American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

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London, December 30: American researchers claim to have solved a cryptic formula that renowned mathematician Srinivasa Ramanujan believed came to him in dreams while on his deathbed, the Daily Mail reported on Saturday.

The formula was contained in a letter he wrote to his mentor, the English mathematician G.H. Hardy, from his deathbed in 1920 outlining several new mathematical functions that had never been heard of before, together with a theory about how they worked. It had baffled mathematicians for more than 90 years, but new findings — presented at a conference at the University of Florida last month — reportedly show that Ramanujan's “hunch” about his formula was right — that it could explain the behaviour of black holes.

“We've solved the problems from his last mysterious letters,” said the well-known American mathematician Ken Ono of Emory University.

“For people who work in this area of math, the problem has been open for 90 years … Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died.”

He said the so-called “deathbed puzzle” which, according to Ramanujan, was revealed to him by the goddess Namagiri, may unlock secrets about black holes. “We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess. No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” said Professor Ono.

The Mail said that Ramanujan's letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

“Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value. Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1,” it said. Nobody at the time understood what the Indian mathematical genius was talking about.

“It wasn't until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Prof. Ono said.

His team, which used modern mathematical tools to solve the puzzle, was “stunned” to find the function could be used even today.

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News Network
July 9,2020

Washington, Jul 9: The United States recorded 55,000 new coronavirus cases in 24 hours on Wednesday (Thursday in Malaysia), a tally by Johns Hopkins University showed, bringing its total to 3,046,351 recorded infections since the pandemic began.

The country, the hardest-hit in the world, had earlier on Wednesday passed the grim milestone of three million infections. The actual number is likely far higher due to issues over getting tested in March and April.

The US also added an additional 833 virus deaths, bringing the death toll to 132,195, the Baltimore-based institution showed at 8.30pm (0030 GMT Thursday).

US President Donald Trump regularly downplays the numbers, attributing them to an increase in testing capacity during the month of June.

Coronavirus cases are surging in several southern hotspots including Texas, Florida, Louisiana and Arizona, but the pandemic has almost entirely receded from its former epicentre in New York and the north-east.

Several states have been forced to suspend their reopening processes or even reverse course, with some ordering bars to close again.

On Wednesday morning, Trump called on schools throughout the country to reopen in the fall, lashing out at his own top health agency to ease health and safety requirements aimed at slowing the spread of the virus, such as social distancing.

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News Network
January 22,2020

Davos, Jan 22: President Donald Trump has said that the US is watching the developments between India and Pakistan over Kashmir "very closely" and repeated his offer to "help" resolve the longstanding dispute between the two neighbours as he met Prime Minister Imran Khan on the sidelines of the World Economic Forum here in the Swiss ski resort.

Addressing the media with the Pakistan Prime Minister prior to their private meeting on Tuesday, President Trump asserted that trade and borders were both critical points for discussion, while Khan said that for him, Afghanistan was the top priority.

Trump told Khan, whom he referred to as "my friend", that he would speak to Prime Minister Narendra Modi about the ongoing Kashmir issue. The US president is expected to visit India in the coming weeks, marking his first visit after taking up his post in the White House.

"What's going on between Pakistan and India … if we can help, we certainly will be willing to. We have been watching it very closely and it's an honour to be here with my friend," he said.

"The Pakistan-India conflict is a very big issue for us in Pakistan and we expect the US to always play its part in deescalating the tensions, because no other country can," Khan said.

President Trump has repeatedly offered to mediate following India's August 5 decision to revoke the special status to Jammu and Kashmir and bifurcate the state into two Union Territories, evoking strong reaction from Pakistan which has been trying to internationalise the Kashmir issue.

New Delhi has defended the move, saying Jammu and Kashmir is an integral part of India and the issue was strictly internal to the country, and the special status provisions only gave rise to terrorism in Jammu and Kashmir.

"The country took the decision of abrogation of Article 370, which had only given separatism and terrorism to that state," Prime Minister Narendra Modi said at a function in October last year.

This is the third meeting between Trump and Khan since Pakistan premier assumed office in 2018 and it came against the backdrop of Pakistan Foreign Minister Shah Mehmood Qureshi's recent trip to the US, amid reports that the US and Afghan Taliban were close to striking a peace deal.

"There are issues we want to talk about. The main issue is Afghanistan because it concerns the US and Pakistan. Fortunately, we are on the same page. Both of us are interested in peace there and an orderly transition in Afghanistan with talks with Taliban and the government," Khan said.

When a reporter asked Trump if he would visit Pakistan considering he was already set to visit India, the US president said he was meeting the Pakistan premier in Davos.

"Well, we're visiting right now. So we don't really have to. I wanted to say that from a relationship standpoint, we got a great relationship. From the standpoint our two countries, we're getting along very well. I would say we've never been closer with Pakistan the way we're right now. And this is a big statement," Trump said.

Khan left for Switzerland to attend the World Economic Forum and meet the world leaders, including President Trump, on the sidelines of the annual event which kicked off at the ski resort town of Davos on Tuesday.

The four-day summit marks the 50th anniversary of the forum.

A total of 53 heads of State are on the guest list. Nearly 3,000 participants from 118 countries are expected to attend the event during which political leaders, business executives, heads of international organisations and civil society representatives are set to deliberate on contemporary economic, geopolitical, social and environmental issues.

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News Network
April 11,2020

Washington, Apr 11: China is considered a developing country, make the United States too a developing one, US President Donald Trump said on Friday, alleging that Beijing has taken advantage of his country.

"China has been unbelievably taken advantage of us and other countries. You know, for instance, they are considered a developing nation. I said well then make us a developing nation too,” Trump told reporters at his daily White House news conference on coronavirus.

The president was responding to a question on China.

“They get big advantages because they are a developing nation. India, a developing nation. The United States is a big developed nation. Well, we have plenty of development to do,” he said.

Reiterating that United States was taken advantage of by the World Trade Organization, Trump said the Chinese economy started booming after it joined WTO with the help of the US.

“If you look at the history of China, it was only since they went into the WTO that they became a rocket ship with their economy. They were flatlined for years and years,” he said.

“Frankly, for many, many decades. And it was only when they came into the WTO that they became a rocket ship because they took advantage of all -- I'm not even blaming them. I'm saying how stupid were the people that stood here and allowed it to happen,” he said.

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The Trump Administration will now allow that to happen, he said.

“If they don't treat us fairly, will leave. But now we're starting to win cases,” he said.

Alleging that China has taken advantage of the United States for 30 years, he said, China has taken advantage of the US through WTO and using rules that are unfair to the United States.

"They should have never been allowed it, this should have never been allowed to happen", he added.

“When China joined and was allowed to join under those circumstances the WTO, that was a very bad day for the United States because they have rules and regulations that were far different and far easier than our rules and regulations,” he said.

“Plus. They took advantage of them down to the last. China took advantage of them like few people would even think to take advantage of them and again they are considered right a developing nation,” he added.

The United States, he rued, is not considered a developing nation.

“The were given advantages (for being a developing nation). For many years China has ripped off the United States. Then I came along and right now, as you know, China is paying 25 percent," said Trump, adding that the US is now gaining "billions and billions and billions of dollars in tariffs from China”.

The US is not paying, he asserted.

“Not every country is China but China would devalue their currency and they would also pour out money and they essentially were paying most of those tariffs not us,” he said.

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