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
March 12,2020

Geneva, Mar 12: For the global economy, virus repercussions were profound, with increasing concerns of wealth- and job-wrecking recessions. U.S. stocks wiped out more than all the gains from a huge rally a day earlier as Wall Street continued to reel.

The Dow Jones Industrial Average dropped 1,464 points, bringing it 20% below its record set last month and putting it in what Wall Street calls a “bear market.” The broader S&P 500 is just 1 percentage point away from falling into bear territory and bringing to an end one of the greatest runs in Wall Street’s history.

WHO officials said they thought long and hard about labeling the crisis a pandemic — defined as sustained outbreaks in multiple regions of the world.

The risk of employing the term, Ryan said, is “if people use it as an excuse to give up.” But the benefit is “potentially of galvanizing the world to fight.”

Underscoring the mounting challenge: soaring numbers in the U.S. and Europe’s status as the new epicenter of the pandemic. While Italy exceeds 12,000 cases and the United States has topped 1,300, China reported a record low of just 15 new cases Thursday and three-fourths of its infected patients have recovered.

China’s totals of 80,793 cases and 3,169 deaths are a shrinking portion of the world’s more than 126,000 infections and 4,600 deaths.

“If you want to be blunt, Europe is the new China,” said Robert Redfield, the head of the U.S. Centers for Disease Control and Prevention.

With 12,462 cases and 827 deaths, Italy said all shops and businesses except pharmacies and grocery stores would be closed beginning Thursday and designated billions in financial relief to cushion economic shocks in its latest efforts to adjust to the fast-evolving crisis that silenced the usually bustling heart of the Catholic faith, St. Peter’s Square.

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News Network
May 20,2020

Washington, May 20: Once dubbed as historic by him, US President Donald Trump on Tuesday said he now feels ‘differently’ about the trade deal he signed with China earlier this year.

He said this while once again venting out his frustration with the Beijing leadership, accusing it of letting coronavirus spread.

Till Tuesday, over 92,000 Americans have died and 1.5 million tested positive for coronavirus that has globally killed around 320,000 people.

The US and China had signed a deal in January to end their 22-month-long trade war during which the two countries slapped tit-for-tat tariff hikes on products worth nearly half a trillion USD.

Under it, Beijing agreed to increase its purchase of US goods by USD 200 billion in 2020-2021.

“I feel differently now about that deal than I did three months ago,” Trump told reporters during a Cabinet meeting at the White House.

“We will see what all happens, but it's been a very disappointing situation. A very disappointing thing happened with China because the plague flowed in and that wasn't supposed to happen and it could have been stopped," he said.

Trump said he was very excited when the trade deal with China was signed.

“But once the virus came in, once the plague, as I called it, came in, I said how did they let that happen? And how come it didn't go into other sections of China? Why did they block it from leaving Wuhan? But they didn't block it from going to the rest of the world, including the United States. Why is that? Beijing doesn't have it. Other places don't have it,” he said.

Trump did not respond to questions on retaliation against China.

Meanwhile, top American senators continued to press the administration that rules of engagement with China needs to change post-coronavirus.

“As we know, they unleashed this virus on America and the world with their classic communist cover-up, deception, continued propaganda campaign, costing now over 90,000 American lives, 35 million Americans losing their jobs so far,” Senator Martha McSally said during a Congressional hearing.

“We don’t know who patient zero is, they destroyed samples, they silenced doctors, they kicked out journalists, they impacted international travel to seed this and their reckless behaviour continues to be the root of all this,” she said.

As a result of coronavirus, the American economy has been thrown into recession; more than 36 million people have lost their job – the worst ever after last century’s great depression.

Many of the US states have now started opening up, after taking necessary precautions.

By conservative estimates, it will take several quarters for the economy to be back on track.

Trump in the last a few weeks has exuded confidence that the economy will be back on track next year.

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News Network
April 12,2020

Apr 12: India and other South Asian countries are likely to record their worst growth performance in four decades this year due to the coronavirus outbreak, the World Bank said on Sunday.

The South Asian region, comprising eight countries, is likely to show economic growth of 1.8 per cent to 2.8 per cent this year, the World Bank said in its South Asia Economic Focus report, well down from the 6.3 per cent it projected six months ago.

India's economy, the region's biggest, is expected to grow 1.5 per cent to 2.8 per cent in the fiscal year that started on April 1. The World Bank has estimated it will grow 4.8 per cent to 5 per cent in the fiscal year that ended on March 31.

"The green shoots of a rebound that were observable at the end of 2019 have been overtaken by the negative impacts of the global crisis," the World Bank report said.

Other than India, the World Bank forecast that Sri Lanka, Nepal, Bhutan and Bangladesh will also see sharp falls in economic growth.

Three other countries - Pakistan, Afghanistan and the Maldives - are expected to fall into recession, the World Bank said in the report, which was based on country-level data available as of April 7.

Measures taken to counter the coronavirus have disrupted supply chains across South Asia, which has recorded more than 13,000 cases so far - still lower than many parts of the world.

India's lockdown of 1.3 billion people has also left millions out of work, disrupted big and small businesses and forced an exodus of migrant workers from the cities to their homes in villages.

In the event of prolonged and broad national lockdowns, the report warned of a worst-case scenario in which the entire region would experience an economic contraction this year.

To minimize short-term economic pain, the Bank called for countries in the region to announce more fiscal and monetary steps to support unemployed migrant workers, as well as debt relief for businesses and individuals.

India has so far unveiled a $23 billion economic plan to offer direct cash transfers to millions of poor people hit by its lockdown. In neighbouring Pakistan, the government has announced a $6 billion plan to support the economy.

"The priority for all South Asian governments is to contain the virus spread and protect their people, especially the poorest who face considerable worse health and economic outcomes," said senior World Bank official Hartwig Schafer.

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