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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April 5,2020

Washington, Apr 5: US President Donald Trump on Saturday said that he has requested Prime Minister Narendra Modi to supply Hydroxychloroquine tablets that can be used to treat COVID-19 patients.

"After call today with Indian Prime Minister Narendra Modi, India is giving serious consideration to releasing the hold it put on a US order for hydroxychloroquine," Trump announced at the White House Coronavirus task force briefing that he requested PM Narendra Modi for more Hydroxychloroquine tablets.

President Trump did not shy away from saying he too will take a tablet of hydroxychloroquine after announcing that he has requested Prime Minister during his telephonic conversation earlier today to lift a hold on the US order of the medicine.

"I may take it too, will have to talk to my doctors," he added.

"India makes a lot of it. They need a lot too for their billion-plus people. 

The hydroxychloroquine, the anti-malaria drug will be released through the Strategic National Stockpile for treatment," he said.

"I said I would appreciate if they would release the amounts that we ordered" of hydroxychloroquine, he said.

The Indian government has put on hold the export of anti-malarial drug hydroxychloroquine and its formulations.

Prime Minister Narendra Modi said on Twitter, "Had an extensive telephone conversation with President @realDonaldTrump. 

We had a good discussion, and agreed to deploy the full strength of the India-US partnership to fight COVID-19."

Prime Minister conveyed deep condolences for the loss of lives in the United States and his prayers for the early recovery of those still suffering from the disease.

As on Sunday, the United States has at least 301,902 cases of coronavirus according to Johns Hopkins University's tally. 

At least 8,175 people have died in the US from coronavirus.

There was a steep rise in the number of cases in the last 24 hours. At least 23,949 new cases were reported, and at least 1,023 new deaths in the US have been reported in the last 24 hours.

US Secretary of State Michael Pompeo had discussions with External Affairs Minister S Jaishankar about the importance of continued close cooperation between the United States and India to combat coronavirus by strengthening global pharmaceutical supply chains.

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News Network
May 3,2020

London, May 3: The British government had a contingency plan for prime minister Boris Johnson’s death as his condition deteriorated while he battled COVID-19 last month in intensive care, Johnson said in an interview with The Sun newspaper.

Johnson returned to work on Monday, a month after testing positive for COVID-19. Johnson, 55, spent 10 days in isolation in Downing Street from late March, but was then was taken to London’s St Thomas’ Hospital where he received oxygen treatment and spent three nights in intensive care.

“They had a strategy to deal with a ‘death of Stalin’-type scenario,” Johnson, 55, was quoted as saying by The Sun. “It was a tough old moment, I won’t deny it.”

After Johnson was discharged, St Thomas’ said it was glad to have cared for the prime minister, but the hospital has given no details about the gravity of his illness beyond stating that he was treated in intensive care.

Johnson and his fiancée, Carrie Symonds, on Saturday announced the name of their newly born son as Wilfred Lawrie Nicholas, partly as a tribute to two of the intensive care doctors who they said had saved Johnson’s life.

“The doctors had all sorts of arrangements for what to do if things went badly wrong,” Johnson said of his COVID-19 battle. “The bloody indicators kept going in the wrong direction.”

He said doctors discussed invasive ventilation.

“The bad moment came when it was 50-50 whether they were going to have to put a tube down my windpipe,” he said. “That was when it got a bit . . . they were starting to think about how to handle it presentationally.”

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News Network
June 26,2020

Washington, Jun 26: The US is reviewing its global deployment of forces to ensure it is postured appropriately to counter the People's Liberation Army, given the increasing threat posed by China to Asian countries like India, Malaysia, Indonesia, and the Philippines, Secretary of State Mike Pompeo said on Thursday.

Mr Pompeo made those remarks in response to a question during the virtual Brussels Forum 2020 of the German Marshall Fund.

"We're going to make sure we're postured appropriately to counter the PLA. We think that the challenge of our times, and we're going to make sure we have resources in place to do that," Mr Pompeo said.
 
The force posture review is being done at the direction of President Donald Trump, as part of which the US is reducing the number of its troops in Germany from about 52,000 to 25,000, he said.

Mike Pompeo said that the force posture would be dictated by the ground realities.

"In certain places there will be fewer American resources. There'll be other places - I just talked about the threat from the Chinese Communist Party, so now threats to India, threats to Vietnam, threats to Malaysia, Indonesia, South China Sea challenges, the Philippines," he said.

"To the extent that that changed, the difference in what the US decided to do impacts adversely a threat some place, it may be that other nations need to step up and take responsibility for their own defense in ways that they hadn't done previously. So, we want to do this in full consultation with all of our partners all around the world, and certainly our friends in Europe," Mr Pompeo said.

President Trump is being criticised for reducing troops from Germany. His critics say that this will increase the threat from Russia to Europe.

Mike Pompeo, however, did not agree with that argument.

It has been a long time since there has been a strategic review of our force posture all across the world. The US undertook that starting about 2.5 years ago, whether that was our forces in Africa, our forces in Asia, the force we have in the Middle East and in Europe, he said.

"We began to say these are often decisions that were made in a different time. Should we reallocate those a different way? Should we have a different composition of those forces? Everyone always wants to talk about ground troops. I get it. I was a young tank officer. You described that. There's nothing I like as much as a good M1 tank.

"But it's often the case that the capacity to deter Russia or other adversaries isn''t determined any longer by just having a bunch of folks garrisoned someplace. So, we really went to back fundamentally relook, what is the nature of the conflict, what''s the nature of the threat, and how should we allocate our resources, whether that''s our resources in the intelligence community, our resources from the Air Force or the Marines and Army," Mr Pompeo said.

Last week, Mike Pompeo criticised the Chinese Army for "escalating" the border tension with India and militarising the strategic South China Sea. He also described the ruling Communist Party of China (CPC) as a "rogue actor".

"Our broad set of allocation of security apparatus, our ability to counter cyber threats, how do we allocate them? What''s the best way to do this? And the decision that you see the president made with respect to Germany is an outcome from a collective set of decisions about how we''re going to posture our resources around the world," said the top American diplomat on Thursday.

Changes in force posture is being taken in consultations with allies and friends, Mr Pompeo said.

"President Trump has spoken to this. (Defense) Secretary (Mark) Esper will be in London today and in Brussels tomorrow. We''ll talk about our plan and how we''re thinking about delivering it," he said.

"But you should understand this, and I hope our European partners will understand this as well. When you see what we ultimately conclude, how we ultimately deliver on the statements of the president made, that they''re aimed squarely at what we believe to be democracies'' fundamental interest and certainly America's most fundamental interest," Mr Pompeo said.

Earlier this month, Mike Pompeo had said that China's actions, be it on the India border, or in Hong Kong or in the South China Sea, were part of the behaviour of the ruling Communist Party in Beijing in the recent past.

China has been fast expanding military and economic influence in the Indo-Pacific region, triggering concern in various countries of the region and beyond.

China is engaged in hotly contested territorial disputes in both the South China Sea and the East China Sea. Beijing has built up and militarised many of the islands and reefs it controls in the region. Both areas are stated to be rich in minerals, oil and other natural resources and are vital to global trade.

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