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 16,2020

Islamabad, Apr 16: The number of coronavirus cases in Pakistan topped 6000 while the death toll due to the virus has reached 117, Dawn reported citing official data on Wednesday.

Over 1,446 people have recovered in the country from the deadly virus that has killed over 1.3 lakh people worldwide.

The total number of cases in the country has reached 6297 with Punjab being the worst affected province with 3,016 cases. Meanwhile, Sindh has 1,688 cases of the deadly virus.

Khyber Pakhtunkhwa has reported 47 new cases of the coronavirus, taking the provincial total to 912. Most of the new cases are of Tableeghi Jamaat members who have travel history.

Balochistan has reported four new cases of COVID-19, taking the provincial total to 281 according to provincial government spokesperson Liaquat Shahwani.

On Tuesday, Prime Minister Imran Khan had announced the extension of the nationwide lockdown with relaxation to some sectors.

Addressing the media in Islamabad on Tuesday, Khan said, "We made the hard decision of imposing lockdown in the country which was very well implemented due to cooperation of the people."

The countrywide lockdown was imposed last month in a bid to stem the spread of coronavirus. Later, a two-week extension was announced in the restrictions until April 14.

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News Network
May 21,2020

Washington, May 21: US President Donald Trump China is on a "massive disinformation" campaign and is desperately trying to deflect the "pain and carnage" that it spread throughout the world, US President Donald Trump has said, upping the ante on Beijing over its handling of the coronavirus outbreak.

Trump, who has expressed disappointment over China's handling of the COVID-19 pandemic, claimed that it was the "incompetence" of Beijing that led to the mass killing across the globe. 

"China is on a massive disinformation campaign because they are desperate to have Sleepy Joe Biden win the presidential race so they can continue to rip-off the United States, as they have done for decades, until I came along!" Trump said in a tweet on Wednesday.

"Spokesman speaks stupidly on behalf of China, trying desperately to deflect the pain and carnage that their country spread throughout the world. Its disinformation and propaganda attack on the United States and Europe is a disgrace… It all comes from the top. They could have easily stopped the plague, but they didn't," he said in a series of tweets.

Trump blamed China for spreading the coronavirus globally and accused it of being incompetent.
"Some wacko in China just released a statement blaming everybody other than China for the Virus which has now killed hundreds of thousands of people. Please explain to this dope that it was the 'incompetence of China', and nothing else, that did this mass Worldwide killing!" Trump said.

China has denied covering up the extent of its coronavirus outbreak and accused the US of attempting to divert public attention by insinuating that the virus originated from a virology laboratory in Wuhan.

"China was the first country to report the COVID-19 to the World Health Organisation (WHO), (and) that doesn't mean the virus originated from Wuhan... There has never been any concealment, and we'll never allow any concealment," Chinese Foreign Ministry spokesman Zhao Lijian said last month.

"A discerning person will understand at a glance that the purpose is to create confusion, divert public attention, and shirk their responsibility," he said.

The novel coronavirus which first originated in Wuhan in December last year has claimed 328,120 lives and infected nearly 5 million people globally. The Us is the worst affected country with 93,439 deaths and over 1.5 million infections, according to Johns Hopkins University data.

Meanwhile, the US Senate passed a bill boosting oversight of companies based in China and other nations that could lead to their removal from American stock exchanges.

The Holding Foreign Companies Accountable Act, proposes to increase oversight of Chinese and other foreign companies listed on American exchanges and delist and ban over-the-counter trading for firms that are out of compliance with US regulators for a period of three years.

In a related development, a group of top Republican Senators led by Marco Rubio sent a letter to Secretary of the Treasury Steven Mnuchin following disturbing reports that China's state-owned and-directed enterprises were looking to exploit the economic crisis by buying US and foreign companies.

As companies backed by the Chinese Communist Party (CCP) approach banks to identify the purchase of companies in the US and in Europe affected by the pandemic, the senators urged Mnuchin to protect against the China's and the CCP's predatory economic behaviour during the COVID-19 crisis.

"We write to express our concerns related to the People's Republic of China's (PRC) efforts to exploit the economic crisis wrought by the COVID-19 pandemic to gain control of distressed companies or shirking its international responsibilities amidst a worldwide crisis.

"In both Chinese Communist Party (CCP) and PRC policy documents, Beijing has made no secret of its intentions to dominate strategic industrial and emerging technology sectors as well as influence standards at the expense of liberal, rules-based governance," wrote the senators.

As the crisis reverberates across the globe, the PRC's predatory lending practices — including the use of non-disclosure agreements for bilateral loans — not only damage the fiscal situation of recipient countries but also undermine the international community's ability to respond effectively to the crisis, they said.

"Without US and international pressure for accountability and transparency, those countries that are in debt to the PRC will not have the political cover or protection to open their financial books. Such countries will face the risk of default or a currency crisis, leaving the International Monetary Fund (IMF), World Bank, and Western countries to clean up the PRC's mess," the senators said.

During a campaign round table Katrina Pierson, Senior Advisor to the Trump 2020 Campaign, said that only the US President will defeat the coronavirus, hold China accountable for their negligence, and defend the American people from socialism. 

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Agencies
July 17,2020

Washington, Jul 17: US President Donald Trump's economic adviser Larry Kudlow has said that TikTok may cut off ties to its Chinese parent and become a 100 per cent American company to circumvent demands to ban it as India has done.

"I think TikTok is going to pull out of the holding company which is China-run and operate as an independent American company," he told reporters at the White House on Thursday.

The US has not made a final decision on whether to ban it - which has been suggested by Secretary of State Mike Pompeo, he said.

TikTok being divested by ByteDance Technology Company "is a much better solution than banning or pushing away", said Kudlow, who is the Director of the National Economic Council.

He said that its services will be located in the US and "it will become an hundred per cent American company".

If it becomes a US company without Chinese links, India may have to reconsider the ban on the short video app wildly popular in the country.

India banned TikTok along with 58 other Chinese apps on June 29 citing threats to its defence and national security.

The ban came after a deadly clash between Indian and Chinese troops along the Line of Actual Control in Ladakh.

Under Beijing's National Security Law, all Chinese companies have to provide intelligence requested by the government, creating risks for users and their countries.

India was TikTok's biggest market outside of China, where it operates as Douyin.

There were about 200 million users in India and over 300 million downloads.

The US comes next with over 30 million users for the app.

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