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 28,2020

Washington, Feb 28: US intelligence agencies are monitoring the global spread of coronavirus and the ability of governments to respond, sources familiar with the matter said on Thursday, warning that there were concerns about how India would cope with a widespread outbreak.

While there are only a few known cases in India, one source said the country's available countermeasures and the potential for the virus to spread given India's dense population was a focus of serious concern.

US intelligence agencies are also focusing on Iran, where the country's deputy health minister has fallen ill during a worsening outbreak.

US Secretary of State Mike Pompeo said on Tuesday the United States was "deeply concerned" Tehran may have covered up details about the spread of coronavirus. A US government source said Iran's response was considered ineffective because the government only has minimal capabilities to respond to the outbreak.

Another source said US agencies were also concerned about the weak ability of governments in some developing countries to respond to an outbreak.

The US House of Representatives Intelligence Committee has received a briefing on the virus from the spy agencies. "The Committee has received a briefing from the IC (intelligence community) on coronavirus, and continues to receive updates on the outbreak on a daily basis," an official of the House Intelligence Committee told Reuters.

"Addressing the threat has both national security and economic dimensions, requiring a concerted government-wide effort and the IC is playing an important role in monitoring the spread of the outbreak, and the worldwide response," the official added.

A source familiar with the activities of the Senate Intelligence Committee, led by Republican Senator Richard Burr and Democratic Senator Mark Warner, said the panel was receiving daily updates. The role of US intelligence agencies in responding to the coronavirus epidemic at this point principally involves monitoring the spread of the illness around the world and assessing the responses of governments.

They are working closely with health agencies, such as the US Center for Disease Control, in sharing information they collect and targeting further intelligence gathering.

One source said US agencies would use a wide range of intelligence tools, ranging from undercover informants to electronic eavesdropping tools, to track the virus' impact.

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News Network
July 17,2020

Jul 17: US President Donald Trump has said that he wants to do everything possible to keep peace for the people of India and China, according to his spokesperson

Over the past several weeks, the Trump administration has come out in support of India against China.

“He (Trump) said I love the people of India and I love the people of China and I want to do everything possible to keep the peace for the people,” White House Press Secretary Kayleigh McEnany told reporters at a news conference here on Thursday.

She was responding to a question on Trump’s message to India, which recently had a standoff with China in eastern Ladakh along the Line of Actual Control.

Earlier in the day, White House Economic Advisor Larry Kudlow described India as a great ally, saying President Trump is a great friend of Prime Minister Narendra Modi.

On Wednesday, Secretary of State Mike Pompeo said that India has been a great partner of the US.

“India has been a great partner… They are an important partner of ours. I have a great relationship with my foreign minister counterpart. We talked frequently about a broad range of issues. We talked about the conflict they had along the border with China. We've talked about the risk that emanates from the Chinese telecommunication infrastructure there,” Pompeo told reporters in response to a question.

Travelling in Europe, US National Security Advisor Robert O’Brien told reporters that China has been very aggressive with India.

O’Brien said that India is a democracy and is a great friend of the United States. Prime Minister “Modi and President Trump have a super relationship,” he said.

“In fact, it was the last foreign trip that I took with the president before the COVID-19 crisis hit, was to India, and we had a great reception of the Indian people there. We have a lot in common with them, we speak English, we're democracies. We've got a growing, very strong relationship with India,” O’Brien said.

Welcoming the White House statement, Al Mason, co-chair of the Trump Victory Indian American Finance Committee, said that unlike his predecessor, President Trump has come out openly in support of India.

“Most of the Indian-Americans have observed that every earlier president - be it a Democrat or Republican, like Clinton or Bush Senior or Bush Jr or Obama have been very scared to side with India openly, for fear of hurting China.

“Only President Trump has had the courage to say that… I love India, America respects India… US stands with India - and that also, to over one billion Indians in India at the Namaste Trump rally held in India… and that too… near India’s neighbour China,” Mason said in a statement.

“And he is consistent in his love for India and Indian-Americans,” he added.

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Agencies
May 8,2020

United Nations, May 8: UN Secretary-General Antonio Guterres said Friday the coronavirus pandemic keeps unleashing a tsunami of hate and xenophobia, scapegoating and scare-mongering. 

The UN chief said anti-foreigner sentiment has surged online and in the streets, anti-Semitic conspiracy theories have spread, and COVID-19-related anti-Muslim attacks have occurred. 

Guterres said migrants and refugees have been vilified as a source of the virus -- and then denied access to medical treatment. 

With older persons among the most vulnerable, contemptible memes have emerged suggesting they are also the most expendable, he said. 

And journalists, whistleblowers, health professionals, aid workers and human rights defenders are being targeted simply for doing their jobs. 

Guterres appealed for an all-out effort to end hate speech globally. The secretary-general called on political leaders to show solidarity with all people, on educational institutions to focus on digital literacy at a time when extremists are seeking to prey on captive and potentially despairing audiences. 

He called on the media, especially social media, to remove racist, misogynist and other harmful content, on civil society to strengthen their outreach to vulnerable people, and on religious figures to serve as models of mutual respect. 

And I ask everyone, everywhere, to stand up against hate, treat each other with dignity and take every opportunity to spread kindness, Guterres said.

The secretary-general stressed that COVID-19 does not care who we are, where we live, what we believe or about any other distinction. His global appeal to address and counter COVID-19-related hate speech follows his April 23 message calling the coronarivus pandemic a human crisis that is fast becoming a human rights crisis. 

Guterres said then that the pandemic has seen disproportionate effects on certain communities, the rise of hate speech, the targeting of vulnerable groups, and the risks of heavy-handed security responses undermining the health response. 

With rising ethno-nationalism, populism, authoritarianism and a push back against human rights in some countries, the crisis can provide a pretext to adopt repressive measures for purposes unrelated to the pandemic, he warned.

In February, Guterres issued a call to action to countries, businesses and people to help renew and revive human rights across the globe, laying out a seven-point plan amid concerns about climate change, conflict and repression.

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