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 29,2020

Beijing, Mar 29: In a rare display of public anger in China, dozens of people in central Hubei province, the epicentre of the coronavirus outbreak till recently, attacked official vehicles after they were stopped from crossing a bridge and travel to neighbouring Jiangxi after the lifting of the lockdown.
Hubei province with over 56 million people was kept under lockdown from January 23 as part of aggressive measures to bring down COVID-19 cases which rapidly spread in the area.

Videos on Chinese social media on Friday showed unprecedented scenes of police from Hubei and Jiangxi clashing on the bridge connecting the two provinces over barricades erected from stopping Hubei people from moving out over fears of coronavirus spreading.

Policemen from both sides argued over how to verify if people were allowed to enter Jiangxi, according to local media reports.

It was a major relief for millions of people in Hubei province, when the Chinese government which kept it under lockdown lifted the restrictions on travel.

The government will permit people from the province to travel if they hold a green health code, meaning no contact with any infected or suspected COVID-19 cases.

But people of Hubei to their shock on Friday found roadblocks on the 1st Yangtze River Bridge that separates Huangmei county in Hubei erected by Huangmei county of Jiangxi province.

In local media reports, witnesses were quoted as saying that Huangmei police in Jiujiang erected roadblocks on the bridge to stop people from Hubei from crossing it, a move they alleged stigmatised them.

Video footage shared online showed rows of police armed with riot shields holding back the crowds, while members of the public could be seen damaging and even overturning police vehicles.

In a clip published by the Huanggang city government, which administers Huangmei, the county's Communist Party chief Ma Yanzhou could be heard speaking to the people through a loud hailer, warning them that by gathering in a large group they were increasing their chances of contracting the virus, Hong Kong-based South China Morning Post reported.

While it is unclear exactly how the clash started, police from the two sides published separate official statements online, which were quickly deleted, it said.

The incident underlines the problems China faces as it seeks a return to normalcy after months of lockdown, the Post said.

After the incident, the governments of Huangmei and Jiujiang on Friday issued a joint statement saying they had agreed to remove the barriers set up to restrict travel during the lockdown, and also to recognise each other's health screening codes to make it easier for people in good health to get to where they needed to be, the Post report said.

An article by the ruling Communist Party of China (CPC) mouthpiece, People''s Daily acknowledged the problems in getting the country back on its feet.

"In the past few days, all walks of life have called for governments to accept workers from Hubei," it said.

"However, it is undeniable that some places, intentionally or not, have set up obstacles for Hubei migrant workers to return to their posts and hold prejudices against them."

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News Network
June 1,2020

Washington, Jun 1: Police fired tear gas outside the White House late Sunday as major US cities were put under curfew to suppress rioting as anti-racism protestors again took to the streets to voice fury at police brutality.

With the Trump administration branding instigators of six nights of rioting as domestic terrorists, there were more confrontations between protestors and police and fresh outbreaks of looting.

Violent clashes erupted repeatedly in a small park next to the White House, with authorities using tear gas, pepper spray and flash bang grenades to disperse crowds who lit several large fires and damaged property.

Local US leaders appealed to citizens to give constructive outlet to their rage over the death of an unarmed black man in Minneapolis, while night-time curfews were imposed in cities including Washington, Los Angeles and Houston.

One closely watched protest was outside the state capitol in Minneapolis' twin city of St. Paul, where several thousand people gathered before marching down a highway.

"We have black sons, black brothers, black friends, we don't want them to die. We are tired of this happening, this generation is not having it, we are tired of oppression," said Muna Abdi, a 31-year-old black woman who joined the protest.

"I want to make sure he stays alive," she added in reference to her son, aged three.

Hundreds of police and National Guard troops were deployed ahead of the protest.

At one point, some of the protestors who had reached a bridge were forced to scramble for cover when a truck drove at speed after having apparently breached a barricade.

The driver was later taken to hospital after the protestors hauled him from the vehicle, although there were no immediate reports of other casualties.

There were other large-scale protests in cities including New York and Miami.

Washington's mayor ordered a curfew from 11:00 pm until 6:00 am, as a report in the New York Times said that President Donald Trump had been rushed by Secret Service agents into an underground bunker at the White House on Friday night during an earlier protest.

Stores ransacked

Large-scale violence has rocked many US cities in recent days, and looters ransacked stores in a neighborhood of Philadelphia on Sunday.

In the Los Angeles suburb of Santa Monica, looting was reported at stores in a popular beachside shopping center.

Officials in LA -- a city scarred by the 1992 riots over the police beating of Rodney King, an African-American man -- imposed a curfew from 4:00 pm Sunday until dawn.

"Please, use your discretion and go early, go home, stay home and help us make sure that those who want to change this conversation from being about racial justice to be about burning things and looting things, don't win the day," the city's mayor Eric Garcetti said on CNN.

The shocking videotaped death last Monday of an unarmed black man, George Floyd, at the hands of police in Minneapolis ignited the nationwide wave of outrage over law enforcement's repeated use of lethal force against unarmed African Americans.

Floyd stopped breathing after Minneapolis police officer Derek Chauvin knelt on his neck for nearly nine minutes.

Chauvin has been charged with third-degree murder and is due to make his first appearance in court on Monday. Three other officers with him have been fired but for now face no charges.

Governor Tim Walz has mobilized all of Minnesota's National Guard troops  -- the state guard's biggest mobilization ever -- to help restore order.

Police fired tear gas and stun grenades to clear streets of curfew violators Saturday night in Minneapolis.

Walz extended a curfew for a third night Sunday and praised police and guardsmen for holding down violence. "They did so in a professional manner. They did so without a single loss of life and minimal property damage," he said.

"Congratulations to our National Guard for the great job they did immediately upon arriving in Minneapolis, Minnesota, last night," President Donald Trump tweeted, adding that they "should be used in other States before it is too late!"

The Department of Defense said that around 5,000 National Guard troops had been mobilized in 15 states as well as the capital Washington, with another 2,000 on standby.

The widespread resort to uniformed National Guards units is rare, and it evoked disturbing memories of the rioting in US cities in 1967 and 1968 in a turbulent time of protest over racial and economic disparities.

Trump blamed the extreme left for the violence, saying he planned to designate a group known as Antifa as a terrorist organization.

"The violence instigated and carried out by Antifa and other similar groups in connection with the rioting is domestic terrorism and will be treated accordingly," added Attorney General Bill Barr.

'A nation in pain'

Atlanta Mayor Keisha Lance Bottoms said Trump, who has often urged police to use tough tactics, was not helping matters.

"We are beyond a tipping point in this country, and his rhetoric only enflames that," she said on CBS.

Joe Biden, Trump's likely Democratic opponent in November's presidential election, visited the scene of one anti-racism protest.

"We are a nation in pain right now, but we must not allow this pain to destroy us," Biden tweeted, posting a picture of him speaking with an African-American family at the site where protesters had gathered in Delaware late Saturday.

Floyd's death has triggered protests beyond the United States, with hundreds rallying outside the US embassy in London in solidarity.

"I'm here because I'm tired, I'm fed up with it. When does this stop?" Doreen Pierre told AFP at the protest.

In Germany, England football international Jadon Sancho marked one of his three goals for Borussia Dortmund against Paderborn by lifting his jersey to reveal a T-shirt bearing the words "Justice for George Floyd".

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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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