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
February 11,2020

Feb 11: China reported 108 new coronavirus deaths on February 10, the highest daily toll since the outbreak began in Wuhan late last year, as two senior officials in the hard-hit province of Hubei were removed from their jobs.

The total number of deaths on the mainland reached 1,016 in the 24 hours until midnight, the National Health Commission said on Tuesday.

Some 2,478 new cases were confirmed, bringing the total to 42,638.

Of the new deaths, 103 were in the province of Hubei, including 67 in the provincial capital of Wuhan. The virus is thought to have originated there in a market that sold seafood as well as wild animals.

Two senior health officials in the province - Zhang Jin who was Party Secretary of the health commission for Hubei and Ling Yingzi who was director of the Hubei Provincial Health Commission - were both removed from their posts, state media reported on Tuesday,  a day after Chinese President Xi Jinping visited health facilities in Beijing.

In his first public appearance since the outbreak began, Xi donned a face mask and had his temperature checked while visiting medical workers and patients in the capital.

"We have seen very little of Xi Jinping since the outbreak began but he was out and about in Beijing on Monday," Al Jazeera's Katrina Yu said from Beijing. "He has been trying to rally the troops saying: 'We can win this battle.' But it's also a sign that the battle is far from over."

The other fatalities on Monday were in the provinces of Heilongjiang, Anhui and Henan and the cities of Tianjin and Beijing, the National Health Commission said.

During a meeting chaired by Premier Li Keqiang on Monday, a group of leaders tasked with beating the virus said it would work to solve raw material and labour shortages and boost supplies of masks and protective clothing.

They said nearly 20,000 medical personnel from around the country had already been sent to Wuhan, and more medical teams were also on the way.

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Agencies
June 6,2020

Seoul, Jun 6: South Korea on Saturday reported 51 new cases of COVID-19, mostly in the densely populated capital region, as authorities scramble to stem transmissions among low-income workers who can't afford to stay home.

The figures announced by South Korea's Centers for Disease Control and Prevention brought national totals to 11,719 workers and 273 deaths.

At least 34 of the new coronavirus cases were linked to door-to-door sellers hired by Richway, a Seoul-based health product provider.

Vice Health Minister Kim Gang-lip said the spread of the virus among Richway sellers was particularly alarming as most of them are in their 60s and 70s. He called for officials to strengthen their efforts to find and examine workplaces vulnerable to infections.

More than 120 infections have also been linked to a massive warehouse operated by Coupang, a local e-commerce giant, which has been accused of failing to properly implement preventive measures and having employees work even when sick.

South Korea was reporting around 500 new cases per day in early March due to a massive outbreak surrounding the southern city of Daegu, before officials managed to stabilize the situation with aggressive tracking and testing.

But the recent resurgence of COVID-19 in the greater capital area, where about half of South Korea's 51 million people live, is now threatening to erase some of the country's hard-won gains. It has also led to second-guessing whether officials were too quick to ease social distancing and reopen schools.

Health authorities and hospital officials on Friday participated in a table-top exercise for sharing hospital capacities between Seoul and nearby cities and ensure swift transports of patients so that a spike of cases in one area doesn't overwhelm its hospital system. 

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News Network
March 2,2020

Paris, Mar 2: A global agency says the spreading new virus could make the world economy shrink this quarter, for the first time since the international financial crisis more than a decade ago.

The Organization for Economic Cooperation and Development says Monday in a special report on the impact of the virus that the world economy is still expected to grow overall this year and rebound next year.

But it lowered its forecasts for global growth in 2020 by half a percentage point, to 2.4 per cent, and said the figure could go as low as 1.5 per cent if the virus lasts long and spreads widely.

The last time world GDP shrank on a quarter-on-quarter basis was at the end of 2008, during the depths of the financial crisis. On a full-year basis, it last shrank in 2009.

The OECD said China's reduced production is hitting Asia particularly hard but also companies around the world that depend on its goods.

It urged governments to act fast to prevent contagion and restore consumer confidence.

The Paris-based OECD, which advises developed economies on policy, said the impact of this virus is much higher than past outbreaks because "the global economy has become substantially more interconnected, and China plays a far greater role in global output, trade, tourism and commodity markets."

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