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
April 29,2020

Apr 29: US President Donald Trump doubled down on China for failing to tame the coronavirus at its very origin, saying it has led to 184 countries "going through hell", as several American lawmakers demanded steps to reduce dependence on Beijing for manufacturing and minerals.

Trump has been publicly blaming China for the global spread of the "invisible enemy" and launched an investigation against it. He has also indicated that the US may be looking at "a lot more money" in damages from China than the USD 140 billion being sought by Germany from Beijing for the pandemic.

Leaders of the US, the UK and Germany believe that the deaths and the destruction of the global economy could have been avoided, had China shared the information about the virus in its early phases.

"It's in 184 countries, as you hear me say often. It's hard to believe. It's inconceivable," Trump told reporters at White House Tuesday. "It should have been stopped at the source, which was China. It should have been stopped very much at the source, but it wasn't. And now we have 184 countries going through hell.”

The virus, which originated in China's Wuhan city in mid-November, has killed more than two lakh people and infected over three million globally. The largest number of them are in the US: nearly 59,000 deaths and over one million infections.

The massive outbreak in the US has put Trump under increasing pressure from American lawmakers to decrease US dependence on Beijing and they have also sought compensation from China.

Senator Ted Cruz and his colleagues have urged Defence Secretary Mark Esper and Interior Secretary David Bernhardt to support the development of a fully domestic supply chain of rare earths and other minerals that are critical for manufacturing defence technologies and supporting national security.

“It is clear that our dependence on China for vital rare earths threatens our US manufacturing and defence-industrial base. As the October 2018 Defence Industrial Base Report states: ‘China represents a significant and growing risk to the supply of materials deemed strategic and critical to US national security.' [...] Ensuring a US supply of domestically sourced rare earths will reduce our vulnerability to supply disruptions that poses a grave risk to our military readiness," the Senators wrote.

The US is 100 percent import-dependent for rare earths as well as 13 other metals and minerals on the US Government Critical Minerals List and more than 75 percent import reliant for an additional 10 minerals.

Congressman Brian Mast on Tuesday introduced a legislation to hold China accountable for its "coronavirus deception". The resolution would empower the US to withhold payments on debts owed to China equal to the costs incurred by the US in response to COVID-19.

“China's total lack of transparency and mishandling of the coronavirus outbreak has cost tens of thousands of lives, millions of jobs and left untold economic destruction. Congress must hold China accountable for their cover-up and force them to pay back the taxpayer dollars that have been spent as a result,” Mast said.

Cruz, member of the Senate Foreign Relations Committee, announced his intention to introduce a legislation to cut off Hollywood studios from assistance they receive from the Department of Defence if those studios censor their films for screening in China.

This legislation is part of Sen. Cruz's comprehensive push to combat China's growing influence over what Americans see and hear, which includes legislation targeting information warfare from the Chinese Communist Party across higher education, sports, films, radio broadcasts, and more.

Indian-American Congressman Ami Bera and Congressman Ted S. Yoho, both members of the House Foreign Affairs Committee, will lead a bipartisan virtual Special Order to highlight the importance of US global leadership during the COVID-19 pandemic.

“If we abdicate our place as a leader in global health, there is another country eager to take the reins. China has not been subtle in asserting itself on global health issues, and often not for the benefit of other nations. China's recent coronavirus debacle should be evidence enough that their communist regime cannot be trusted to lead with accountability, transparency, or pragmatism, traits that are essential when fighting widespread disease,” Yoho said.

“As for how China would fare as a global health leader, look no further than the disastrous initial response by the WHO to coronavirus, one that was clearly influenced by Beijing. Information was slow-walked, warnings from nations like Taiwan were ignored at crucial turning points, and cooperation with outside health experts was spurned until it was too late. And it has resulted in the largest public health disaster the world has seen in over a century,” he said.

In an interview to Fox News, Senator Marco Rubio alleged that if China had acted when those warnings were being made, instead of silencing the people that were talking about it, they could have limited the spread.

“So there was no doubt that that was a deliberate decision made on their part. The one way to hold them accountable is to do what we should be doing anyway. That is moving the means of production to become less and less dependent upon them. What you're going to see after this pandemic is that more and more countries are going to prioritize their healthcare manufacturing capabilities and other industries,” he said.

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Agencies
June 28,2020

Paris, Jun 28: More than 10 million cases of the new coronavirus have been officially declared around the world, half of them in Europe and the United States, according to an AFP tally on Sunday based on official sources.

At least 10,003,942 infections, including 498,779 deaths, have been registered globally.

Europe remains the hardest hit continent with 2,637,546 cases including 195,975 fatalities, while the United States has 2,510,323 infections including 125,539 deaths.

The rate of infections worldwide continues to rise, with one million new cases recorded in just six days.

The tallies, using data collected by AFP from national authorities and information from the World Health Organization (WHO), probably reflect only a fraction of the actual number of infections.

Many countries are testing only symptomatic or the most serious cases and some do not have the capacity to carry out widescale testing.

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News Network
May 18,2020

Washington, May 18: US President Donald Trump on Sunday called his predecessor Barak Obama a ‘grossly incompetent president’.

The Trump’s reaction came after Obama on Saturday criticised the US authorities' response to the coronavirus outbreak.

“He (Obama) was an incompetent president. That’s all I can say. Grossly incompetent,” Trump told reporters at the White House on his arrival from Camp David.

Trump was responding to a question on the virtual commencement address by Obama a day earlier.

In his address to college graduates, Obama had said that the COVID-19 pandemic has exposed the American leadership.

“More than anything, this pandemic has fully, finally torn back the curtain on the idea that so many of the folks in charge know what they’re doing,” Obama said without naming officials.

“A lot of them aren’t even pretending to be in charge,” he added.

There was no immediate response from the office of the former president on the remarks made by Trump.

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