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
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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Agencies
May 17,2020

Washington, May 17: The overall number of global coronavirus cases has increased to over 4.6 million, while the death toll has surpassed 311,000, according to the Johns Hopkins University.

As of Sunday morning, the total number of cases stood at 4,634,068, while the death toll increased to 311,781, the University's Center for Systems Science and Engineering (CSSE) revealed in its latest update.

The US currently accounts for the world's highest number of cases and deaths at 1,467,796 and 88,754, respectively.

In terms of cases, Russia has the second highest number of infections at 272,043, followed by the UK (241,461), Brazil (233,142), Spain (230,698), Italy (224,760), France (179,630), Germany (175,752), Turkey (148,067) and Iran (118,392), the CSSE figures showed.

Meanwhile, the UK accounted for the second highest COVID-19 deaths worldwide at 34,546.

The other countries with over 10,000 deaths are Italy (31,763), Spain (27,563), France (27,532), and Brazil (15,662).

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News Network
May 5,2020

May 5: Global coronavirus deaths reached 250,000 on Monday after recorded infections topped 3.5 million, a news agency tally of official government data showed, although the rate of fatalities has slowed.

North America and European countries accounted for most of the new deaths and cases reported in recent days, but numbers were rising from smaller bases in Latin America, Africa and Russia.

Globally, there were 3,062 new deaths and 61,923 new cases over the past 24 hours, taking total cases to 3.58 million.

That easily exceeds the estimated 140,000 deaths worldwide in 2018 caused by measles, and compares with around 3 million to 5 million cases of severe illness caused annually by seasonal influenza, according to the World Health Organization (WHO).

While the current trajectory of COVID-19 falls far short of the 1918 Spanish flu, which infected an estimated 500 million people, killing at least 10% of patients, experts worry the available data is underplaying the true impact of the pandemic.

The concerns come as several countries begin to ease strict lockdowns that have been credited with helping contain the spread of the virus.

"We could easily have a second or a third wave because a lot of places aren't immune," Peter Collignon, an infectious diseases physician and microbiologist at Canberra Hospital, told Reuters. He noted the world was well short of herd immunity, which requires around 60% of the population to have recovered from the disease.

The first death linked to COVID-19 was reported on Jan. 10 in Wuhan, China after the coronavirus first emerged there in December. Global fatalities grew at a rate of 1-2% in recent days, down from 14% on March 21, according to the Reuters data.

DEATH RATE ANOMALIES

Mortality rates from recorded infections vary greatly from country to country.

Collignon said any country with a mortality rate of more than 2% almost certainly had underreported case numbers. Health experts fear those ratios could worsen in regions and countries less prepared to deal with the health crisis.

"If your mortality rate is higher than 2%, you've missed a lot of cases," he said, noting that countries overwhelmed by the outbreak were less likely to conduct testing in the community and record deaths outside of hospitals.

In the United States, around half the country's state governors partially reopened their economies over the weekend, while others, including New York Governor Andrew Cuomo, declared the move was premature.

In Britain, Prime Minister Boris Johnson, who battled COVID-19 last month, has said the country was over the peak but it was still too early to relax lockdown measures.

Even in countries where the suppression of the disease has been considered successful, such as Australia and New Zealand which have recorded low daily rates of new infections for weeks, officials have been cautious.

Australian Prime Minister Scott Morrison has predicated a full lifting of curbs on widespread public adoption of a mobile phone tracking app and increased testing levels.

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