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
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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Agencies
June 9,2020

Wuhan, Jun 9: China on Tuesday dismissed as "incredibly ridiculous" a Harvard study, which pointed to a surge in traffic outside Wuhan hospitals from August 2019 suggesting that the coronavirus hit the area far earlier than reported.

A whitepaper on coronavirus released by China on Sunday said the virus was first noticed on December 17 and Chinese virologists confirmed human-to-human transmission on January 19, prompting authorities to impose lockdown of Wuhan from January 23.

US President Donald Trump and leaders of several countries have accused China of not being transparent in reporting the deadly disease, leading to huge human casualties and economic crisis across the world.

The new study by Harvard researchers says satellite images show an increase in traffic outside five hospitals in Wuhan from late August to December.

The traffic spike coincided with a rise in online searches for information on symptoms like "cough" and "diarrhoea".

China said the study was "ridiculous" and based on "superficial" information, BBC reported.

It is believed that the virus first appeared in China some time in November. Authorities reported a cluster of pneumonia cases with an unknown cause to the World Health Organization (WHO) on December 31.

"Clearly, there was some level of social disruption taking place well before what was previously identified as the start of the novel coronavirus pandemic," Dr John Brownstein, who led the research, told ABC news.

The study has not been peer-reviewed.

The researchers examined commercial satellite data from outside five Wuhan hospitals, comparing data from late summer and autumn 2018 to the same time period in 2019.

In one case, researchers counted 171 cars parked at one of Wuhan''s largest hospitals, Tianyou Hospital, in October 2018.

Satellite data from the same time in 2019 showed 285 vehicles in the same place, an increase of 67 per cent.

A surge in online searches for words associated with the symptoms of coronavirus on the Chinese search engine Baidu seemed to emerge at the same time.

"This is all about a growing body of information pointing to something taking place in Wuhan at the time," Dr Brownstein said.

"Many studies are still needed to fully uncover what took place and for people to really learn about how these disease outbreaks unfold and emerge in populations. So this is just another point of evidence," he said.

Asked for her reaction at the media briefing, Chinese Foreign Ministry spokeswoman Hua Chunying dismissed the findings as "incredibly ridiculous".

"I think it is ridiculous, incredibly ridiculous, to come up with this conclusion based on superficial observations such as traffic volume," she said.

"(I have) Not seen the research you mentioned. If the conclusion is drawn based on traffic volumes (and) other superficial observations, it won’t be a sound conclusion," she said and referred to the allegations about the COVID-19 originating from the Wuhan Institute of Virology (WIV) by Trump.

"That allegation was proved to be wrong," she said.

When pointed out that China says it respects science based inquiry and Harvard is one of the top universities in the world, Hua said, "on the origin of virus there are lot of conspiracy theories against China”.

"That is very unfair. At the moment, the pressing task is to enhance coordination to contain the spread of the virus. Someday, I am sure the truth will be out. China deserves a fair and objective evaluation," she said and referred to the whitepaper released by the Chinese government detailing evolution of coronavirus in Wuhan and how Beijing handled the situation.

Recently, the World Health Assembly (WHA), the decision-making body of Geneva-based World Health Organization (WHO), passed a resolution to probe the origin of the virus. China also backed the resolution.

As of Monday, the overall confirmed cases on the mainland had reached 83,043, including 58 patients who were still being treated, with no one in severe condition, China’s National Health Commission, (NHC) said.

Altogether 78,351 people had been discharged after recovery and 4,634 people had died of the disease, it said.

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News Network
April 26,2020

Apr 26: The Chinese city of Wuhan, where the global coronavirus pandemic began, now has no remaining cases in its hospitals, a health official told reporters on Sunday.

"The latest news is that by April 26, the number of new coronavirus patients in Wuhan was at zero, thanks to the joint efforts of Wuhan and medical staff from around the country," National Health Commission spokesman Mi Feng said at a briefing.

The city had reported 46,452 cases, 56% of the national total. It saw 3,869 fatalities, or 84% of China's total.

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