# Hardy ramanujan relationship help

### A passage to infinity: The untold story of Srinivasa Ramanujan | Lifestyle News, The Indian Express

Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in . Ramanujan's father did not participate in the marriage ceremony. With Aiyer's help, Ramanujan had his work published in the Journal of the. It was only with Hardy's care and mentoring that Ramanujan became the with a great deal of Hardy's help in the proofs and presentation. Srinivasa Ramanujan (middle) with fellow scientists at Cambridge. . another, with a great deal of Hardy's help in the proofs and presentation.

Ramanujan is said to have stated on the spot that, on the contrary, it was actually a very interesting number mathematically, being the smallest number representable in two different ways as a sum of two cubes. Such numbers are now sometimes referred to as "taxicab numbers". It is estimated that Ramanujan conjectured or proved over 3, theorems, identities and equations, including properties of highly composite numbers, the partition function and its asymptotics and mock theta functions.

He also carried out major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory.

Eventually, though, the frustrated Ramanujan spiralled into depression and illness, even attempting suicide at one time. After a period in a sanatorium and a brief return to his family in India, he died in at the tragically young age of Some of his original and highly unconventional results, such as the Ramanujan prime and the Ramanujan theta function, have inspired vast amounts of further research and have have found applications in fields as diverse as crystallography and string theory.

After six weeks, Ramanujan moved out of Neville's house and took up residence on Whewell's Court, a five-minute walk from Hardy's room. Hardy had already received theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks.

Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs. Littlewood commented, "I can believe that he's at least a Jacobi ", [51] while Hardy said he "can compare him only with Euler or Jacobi. Hardy and Ramanujan had highly contrasting personalities.

Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades, the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognized. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights.

While in England, Hardy tried his best to fill the gaps in Ramanujan's education and to mentor him in the need for formal proofs to support his results, without hindering his inspiration—a conflict that neither found easy. Ramanujan was awarded a Bachelor of Science degree by research this degree was later renamed PhD in March for his work on highly composite numbersthe first part of which was published as a paper in the Proceedings of the London Mathematical Society.

The paper was more than 50 pages and proved various properties of such numbers.

### The man who taught infinity: how GH Hardy tamed Srinivasa Ramanujan's genius

Hardy remarked that it was one of the most unusual papers seen in mathematical research at that time and that Ramanujan showed extraordinary ingenuity in handling it. At age 31 Ramanujan was one of the youngest Fellows in the history of the Royal Society.

He was elected "for his investigation in Elliptic functions and the Theory of Numbers. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion in England and wartime rationing during — He was diagnosed with tuberculosis and a severe vitamin deficiency at the time, and was confined to a sanatorium. In he returned to KumbakonamMadras Presidencyand soon thereafter, indied at the age of Fearless mentoring I cannot but admire Hardy for his care in mentoring Ramanujan.

- Srinivasa Ramanujan
- G. H. Hardy

His main worry was how to teach this astounding talent much mathematics without destroying his confidence. The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations, and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world … It was impossible to ask such a man to submit to systematic instruction, to try to learn mathematics from the beginning once more.

On the other hand there were things of which it was impossible that he would remain in ignorance … so I had to try to teach him, and in a measure I succeeded, though I obviously learnt from him much more than he learnt from me. Warner Bros For almost three years, things went extremely well. In Ramanujan got his BA from Cambridge and his research went from strength to strength.

## A passage to infinity: The untold story of Srinivasa Ramanujan

They also collaborated on several great projects, and published wonderful joint papers. Sadly, in the spring of Ramanujan fell ill, and was in and out of sanatoria for the rest of his stay in Cambridge. By early Ramanujan seemed to have recovered sufficiently, and decided to travel back to India. Hardy was alarmed not to have heard from him for a considerable time, but a letter in February made it clear that Ramanujan was very active in research.

A main conjecture about them was solved 80 years laterand these functions are now seen as interesting examples of a much larger class of mock modular forms in mathematics, which have applications to elliptic curves, Borcherds productsEichler cohomology and Galois representations — and the nature of black holes.