Instead, I often talk about what makes an essay good.

The second was new to Hardy, and was derived from a class of functions called hypergeometric serieswhich had first been researched by Leonhard Euler and Carl Friedrich Gauss.

Hardy found these results "much more intriguing" than Gauss's work on integrals. Littlewoodto take a look at the papers. Littlewood was amazed by Ramanujan's genius. After discussing the papers with Littlewood, Hardy concluded that the letters were "certainly the most remarkable I have received" and said that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and power".

Nevillelater remarked that "not one [theorem] could have been set in the most advanced mathematical examination in the world". Hanumantha Rao, a mathematics professor at an engineering college, invited Ramanujan's colleague Narayana Iyer to a meeting of the Board of Studies in Mathematics to discuss "what we can do for S.

In one instance, Narayana Iyer submitted some of Ramanujan's theorems on summation of series to the journal, adding, "The following theorem is due to S.

Ramanujan, the mathematics student of Madras University.

Ross of Madras Christian Collegewhom Ramanujan had met a few years before, stormed into his class one day with his eyes glowing, asking his students, "Does Ramanujan know Polish? Working off Giuliano Frullani's integral theorem, Ramanujan formulated generalisations that could be made to evaluate formerly unyielding integrals.

Hardy enlisted a colleague lecturing in Madras, E. Neville, to mentor and bring Ramanujan to England. Ramanujan apparently had now accepted the proposal; as Neville put it, "Ramanujan needed no converting and that his parents' opposition had been withdrawn".

Life in England[ edit ] Ramanujan centre and his colleague G. Hardy extreme rightwith other scientists, outside the Senate House, Cambridgec.

Nevasa on 17 March Four days later, Neville took him to his house on Chesterton Road in Cambridge. Ramanujan immediately began his work with Littlewood and Hardy.

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.Free Elizabethan papers, essays, and research papers. Education in Elizabethan England - The Elizabethan Era was a turning point in England's history.

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18 Unconventional Essays on the Nature of Mathematics - Kindle edition by Reuben (Ed.) Hersh, Reuben Hersh. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading 18 Unconventional Essays on the Nature of Mathematics.2/5(1). Eighteen unconventional essays Mo Nastri Reuben Hersh's Eighteen unconventional essays on the nature of mathematics is a treasure trove of perspectives by authors of wildly different backgrounds who all try to address, in one way or another, what math is.

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