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
June 30,2020

Six months since the new coronavirus outbreak, the pandemic is still far from over, the World Health Organization said Monday, warning that "the worst is yet to come".

Reaching the half-year milestone just as the death toll surpassed 500,000 and the number of confirmed infections topped 10 million, the WHO said it was a moment to recommit to the fight to save lives.

"Six months ago, none of us could have imagined how our world -- and our lives -- would be thrown into turmoil by this new virus," WHO chief Tedros Adhanom Ghebreyesus told a virtual briefing.

"We all want this to be over. We all want to get on with our lives. But the hard reality is this is not even close to being over.

"Although many countries have made some progress, globally the pandemic is actually speeding up.

"We're all in this together, and we're all in this for the long haul.

"We will need even greater stores of resilience, patience, humility and generosity in the months ahead.

"We have already lost so much -- but we cannot lose hope."

Tedros also said that the pandemic had brought out the best and worst humanity, citing acts of kindness and solidarity, but also misinformation and the politicisation of the virus.

In an atmosphere of global political division and fractures on a national level, "the worst is yet to come. I'm sorry to say that," he said.

"With this kind of environment and condition, we fear the worst."

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News Network
January 20,2020

Langkawi, Jan 20: Malaysia will not take retaliatory trade action against India over its boycott of palm oil purchases amid a political row between the two countries, Prime Minister Mahathir Mohamad said on Monday.

India, the world’s largest edible oil buyer, this month effectively halted imports from its largest supplier and the world’s second-biggest producer in response to comments from Mahathir attacking India’s domestic policies.

“We are too small to take retaliatory action,” Mahathir told reporters in Langkawi, a resort island off the western coast of Malaysia. “We have to find ways and means to overcome that,” he added.

The 94-year-old premier of Muslim-majority Malaysia has criticised New Delhi’s new religion-based citizenship law and also accused India of invading the disputed region of Kashmir.

Mahathir again criticised India’s citizenship law on Monday, saying he believed it was “grossly unfair”.

India has been Malaysia’s largest palm oil market for the past five years, presenting the Southeast Asian country with a major challenge in finding new buyers for its palm oil.

Benchmark Malaysian palm futures fell nearly 10% last week, their biggest weekly decline in more than 11 years.

New Delhi is also unhappy with Malaysia’s refusal to revoke permanent resident status for controversial Indian Islamic preacher Zakir Naik, who has lived in Malaysia for about three years and faces charges of money laundering and hate speech in India.

Mahathir said even if the Indian government guarantees a fair trial, Naik faces the real threat of vigilante action and that Malaysia will only relocate the preacher if it can find a third country where he would be safe.

“If we can find a place for him, we will send him out.”

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News Network
April 22,2020

London, Apr 22: The UK government on Tuesday announced a 20 million pounds funding for a University of Oxford project working on developing a vaccine against the novel coronavirus, which is now ready for acceleration as it begins human trials from Thursday.

UK Health Secretary Matt Hancock told the daily Downing Street briefing that the Department for Health was “throwing everything” at trying to find a vaccine because it is a critical aspect of the COVID-19 pandemic fight and lifting the strict lockdown measures in place to curb its spread.

Another 22.5 million pounds is being made available to Imperial College London to support its phase-two clinical trials for them to begin the work on a very large phase three trial.

"Normally it would take years to get to this point," said Hancock.

"The UK is at the forefront of the global effort – we've put in more money than any other into the global search for a vaccine. Nothing about this is inevitable. Vaccine production is a matter of trial and error. But the UK will throw everything it has at trying to find one,” he said.

The announcement came as Britain had another major daily leap in the hospital death toll from coronavirus, up by 823 to hit 17,337 on Tuesday.

But the Cabinet minister said the government's plan to control the rapid spread of the virus and prevent the state-funded National Health Service (NHS) from being overwhelmed is working as the number of hospitalisations with COVID-19 was showing a downward trajectory.

In reference to a major issue in the last few weeks of a critical shortage of personal protective equipment (PPE) for doctors and nurses on the frontlines of COVID-19 treatment, the minister said the supply problems are being addressed by actively engaging with thousands of companies, including 159 UK manufacturers.

“We are determined to get people the PPE they need. This is a 24/7 operation, one of the biggest cross-government operation I have ever seen," said Hancock.

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