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 1,2020

Washington, May 1: The United States on Thursday recorded 29,625 new coronavirus cases, and 2,035 deaths in the last 24 hours, according to Johns Hopkins University.

The total number of coronavirus cases has reached 1,069,534 and the death toll stands at 63,001, CNN reported.

The novel coronavirus has infected more than 3.2 million people and killed at least 233,000 globally, according to Johns Hopkins University.

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Agencies
January 25,2020

Pentagon, Jan 25: Thirty-four US troops had been diagnosed with concussions and traumatic brain injury (TBI) as a result of the January 8 Iranian missile attack on two military bases in Iraq housing American soldiers, the Pentagon said.

"Eight service members who were previously transported to Germany have been brought to the US, they would continue to receive treatment in the US either at Walter Reed or their home bases," Pentagon spokesman Jonathan Hoffman told the media on Friday.

Hoffman said that nine service members were still undergoing treatment in Germany, and the rest of the 17 injured troops have already returned to duty in Iraq, reports Xinhua news agency.

Lat week, the US military had said that 11 service members were treated for concussion symptoms due to the missile attacks.

Hoffman noted that the symptoms "are late developing and manifested over a period of time".

In retaliation for the killing of Iranian Major General Qasem Soleimani in an American drone attack on January 3 in Baghdad, Tehran launched over 13 ballistic missiles on the two military bases in Anbar and near the city of Erbil.

US military initially said that no casualty was reported from the Iranian attack. President Donald Trump then downplayed the seriousness of those injures.

"I heard that they had headaches and a couple of other things, but I would say and I can report that it's not very serious," Trump told reporters on Wednesday at a press conference in Davos, Switzerland.

More than 5,000 US troops are deployed in Iraq to support the country's forces in the battle against Islamic State militants.

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News Network
May 6,2020

Washington, May 6: The Chinese Army is indulging in aggressive behaviour in the South China Sea and the Chinese Communist Party has ramped up its disinformation campaign to try to shift the blame on coronavirus and burnish its image, US Defense Secretary Mark Esper said on Tuesday.

"While the Chinese Communist Party ramps up its disinformation campaign to try to shift blame and burnish its image, we continue to see aggressive behaviour by the PLA in the South China Sea, from threatening a Philippine Navy ship to sinking a Vietnamese fishing boat and intimidating other nations from engaging in offshore oil and gas development," Esper told reporters at a Pentagon news conference.

Last week, two US Navy ships conducted freedom of navigation operations in the South China Sea to send a clear message to Beijing that America will continue to protect the freedom of navigation and commerce for all nations large and small, he said.

Many countries, Esper said, have turned inward to recover from the pandemic and in the meantime, America's strategic competitors are attempting to exploit this crisis to their benefit at the expense of others.

Responding to a question, he said the Chinese have not been transparent from the beginning on the coronavirus pandemic.

"If they had been more transparent, more open, upfront in terms of giving us access, the reporting, giving us access not to the people on the ground but to the virus they had so we could understand it, we would probably be in a far different place right now. But where we are now is this," Esper said.

China needs to allow the United States in to talk to early patients, Chinese researchers and scientists, and to have access, he added.

Instead, Esper alleged that the Chinese are trying to capitalise on this by promoting their own image that somehow, China is the good guy here.

"Despite everything they did or, more importantly, failed to do, now they want to go out and say well, here's masks. We will give you masks, provide this, or provide that, we will provide you funding. Look at all the good things we are doing," he said.

"Yet, what we know is that they provide masks, they provide supplies. In many cases, it is not good. It does not do what it is supposed to do. It is broken equipment. Also, the strings attached are enormous in many cases. So, they are telling a country you can take these masks, but please, put out publicly how good China is, how great we are doing, et cetera, et cetera," Esper said.

"So there is a number of things they are doing to try and burnish their image. That is just two of them right there," he said.

The Chinese are also doing a lot of strong-arming behind the scenes, Esper said and referred to the war of words between China and Australia. He said he plans to talk to his Australian counterpart later in the day.

"All these activities are going on. It is straight from the Chinese playbook. Once again, it is just a little bit more obvious this time with what they are doing and how they are using a combination of compelling and coercion and everything else to try and shape the narrative and burnish the image of the Chinese Communist Party," Esper said.

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