Hall of Fame - Mathematicians

22 December - Remembering Srinivasa Ramanujan

(22 December 1887 - 26 April 1920)

A compilation of information from different sites.

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras (now Chennai). When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop.

mathshistory.st-andrews.ac.uk

Ramanujan made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

Some of his works include:

1. Get pi fast In his notebooks, Ramanujan wrote down 17 ways to represent 1/pi as an infinite series. Series representations have been known for centuries. For example, the Gregory-Leibniz series, discovered in the 17th century is pi/4 = 1 - ⅓ + ⅕ -1/7 + … However, this series converges extremely slowly; it takes more than 600 terms to settle down at 3.14, let alone the rest of the number. Ramanujan came up with something much more elaborate that got to 1/pi faster: 1/pi = (sqrt(8)/9801) * (1103 + 659832/24591257856 + …). This series gets you to 3.141592 after the first term and adds 8 correct digits per term thereafter. This series was used in 1985 to calculate pi to more than 17 million digits even though it hadn’t yet been proven.
   

2. Taxicab numbers In a famous anecdote, Mathematician G Hardy took a cab to visit Ramanujan. When he got there, he told Ramanujan that the cab’s number, 1729, was “rather a dull one.” Ramanujan said, “No, it is a very interesting number. It is the smallest number expressible as a sum of two cubes in two different ways. That is, 1729 = 1^3 + 12^3 = 9^3 + 10^3. This number is now called the Hardy-Ramanujan number, and the smallest numbers that can be expressed as the sum of two cubes in n different ways have been dubbed taxicab numbers. The next number in the sequence, the smallest number that can be expressed as the sum of two cubes in three different ways, is 87,539,319.

www.britannica.com

Some things to know about one of the world’s greatest mathematicians.

There is another article showing how Ramanujan was so close to finding a counter-example of Fermat's last theory. Below is a link on his work.

plus.maths.org

Ramanujan's manuscript. The representations of 1729 as the sum of two cubes appear in the bottom right corner. The equation expressing the near counter examples to Fermat's last theorem appears further up: α3 + β3 = γ3 + (-1)n. Image courtesy Trinity College library. Click here to see a larger image. A box of manuscripts and three notebooks. That's all that's left of the work of Srinivasa Ramanujan, an Indian mathematician who lived his remarkable but short life around the beginning of the twentieth century. Yet, that small stash of mathematical legacy still yields surprises.