Srinivasa Ramanujan, almost entirely self-taught in advanced mathematics, was born in 1887 in which present-day state?

Tamil Nadu. MacTutor gives Ramanujan's birth as 22 December 1887 in Erode, Tamil Nadu. The Dictionary of Scientific Biography also gives Erode and the same date. It names the region Madras province. His family moved to Kumbakonam, also in Tamil Nadu. MacTutor says he later ran away to Vizagapatnam, but that was not his birthplace. Neither source places his birth in Karnataka or Kerala.

In which year did Ramanujan become a clerk at the Madras Port Trust?

1912. MacTutor says he began his duties as a clerk on 1 March 1912. The Dictionary of Scientific Biography also dates the Madras Port Trust job to 1912. MacTutor dates his Bernoulli-numbers paper to 1911 and his first letter to Hardy to January 1913. It says he sailed for England in March 1914.

Consider the following statements about Srinivasa Ramanujan. 1. He taught himself mathematics from G. S. Carr's Synopsis. 2. He was elected a Fellow of the Royal Society in 1918. 3. He reached Cambridge in 1913. Which of these statements is/are correct?

1 and 2 only. MacTutor and the Dictionary of Scientific Biography both name Carr's Synopsis, so statement 1 is correct. Both also date his Royal Society election to 1918, so statement 2 is correct. MacTutor says he arrived in London on 14 April 1914. Statement 3 is wrong. The year 1913 is when he wrote his first letter to Hardy.

In Hardy's account, what did Ramanujan say makes the number 1729 interesting?

It is the smallest number expressible as the sum of two cubes in two different ways. Hardy's own words, quoted by Ono and Trebat-Leder, give Ramanujan's reply. He said it is the smallest number expressible as the sum of two cubes in two different ways. MathWorld gives the same property. The two ways are 1 cubed plus 12 cubed, and 9 cubed plus 10 cubed. The next two sentences are our own arithmetic. The number is not a cube, because 12 cubed is 1,728 and 13 cubed is 2,197. It is not prime, because 7 times 247 equals 1,729.

Who later established that the Hardy and Ramanujan formula for the partition function gives exact values?

Hans Rademacher. The Dictionary of Scientific Biography says Rademacher later established that the formula was exact. MacTutor says it was later proved by Rademacher. Crossref lists Hans Rademacher as the author of a paper titled On the Partition Function p(n). MacTutor names Watson as the author of 14 papers called Theorems stated by Ramanujan. It says Neville helped overcome the obstacles to Ramanujan travelling. Littlewood studied the first letter with Hardy.

On 26 December 2011, the Prime Minister said the government had decided to declare which date National Mathematics Day?

22 December. In his speech of 26 December 2011, Manmohan Singh said the government had decided to declare Ramanujan's birthday, 22 December, National Mathematics Day. He also said the government had decided to declare 2012 as National Mathematical Year. The Hindu reported the same decision the next day. The date 26 December is only the date of the speech. The date 26 April is when Ramanujan died in 1920. MacTutor says his Royal Society election was confirmed on 2 May 1918.

From which book did Ramanujan teach himself mathematics at school?

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