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
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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News Network
June 13,2020

Paris, Jun 13: The coronavirus pandemic has killed 425,000 people since it emerged in China late last year, according to an AFP tally of official sources at 0130 GMT on Saturday.

A total of 425,282 deaths have now been recorded from 7,632,517 cases.

Europe has registered 186,843 deaths from 2,363,538 cases, but the epidemic is progressing most rapidly in Latin America, where there have been a total of 76,343 deaths recorded from 1,569,938 cases.

The United States remains the country with the most recorded deaths at 114,643, ahead of Brazil which on Friday became the second worst-hit nation with 41,828 deaths. Britain is next with 41,481 deaths, followed by Italy (34,223) and France (29,374).

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News Network
March 30,2020

Geneva, Mar 30: The number of confirmed COVID-19 cases worldwide has reached 634,835, among them 29,957 fatalities, the World Health Organization (WHO) said on Sunday.

Over the past 24 hours, 63,159 people were confirmed to be infected with the novel coronavirus and 3,464 people died, the WHO said.

According to the latest situation report, the majority of the confirmed cases - more than 361,000 - are presently concentrated in Europe, with Italy leading the tally with over 92,000 cases, followed by Spain with over 72,000 cases, and Germany with over 52,000 cases.

Italy and Spain are also the countries that top the worldwide death toll from COVID-19, with 10,023 and 5,690 fatalities, respectively.

The second most affected region is currently the Americas with over 120,000 verified COVID-19 cases, of which the majority - over 103,000 - have been found in the United States. The US is also the country with the highest single tally of COVID-19 cases at the moment.
The WHO declared COVID-19 a pandemic on March 11.

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