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 22,2020

London, Apr 22: The toll from coronavirus in the United Kingdom has jumped above 18,000 after 759 more deaths were reported in the last 24 hours, the Department of Health and Social Care announced in a statistical bulletin on Wednesday.

In total, 18,100 people have died in the UK hospitals after contracting COVID-19 as of 16:00 GMT on Tuesday.

A further 4,451 new cases of the disease were reported over the preceding 24 hours up to 08:00 GMT on Wednesday, the ministry said. The total number of cases reported since the start of the outbreak now stands at 1,33,495.

On Tuesday, the Office of National Statistics published a report stating that the coronavirus disease death toll as of April 10, when accounting for deaths in care homes and private residences, was 41 per cent higher than the government's figures.

In parliament on Wednesday, Health Secretary Matt Hancock stated that the United Kingdom has reached the peak of the COVID-19 outbreak, praising the social distancing measures enforced in the country.

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Agencies
January 7,2020

Tehran, Jan 7: The Iranian Parliament on Tuesday ratified a motion dubbed as "harsh revenge", that considers all members of the US Pentagon and those responsible for the death of Major General Qasem Soleimani as "terrorist forces".

The triple-urgency motion is a modification of a previously ratified bill on April 23, 2019, that designated the US Central Command (CENTCOM) as a terrorist organization in retaliation to the same designation imposed on Iran's Islamic Revolutionary Guard Corps (IRGC) by Washington, the Tehran-based Mehr News Agency said in a report.

Parliament Speaker Ali Larijani said in Tuesday's open session that in the previous anti-US law, CENTCOM was designated as a terrorist entity.

"Today, following the cruel US measure in assassinating General Soleimani, the responsibility of which was accepted by the US President, we modify the previous law and announce that all members of Pentagon, commanders, agents and those responsible for the martyrdom of Gen Soleimani will be considered as terrorist forces," Larijani was quoted as saying in the report.

All of Iran nation supports the resistance, he added.

The modified law also allows withdrawal of $223 million to the IRGC's Quds Force from the National Development Fund of Iran for the next two months, added Larijani.

He said that the Supreme Leader Ayatollah Ali Khamenei's permission to withdraw the fund has been obtained, the Mehr report added.

Following its ratification, MPs chanted anti-US slogans at the Parliament.

Soleimani and his son-in-law and Abu Mahdi al-Muhandis, the second-in-command of Iraq's Popular Mobilization Front (PMF), along with eight other people were killed in the January 3 drone attack ordered by US President Donald Trump.

Soleimani, 63, was the elite Quds Force chief in charge of IRGC operations outside Iran, and has been on the ground in Syria and Iraq supervising militias backed by Tehran.

The Quds Force holds sway over a large number of militias across the region ranging from Lebanon to Syria and Iraq.

The attack has led to widespread condemnation in Iran. Supreme Leader Khamenei and President Hassan Rouhani has vowed revenge on the US.

On Sunday, Iranian MP Abolfazl Aboutorabi threatened to attack the heart of American politics.

During an open session of the Iranian Parliament on Sunday afternoon, President Trump was called a "terrorist in a suit" after he threatened to hit 52 Iranian sites hard if Tehran attacks Americans or US assets.

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Agencies
February 11,2020

The head of the World Health Organisation on Tuesday warned the novel coronavirus was a "very grave threat" for the world as he opened a conference to combat the epidemic.

"With 99% of cases in China, this remains very much an emergency for that country, but one that holds a very grave threat for the rest of the world," Tedros Adhanom Ghebreyesus said in Geneva.

Some 400 scientists will review how the virus is transmitted and possible vaccines at the two-day forum.

"What matters most is stopping the outbreak and saving lives. With your support, that's what we can do together," Tedros said.

The virus, first identified in China on December 31, has killed more than 1,000 people, infected over 42,000 and reached some 25 countries.

Participants will also discuss the source of the virus, which is thought to have originated in bats and reached humans via another animal such as snakes or pangolins.

There is no specific treatment or vaccine against the virus, which can cause respiratory failure.

Tedros, who has repeatedly urged countries affected to share their data, called for global "solidarity".

"That is especially true in relation to the sharing of samples and sequences. To defeat this outbreak, we need open and equitable sharing, according to the principles of fairness and equity," he said.

"We hope that one of the outcomes of this meeting will be an agreed roadmap for research around which researchers and donors will align," Tedros said.

Several companies and institutes in Australia, China, France, Germany and the United States are racing to develop a vaccine -- a process that normally takes years.

Asked whether scientists from Taiwan would be allowed to take part in this week's Geneva conference, WHO officials said that they would do so but only online -- along with colleagues from other parts of China.

While the WHO does not deal with Taiwan directly and only recognises Beijing, Taiwan was often allowed to attend annual assemblies and sideline meetings as an observer.

But in recent years it has been frozen out as Beijing takes an increasingly combative stance towards democratic Taiwan, which it considers its own territory.

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