta functions in 1920, the year of his death. These were revolutionary functions that didn't fit existing categories and puzzled mathematicians for decades. Approximation of pi and Bernoulli theorems were earlier works, and relativity is unrelated to Ramanujan's field.

P.C. Mahalanobis, the famous Indian statistician and economist, was a close friend of Ramanujan during his Cambridge days. Mahalanobis wrote about their interactions and helped Ramanujan with practical matters. Thomas Hardy was his mathematical collaborator, not an economist, and the other options are not correct.

Ramanujan was married to Janaki Ammal in 1909, when he was 21 and she was just 9 years old (a child marriage according to the customs of that time). She was his only wife. The other names are not historically correct.

Eric Neville, a British mathematician, was instrumental in persuading Ramanujan to come to Cambridge. Neville was impressed by Ramanujan's theorems and personally traveled to India to escort him back to England. Jacob Bernoulli was a 17th-century Swiss mathematician long before Ramanujan's time, and Pierre Deligne is a 20th-century mathematician born after Ramanujan's death.

Ramanujan's first paper in the Journal of the London Mathematical Society was on Bernoulli numbers, named after Jacob Bernoulli. This paper presented his elegant formulas for calculating Bernoulli numbers. Thomas Hardy was his collaborator, not the namesake of the series.

Ramanujan was deeply devoted to Goddess Namagiri of Namakkal, who he believed inspired his mathematical discoveries. He credited his mathematical insights to the goddess's blessings. The other deities and locations are not associated with Ramanujan's spiritual life.

Ramanujan spent his last days in Kodumudi (near his hometown in Tamil Nadu) after returning from England in deteriorating health. He died in Chennai (Madras) in 1920, but his final days were in Kodumudi. Erode was his birthplace, not where he spent his last days.

Ramanujan died on April 26, 1920 at age 32. He was born on December 22, 1887, making him 32 years old at the time of his death. Option A (30) and B (28) are too young, while C (31) is close but not exact.

1729 is the famous Hardy-Ramanujan number, the smallest integer expressible as the sum of two positive cubes in two different ways: 1729 = 1^3 + 12^3 = 9^3 + 10^3. This number was mentioned in a conversation between G.H. Hardy and Ramanujan.