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
January 23,2020

Beijing, Jan 23: China is putting on lockdown a city of 11 million people considered the epicenter of the new coronavirus outbreak that has killed 17 and infected nearly 600 people, as health authorities around the world work to prevent a global pandemic.

The previously unknown coronavirus strain is believed to have emerged late last year from illegally traded wildlife at an animal market in the central Chinese city of Wuhan. Cases have been detected as far away as the United States, stoking fears the virus is already spreading worldwide.

Wuhan's local government said it would shut down all urban transport networks and suspend outgoing flights from the city as of 10 a.m. (0200 GMT) Thursday, state media reported, adding that the government is urging citizens to not leave the city in the absence of special circumstances.

Contrasting with its secrecy over the 2002-03 Severe Acute Respiratory Syndrome (SARS), which killed nearly 800 people, China's communist government has this time given regular updates to try to avoid panic as millions of people travel for the Chinese Lunar New Year holiday.

Chinese authorities have confirmed 571 cases and 17 deaths as of end-Wednesday, state television reported on Thursday. There are eight other known cases around the world - Thailand has confirmed four cases, while the United States, Taiwan, South Korea and Japan have each reported one.

Vice Premier Sun Chunlan said during a visit to Wuhan that authorities needed to be open about the spread of the virus and their efforts to contain it, the official Xinhua news agency reported on Thursday, comments likely to reassure global health experts.

After a meeting at its Geneva headquarters on Wednesday, the World Health Organization (WHO) said it would decide on Thursday whether to declare the outbreak a global health emergency, which would step up the international response.

If it does so, it will be the sixth international public health emergency to be declared in the last decade.

WHO Director-General Tedros Adhanom Ghebreyesus told reporters in Geneva that China's actions so far were "very strong" but called in Beijing to take "more and significant measures to limit or minimise the international spread".

"We stressed to them that by having a strong action not only they will control the outbreak in their country but they will also minimise the chances of this outbreak spreading internationally. So they recognise that," he said.

A senior U.S. State Department official also called on China to "play a bigger role in global health so they taking more and significant measures to limit or minimise the international spread".

"The lack of transparency in the past, especially with SARS ... gives us concern that that may be the case here," the official said, adding however that there were "positive signs that they have taken action in Wuhan".

Fears of a pandemic initially spooked markets but they regained their footing on Wednesday, with investors citing the robust response from authorities as reassuring.

VIRUS SPREADING

The outbreak began in Wuhan, a major transportation hub as well as central China's main industrial and commercial centre, and has now spread to other major population centers including Beijing, Shanghai and Hong Kong.

There is no known cure for the virus. Symptoms include fever, difficulty in breathing and cough, similar to many other respiratory illnesses, and can cause pneumonia.

Chinese authorities are still investigating the origins of the virus, though they confirmed the outbreak began at a market in Wuhan with illegal wildlife transactions and that it can spread from one person to another via respiratory transmission. Among confirmed patients are 15 medical workers, further adding to worries about a possible global pandemic.

Many Chinese were canceling trips, buying face masks, avoiding public places such as cinemas and shopping centers, and even turning to an online plague simulation game as a way to cope.

Airports globally stepped up screening passengers from China and the European Centre for Disease Control and Prevention (ECDC) said in a risk assessment that further global spread of the virus was likely.

Britain joined other countries including Australia in advising citizens against all but essential travel to Wuhan.

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Agencies
March 14,2020

San Francisco, Mar 14: Microsoft on friday announced that co-founder Bill Gates has left its board of directors to devote more time to philanthropy.

The 64-year-old stopped being involved in day-to-day operations at the firm more than a decade ago, turning his attention to the foundation he launched with his wife, Melinda.

Gates served as chairman of Microsoft's board of directors until early in 2014 and has now stepped away entirely, according to the Redmond-based technology giant.

“It's been a tremendous honor and privilege to have worked with and learned from Bill over the years,” Microsoft chief executive and company veteran Satya Nadella said in a release.

Nadella said Microsoft would continue to benefit from Gates' “technical passion and advice” in his continuing role as a technical advisor.
“I am grateful for Bill's friendship and look forward to continuing to work alongside him,” he added.

Gates left his CEO position in 2000, handing the company reins to Steve Ballmer to devote more time to his charitable foundation.

He gave up the role of chairman at the same time Nadella became Microsoft's third CEO in 2014.

Regularly listed among the world's richest people, William H. Gates was a geeky-looking young man when he and Paul Allen co-founded Microsoft in 1975.

Gates went on to turn his attention from software to fighting disease and other humanitarian challenges with his wife, under the auspices of the Bill and Melinda Gates Foundation.

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News Network
June 2,2020

Washington, Jun 2: US President Donald Trump said that peaceful protests following the death of African-American man George Floyd in police custody were derailed by acts of domestic terrorism.

"These are not acts of peaceful protests, these are acts of domestic terror - the destruction of innocent life, and the spilling of innocent blood is an offence to humanity and a crime against God," Trump said during a press briefing on Monday.

Trump also added that the chaos is the work of professional agitators and provocateurs - anarchists and the far-left movement Antifa, among others - and put them on notice, vowing to enforce law and order.

He further said, "Those who threaten innocent life and property will be arrested, detained and prosecuted to the fullest extent of the law. I want the organizers of this terror to be on notice that you will face severe criminal penalties and lengthy sentences in jail. This includes Antifa and others who are leading instigators."

The US president also that he is invoking an 1807 law to mobilize the military around the country to "quickly solve the problem."

"I am also taking swift and decisive action to protect our capital Washington DC. As we speak, I am dispatching thousands and thousands of heavily armed soldier, military personnel and enforcement officers to stop the rioting," Trump said during a press briefing.

"I am mobilizing all available federal resources, civilian and military, to stop the rioting and looting, to end the destruction and arson. And to protect the rights of law-abiding Americans, including your Second Amendment rights," he added.

Trump said mayors and governors must establish an "overwhelming law enforcement presence until the violence has been quelled." If the city or state refuses to take the actions, Trump said he would deploy the US military.

Trump on Monday also said that all Americans are rightly 'sickened by the brutal death' of George Floyd and his administration is fully committed to providing justice to George and his family.

"All Americans were rightly sickened and revolted by the brutal death of George Floyd. My administration is fully committed, the justice will be fully served for George and his family and He will not have died in vain," Trump said.

"My first and highest duty as president is to defend and protect the great country and the American people. I have sworn an oath to uphold the laws of our nation and that is exactly what I will do," he added.

After the media address, Trump made a surprise visit to the damaged St Johns church near White House, walking through park violently cleared of protesters. He walked to the church across the street from the White House after tear gas was fired at protesters in the area.

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