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 4,2020

Geneva, Jul 4: The World Health Organization has updated its account of the early stages of the COVID crisis to say it was alerted by its own office in China, and not by China itself, to the first pneumonia cases in Wuhan.

The UN health body has been accused by US President Donald Trump of failing to provide the information needed to stem the pandemic and of being complacent towards Beijing, charges it denies.

On April 9, WHO published an initial timeline of its communications, partly in response to criticism of its early response to the outbreak that has now claimed more than 521,000 lives worldwide.

In that chronology, WHO had said only that the Wuhan municipal health commission in the province of Hubei had on December 31 reported cases of pneumonia. The UN health agency did not however specify who had notified it.

WHO director Tedros Adhanom Ghebreyesus told a press conference on April 20 the first report had come from China, without specifying whether the report had been sent by Chinese authorities or another source.

But a new chronology, published this week by the Geneva-based institution, offers a more detailed version of events.

It indicates that it was the WHO office in China that on December 31 notified its regional point of contact of a case of "viral pneumonia" after having found a declaration for the media on a Wuhan health commission website on the issue.

The same day, WHO's epidemic information service picked up another news report transmitted by the international epidemiological surveillance network ProMed -- based in the United States -- about the same group of cases of pneumonia from unknown causes in Wuhan.

After which, WHO asked the Chinese authorities on two occasions, on January 1 and January 2, for information about these cases, which they provided on January 3.

WHO emergencies director Michael Ryan told a press conference on Friday that countries have 24-48 hours to officially verify an event and provide the agency with additional information about the nature or cause of an event.

Ryan added that the Chinese authorities immediately contacted WHO's as soon as the agency asked to verify the report.

US President Donald Trump has announced that his country, the main financial contributor to WHO, will cut its bridges with the institution, which he accuses of being too close to China and of having poorly managed the pandemic.

The WHO denies any complacency toward China.

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News Network
May 29,2020

Washington, May 29: Reiterating his offer to mediate on the border dispute between India and China, US President Donald Trump has said that he spoke with Narendra Modi about the "big conflict" and asserted that the Indian Prime Minister is not in a "good mood" over the latest flare-ups between the two countries.

Speaking with the reporters in the Oval Office of the White House on Thursday, Trump said a "big conflict" was going on between India and China.

"I like your prime minister a lot. He is a great gentleman," the president said.

"Have a big conflict …India and China. Two countries with 1.4 billion people (each). Two countries with very powerful militaries. India is not happy and probably China is not happy," he said when asked if he was worried about the border situation between India and China.

"I can tell you; I did speak to Prime Minister Modi. He is not in a good mood about what is going on with China," Trump said.

A day earlier, the president offered to mediate between India and China.

Trump on Wednesday said in a tweet that he was "ready, willing and able to mediate" between the two countries.

Responding to a question on his tweet, Trump reiterated his offer, saying if called for help, "I would do that (mediate). If they thought it would help" about "mediate or arbitrate, I would do that," he said.

India on Wednesday said it was engaged with China to peacefully resolve the border row, in a carefully crafted reaction to Trump's offer to arbitrate between the two Asian giants to settle their decades-old dispute.

"We are engaged with the Chinese side to peacefully resolve it," External Affairs Ministry Spokesperson Anurag Srivastava said, replying to a volley of questions at an online media briefing.

While the Chinese Foreign Ministry is yet to react to Trump's tweet which appears to have caught Beijing by surprise, an op-ed in the state-run Global Times said both countries did not need such a help from the US President.

"The latest dispute can be solved bilaterally by China and India. The two countries should keep alert on the US, which exploits every chance to create waves that jeopardise regional peace and order," it said.

In Beijing, Chinese Foreign Ministry spokesman Zhao Lijian said on Wednesday that both China and India have proper mechanisms and communication channels to resolve the issues through dialogue and consultations.

Trump previously offered to mediate between India and Pakistan on the Kashmir issue, a proposal which was rejected by New Delhi.

The situation in eastern Ladakh deteriorated after around 250 Chinese and Indian soldiers were engaged in a violent face-off on the evening of May 5 which spilled over to the next day before the two sides agreed to "disengage" following a meeting at the level of local commanders.

Over 100 Indian and Chinese soldiers were injured in the violence.

The incident in Pangong Tso was followed by a similar incident in north Sikkim on May 9.

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Agencies
February 23,2020

Wuhan, Feb 23: Ninety-seven more people died in China due to coronavirus, taking the death toll to 2,442, officials said on Sunday, as a team of WHO experts visited the worst-affected Wuhan city in Hubei province.

By the end of Saturday, a total of 2,442 people had died of the disease and 76,936 confirmed cases of novel coronavirus infection had been reported in 31 provincial-level regions, China's National Health Commission (NHC) said in its daily update on Sunday.

Ninety-six deaths were reported from Hubei province and one from Guangdong province on Saturday besides 648 new confirmed cases of coronavirus infections, it said.

Hubei province, where the virus first emerged in December last, reported 630 new confirmed cases, taking the total confirmed cases in the hard-hit province to 64,084, state-run Xinhua news agency reported.

The NHC also said China's daily number of newly cured and discharged novel coronavirus patients has surpassed that of new confirmed infections for the fifth consecutive day, indicating that cases of infections are coming down.

Saturday saw 2,230 people walk out of hospital after recovery, much higher than the number of the same day's new confirmed infections, which was 648, Xinhua reported.

A total of 22,888 patients infected with the novel coronavirus had been discharged from hospital after recovery by the end of Saturday, NHC said.

Meanwhile, a team of public health experts from the World Health Organisation (WHO) visited Wuhan on Saturday to conduct a detailed probe about the virus which reportedly originated from a seafood market in the city in December last year.

The NHC said WHO experts along with their Chinese counterparts who formed a joint investigation team have held talks with the local health authority in Wuhan and visited relevant healthcare institutions.

The UN team comprises specialists from the United States, Germany, Japan, Nigeria, Russia, Singapore and South Korea, Hong-Kong based South China Morning Post reported.

The 12-member team, which arrived in China on Monday, was initially designated to visit only Beijing, Guangdong and Sichuan provinces, while the worst-affected Hubei province and its capital Wuhan were missing from the list.

However, the team was finally given permission to visit Wuhan by the Chinese government.

Besides controlling the spread of the virus, a major task for the WHO team along with their Chinese counterparts was to come up with standard medicine to cure the disease.

The NHC said on Saturday that the team had met top Chinese respiratory disease expert Zhong Nanshan in Guangdong, and visited the centre for disease control and prevention in Guangdong and the city of Shenzhen, and Sichuan.

The specialists also discussed quarantine measures, the wild animal trade and community prevention measures with their Chinese counterparts, it said.

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