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October 20, 2019

Who is/was the most mysterious mathematician?

Well I think it may be Srinivasa Ramanujan. Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.He was the youngest fellow of royal society and the only second Indian member and the first Indian to be elected a fellow of Trinity college Cambridge.

He lived for only 32 years but in those years of his life he discovered 3900 results. He achieved many highly mathematical and innovative results , which includes Ramanujan Prime, Ramanujan Conjecture , Ramanujan Theta FunctionPartition formulae,Ramanujan’s Master Theorem and Mock Theta Function. These results has not only motivated and encouraged many mathematicians to research on these fields but also provided a new vision of work on the mentioned results.These research works opened a pathway to a number of segments of research which includes the intriguing concepts of the infinite series of π

\(\frac{1}{π} = \sum_{k=0}^{\infty} \frac{(4k!)(1103+26390k)}{({k!}^4)(396^4)}\)

Another research includes his vivid work on composite numbers which gave birth to a distinct number of researchers in the filed of those numbers.Ramanujan is believed to be a man of remarkable rapid problem solving techniques. We are all quite familiar with the famous Hardy-Ramanujan number 1729 which was described as the smallest number that can be expressed as sum of two cubes in two different ways which are

1729 = \(10^3\)+\(9^3\)

1729 = \(1^3\)+\(12^3\)

Ramanujan discovered a wide range of formulas to be worked in later in detail. As per G.H Hardy’s view the discoveries made by Ramanujan have a more impactful insight than what one could usually see. Also Ramanujan’s original letter are enough to show his extreme high calibre that can be compared to mathematical legends like Euler and Jacobi.

Also some of his collaborative works are like

Brocard-Ramanujan Diophantine Equation

Dougall-Ramanujan Identity

Ramanujan-Negell Equation

Ramanujan-Peterssen Conjucture

Ramanujan-Soklem’s Constant

Landau-Ramanujan Constant

Ramanujan-Soldner Constant

Rogers-Ramanujan Identities

Ramanujan-Sato Seris

He published 37 papers in total. B.C Berndt said that "A huge part of his work was not taken in sight which is spread in three notebooks and a lost notebook. These notebooks contain approximately 4000 claims, all without proofs. Most of these claims have now been proved”. It is believed even on his last years he accounted certain functions that approached to him in his dreams.

But research is still going on , on his works.

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