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 30,2020

Washington, May 30: The United States will end its relationship with the World Health Organization over the body’s handling of the coronavirus pandemic, U.S. President Donald Trump said on Friday, accusing the U.N. agency of becoming a puppet of China.

The move to quit the Geneva-based body, which the United States formally joined in 1948, comes amid growing tensions between Washington and Beijing over the coronavirus outbreak. The virus first emerged in China’s Wuhan city late last year.

Speaking in the White House Rose Garden, Trump said Chinese officials “ignored their reporting obligations” to the WHO about the virus - that has killed hundreds of thousands of people globally - and pressured the agency to “mislead the world.”

“China has total control over the World Health Organization despite only paying $40 million per year compared to what the United States has been paying which is approximately $450 million a year,” he said.

Trump’s decision follows a pledge last week by Chinese President Xi Jinping to give $2 billion to the WHO over the next two years to help combat the coronavirus. The amount almost matches the WHO’s entire annual program budget for last year.

Trump last month halted funding for the 194-member organization, then in a May 18 letter gave the WHO 30 days to commit to reforms.

“Because they have failed to make the requested and greatly needed reforms, we will be today terminating our relationship with the World Health Organization and redirecting those funds to other worldwide and deserving urgent global public health needs,” Trump said on Friday.

It was not immediately clear when his decision would come into effect. A 1948 joint resolution of Congress on U.S. membership of the WHO said the country “reserves its right to withdraw from the organization on a one-year notice.”

The World Health Organization did not immediately respond to a request for comment on Trump’s announcement. It has previously denied Trump’s assertions that it promoted Chinese “disinformation” about the virus.

“It’s important to remember that the WHO is a platform for cooperation among countries,” said Donna McKay, executive director of Physicians for Human Rights. “Walking away from this critical institution in the midst of an historic pandemic will hurt people both in the United States and around the world.”

‘ABSOLUTELY CRITICAL’

The United States currently owes the WHO more than $200 million in assessed contributions, according to the WHO website. Washington also gives several hundred million dollars annually in voluntary funding tied to specific WHO programs such as polio eradication, HIV, hepatitis and tuberculosis.

Amesh A. Adalja, a senior scholar at Johns Hopkins Center for Health Security, said that in practice Trump’s decision was unlikely to change the operations of the WHO.

“From a symbolic or moral standpoint it’s the wrong type of action to be taking in the middle of a pandemic and seems to deflect responsibility for what we in the U.S. failed to do and blame the WHO,” said Adalja.

When Trump halted funding to the WHO last month, two Western diplomats said the U.S. suspension was more harmful politically to the WHO than to the agency’s current programs, which are funded for now.

The WHO is an independent international body that works with the United Nations. U.N. Secretary-General Antonio Guterres said last month that the WHO is “absolutely critical to the world’s efforts to win the war against COVID-19.”

When asked about Trump’s decision, a U.N. spokesman said: “We have consistently called for all states to support WHO.”

Trump has long scorned multilateralism as he focuses on an “America First” agenda. Since taking office, he has quit the U.N. Human Rights Council, the U.N. cultural agency, a global accord to tackle climate change and the Iran nuclear deal. He has also cut funding for the U.N. population fund and the U.N. agency that aids Palestinian refugees.

“The WHO is the world’s early warning system for infectious diseases,” said U.S. Representative Nita Lowey, a Democrat who chairs the House Committee on Appropriations. “Now, during a global pandemic that has cost over 100,000 American lives, is not the time to put the country further at risk.”

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News Network
May 30,2020

Washington, May 30: President Donald Trump said Friday he would strip several of Hong Kong's special privileges with the United States and bar some Chinese students from US universities in anger over Beijing's bid to exert control in the financial hub.

In a day of concerted action, the United States and Britain also raised alarm at the UN Security Council over a controversial new security law for Hong Kong, angering Beijing which said the issue had no place at the world body.

In a White House appearance that Trump had teased for a day, the US president attacked China over its treatment of the former British colony, saying it was "diminishing the city's longstanding and proud status."

"This is a tragedy for the people of Hong Kong, the people of China and indeed the people of the world," Trump said.

Trump also said he was terminating the US relationship with the World Health Organization, which he has accused of pro-China bias in its management of the coronavirus crisis.

But Trump was light on specifics and notably avoided personal criticism of President Xi Jinping, with whom he has boasted of having a friendship even as the two powers feud over a rising range of issues.

"I am directing my administration to begin the process of eliminating policy that gives Hong Kong different and special treatment," Trump said.

"This will affect the full range of agreements, from our extradition treaty to our export controls on dual-use technologies and more, with few exceptions," he said.

Secretary of State Mike Pompeo on Wednesday informed Congress that the Trump administration would no longer consider Hong Kong to be separate under US law, but it was up to Trump to spell out the consequences.

China this week pressed ahead on a law that would ban subversion and other perceived offenses against its rule in Hong Kong, which was rocked by months of massive pro-democracy protests last year.

US restricts students

In one move that could have long-reaching consequences, Trump issued an order to ban graduate students from US universities who are connected to China's military.

"For years, the government of China has conducted elicit espionage to steal our industrial secrets, of which there are many," Trump said.

Hawkish Republicans have been clamoring to kick out Chinese students enrolled in sensitive fields. The FBI in February said it was investigating 1,000 cases of Chinese economic espionage and technological theft.

But any move to deter students is unwelcome for US universities, which rely increasingly on tuition from foreigners and have already been hit hard by the COVID-19 shutdown.

China has been the top source of foreign students to the United States for the past decade with nearly 370,000 Chinese at US universities, although Trump's order will not directly affect undergraduates.

Critics say Trump has been eager to fan outrage about China to deflect attention from his own handling of the coronavirus pandemic that has killed more than 100,000 people in the United States, the highest number of deaths of any country.

Chuck Schumer, the top Democrat in the Senate, called Trump's announcement "just pathetic."

Eliot Engel, a Democrat who heads the House Foreign Affairs Committee, noted that Trump treaded lightly on Hong Kong during last year's protests as he sought a trade deal with Xi.

"Now, the president wants to shift the blame for his failures onto China, so he's doing the right thing for the wrong reason," Engel said.

Trump's order could also trigger retaliation. China in March expelled US journalists after the Trump administration tightened visa rules for staff at Chinese state media.

Clash at UN

The United States and Britain earlier in the day urged China to reconsider the Hong Kong law during talks at the UN Security Council, where China wields a veto -- making any formal session, let alone action against Beijing, impossible.

The Western allies raised Hong Kong in an informal, closed-door videoconference where China cannot block the agenda.

They said China was violating an international commitment as the 1984 handover agreement with Britain, in which Beijing promised to maintain the financial hub's separate system until at least 2047, was registered with the United Nations.

"The United States is resolute, and calls upon all UN members states to join us in demanding that the PRC immediately reverse course and honor its international legal commitments to this institution and to the Hong Kong people," said US Ambassador Kelly Craft, referring to the People's Republic of China.  

China demanded that the United States and Britain "immediately stop interfering in Hong Kong affairs," saying the law did not fall under the Security Council's mandate.

"Any attempt to use Hong Kong to interfere in China's internal matters is doomed to fail," warned a statement from China's UN mission.

"There was no consensus, no formal discussion in the Security Council, and the US and the UK's move came to nothing," it said.

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News Network
February 4,2020

Kuala Lumpur, Feb 4: Malaysia said on Tuesday that India's move to cut back on palm oil purchases is "temporary" and will be resolved amicably between the two nations.

Last month, India restricted imports of refined palm oil and asked importers to avoid purchases from Malaysia after its criticism of actions in Kashmir and a new citizenship law.

"Having long-standing bilateral ties, the two nations will overcome the current challenges, and prevail towards mutual and beneficial outcomes," the Malaysian Palm Oil Council said in a statement, citing Primary Industries Minister Teresa Kok.

Malaysia's push to implement B20 biodiesel starting this month will also help sustain high crude palm oil prices, the statement read.

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