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 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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News Network
January 22,2020

Davos, Jan 22: President Donald Trump has said that the US is watching the developments between India and Pakistan over Kashmir "very closely" and repeated his offer to "help" resolve the longstanding dispute between the two neighbours as he met Prime Minister Imran Khan on the sidelines of the World Economic Forum here in the Swiss ski resort.

Addressing the media with the Pakistan Prime Minister prior to their private meeting on Tuesday, President Trump asserted that trade and borders were both critical points for discussion, while Khan said that for him, Afghanistan was the top priority.

Trump told Khan, whom he referred to as "my friend", that he would speak to Prime Minister Narendra Modi about the ongoing Kashmir issue. The US president is expected to visit India in the coming weeks, marking his first visit after taking up his post in the White House.

"What's going on between Pakistan and India … if we can help, we certainly will be willing to. We have been watching it very closely and it's an honour to be here with my friend," he said.

"The Pakistan-India conflict is a very big issue for us in Pakistan and we expect the US to always play its part in deescalating the tensions, because no other country can," Khan said.

President Trump has repeatedly offered to mediate following India's August 5 decision to revoke the special status to Jammu and Kashmir and bifurcate the state into two Union Territories, evoking strong reaction from Pakistan which has been trying to internationalise the Kashmir issue.

New Delhi has defended the move, saying Jammu and Kashmir is an integral part of India and the issue was strictly internal to the country, and the special status provisions only gave rise to terrorism in Jammu and Kashmir.

"The country took the decision of abrogation of Article 370, which had only given separatism and terrorism to that state," Prime Minister Narendra Modi said at a function in October last year.

This is the third meeting between Trump and Khan since Pakistan premier assumed office in 2018 and it came against the backdrop of Pakistan Foreign Minister Shah Mehmood Qureshi's recent trip to the US, amid reports that the US and Afghan Taliban were close to striking a peace deal.

"There are issues we want to talk about. The main issue is Afghanistan because it concerns the US and Pakistan. Fortunately, we are on the same page. Both of us are interested in peace there and an orderly transition in Afghanistan with talks with Taliban and the government," Khan said.

When a reporter asked Trump if he would visit Pakistan considering he was already set to visit India, the US president said he was meeting the Pakistan premier in Davos.

"Well, we're visiting right now. So we don't really have to. I wanted to say that from a relationship standpoint, we got a great relationship. From the standpoint our two countries, we're getting along very well. I would say we've never been closer with Pakistan the way we're right now. And this is a big statement," Trump said.

Khan left for Switzerland to attend the World Economic Forum and meet the world leaders, including President Trump, on the sidelines of the annual event which kicked off at the ski resort town of Davos on Tuesday.

The four-day summit marks the 50th anniversary of the forum.

A total of 53 heads of State are on the guest list. Nearly 3,000 participants from 118 countries are expected to attend the event during which political leaders, business executives, heads of international organisations and civil society representatives are set to deliberate on contemporary economic, geopolitical, social and environmental issues.

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Agencies
June 6,2020

The President of United States Donald Trump has said that countries like India and China would have much more coronavirus cases than America if they conduct more tests.

“I say to my people every time we test; you find cases because we do more testing. If we have more cases, if we wanted to do testing in China or in India or other places, I promise you there would be more cases you are doing a fantastic job in getting out the swabs,” the US president said on Friday.

Trump said that the US has carried out 20 million tests while compared to America, Germany is at four million and much talked about South Korea is about three million tests. He made the remarks at Puritan Medical Products in Maine, according to Johns Hopkins Coronavirus Resource Center.

The US has reported nearly 1.9 million cases and over 1,09,000 deaths while the total number of coronavirus cases in India and China stand at 2,36,184 and 84,177 respectively, according to Johns Hopkins Coronavirus Resource Center data.

India has so far conducted over 4 million COVID-19 tests, according to the health ministry.

Trump said, “we will be well over 20 million tests. Remember this, when you test more, you have more cases.”

“Puritan is one of the only manufacturers in the world producing high-quality medical swabs that are crucial for rapid testing. And every swab you make at Puritan is proudly stamped with the beautiful phrase made in the USA,” Trump said.

“Thanks to the testing capacity that you are making possible, our country is reopening and our economy is recovering like nobody would’ve thought possible,” he added.

Trump also spoke about the huge unemployment problem the country is currently facing. He said that the economy is now back on track, referring to the latest monthly employment numbers,.

“We absolutely shattered expectations, and this is the largest monthly jobs increase in American history, think of that; that’s a long time,” Trump said

“I think it’s more than double or about double of what our highest was before so this is the largest monthly job increase in American history. And we’re going to have a phenomenal next year. We’re going to have a tremendous couple of months prior to the election on November 3 very, very important date,” the president said.

Keeping an eye on the November 3 presidential elections, Trump is seeking re-election for his second consecutive term. He is pitted against Democratic presidential nominee Joe Biden who in opinion polls is surging several points of Trump.

“It’s going to be a very important election because the only thing that can screw it up is if you get the wrong president and they raise your taxes, and they open up your borders so that everybody pours into our country,” Trump said.

Trump also vowed to bring the American economy back on track, which has been badly hit by the coronavirus pandemic. He reiterated that his administration has built a strong economy in the last three years.

Describing the fight against coronavirus as the greatest national and industrial mobilisation since the World War II, Trump said that his administration has marshaled the full power of the US government and US industry to defeat the invisible enemy.

“It is indeed an enemy. It came from China, should have been stopped in China. They didn’t do that,” he alleged.

The administration, he said, has delivered over 1.5 billion pieces of personal protective equipment to doctors and nurses on the front lines. We slashed the red tape to speed up the development of vaccines.

“And vaccines are coming along incredibly well, wait till you see, and therapeutics. And we partnered at private sector leaders such as Puritan to build the largest and most advanced testing capacity on the face of the earth, like this one,” the US president said.

The Puritan factory in Maine, he said, quickly ramped up the production to produce nearly 20 million foam-tipped swabs each month.

“Then in April, my administration invoked the Defence Production Act to help you scale up even more. Under a USD 75 million public-private partnership, Puritan will soon double production to 40 million swabs per month,” Trump added.

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