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
June 25,2020

Ottawa, Jun 25: Prime Minister Justin Trudeau took his son out for ice cream on Wednesday in his first family outing since Canada started easing out of its pandemic lockdown.

It was also Saint-Jean-Baptiste Day in Quebec province.

Wearing masks, the Canadian leader and his six-year-old son Hadrien were cheered at Chocolats Favoris in Gatineau, Quebec.

According to a pool report, Trudeau said the shop tapped into a federal emergency wage subsidy and business loan in order to weather the pandemic, and "avoid being frozen out of the frozen treat market."

Hadrien is said to have bounced with excitement, settling on a vanilla cone with a cookie topping while dad bought a vanilla cone dipped in chocolate for himself.

Father and son then headed out to the patio, where they doffed their masks to eat their cones.

Canada's provinces and territories declared states of emergency mid-March, closing schools and non-essential businesses in response to the pandemic.

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Agencies
April 28,2020

Washington, Apr 28: US President while addressing a news conference on coronavirus pandemic said his administration has launched "very serious investigations" into China's response to the novel coronavirus.

"And we are not happy with China, we are not happy with that whole situation, because we believe it could have been stopped at the source," he said. "It could have been stopped quickly and it wouldn't have spread all over the world," the BBC reported.

Trump has been critical of China as the pandemic has progressed and has frequently touted his decision to close the US borders to China in an effort to curb the outbreak. Some health experts have said the effort bought time for the US to prepare, but the Trump administration has been accused of squandering the opportunity.

"Nobody except one country can be held accountable for what happened," Trump said.

"Nobody's blaming anybody here, we're looking at a group of people that should've stopped it at the source."

The US will never forget those who were "sacrificed for a reason of incompetence or something else other than incompetence," he added.

"They" - referring to China - "could've protected the whole world - not just us - the whole world," he said.

At the starting of the conference Trump said COVID-19 cases are declining or stablising across the country.

"In all cases getting better," he said. "Really a horrible situation that we've been confronted with, but they're moving along."

He added there's a "hunger" to get back to work.

"Ensuring the health of our economy is vital to ensuring the health of our nation - these goals work in tandem."

The president has suggested an unnamed individual "a long time ago" could have stopped the "unnecessary death[s]" due to COVID-19.

"There has been so much unnecessary death in this country," he said.

"It could've been stopped and it could've been stopped short, but somebody a long time ago, it seems, decided not to do it that way and the whole world is suffering because of it."

He did not say who he was referencing and gave no other details.

Trump was asked if he has considered delaying the November presidential election.

"I never even thought of changing the date of the election," he answered. "Why would I do that? November 3rd. That's a good number."

Trump called the suggestion "made up propaganda" and said that "sleepy Joe" Biden - his presumptive Democratic rival - was likely unaware his campaign had put the statement out.

Former Vice-President Joe Biden said at a virtual fundraiser last week that he thought Trump would "try to kick back the election somehow".

The president has frequently levelled insults at his Democratic opponent by questioning the former vice-president's mental fortitude.

"I look forward to that election," Trump said.

The president responded to a question criticising Health Secretary Alex Azar's early downplaying of the disease by saying it was "unfair". He claimed Democrats did the same, including Speaker of the House of Representatives Nancy Pelosi.

"I was very fortunate through luck or whatever that we closed the border, we put a ban on China," he said.

"But I could tell you that Nancy Pelosi was dancing in the streets in Chinatown. She wanted to go, let's go out and party. That was late in February."

Back in February, Pelosi had encouraged people to visit San Francisco's Chinatown to help struggling businesses. She did not propose any parties, as the president suggested.

The city issued a stay-at-home order in March.

A reporter asked: If an American president loses more Americans over the course of six weeks than died during the entirety of the Vietnam war, does he deserve to be reelected?

Trump took the question in stride.

"So, yeah, we've lost a lot of people but if you look at what original projections were, 2.2 million, we're probably heading to 60,000 - 70,000," he said.

"It's far too many - one person is too many for this. I think we've made a lot of really good decisions," he added. "The big decision was closing the border, doing the ban on people coming in from China."

He also brings up the "unbelievable" job his administration did with ventilators.

"I think we've done a great job. And I will say this - one person is too many."

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News Network
March 16,2020

Manila, Mar 16: The Philippines has detected an outbreak of avian flu in a northern province after tests showed presence of the highly infectious H5N6 subtype of the influenza A virus in a quail farm, the country's farm minister said on Monday.

Agriculture Secretary William Dar said the bird flu virus, the same strain that hit some local poultry farms in 2017, was detected in Jaen municipality in Nueva Ecija province, where about 1,500 quails had died on one farm alone.

A total of 12,000 quails have been destroyed and buried to prevent further infections, Dar said, citing field reports.

"We are on top of the situation," he said. "Surveillance around the 1-km and 7-km radius will be carried out immediately to ensure that the disease has not progressed around the said perimeter."

Animal quarantine checkpoints have also been set up to restrict the movement of all live domestic birds to and from the quarantine area, he said.

"We would like to emphasise that this is a single case affecting one quail farm only," Dar said.

Dr. Arlene Vytiaco, technical spokeswoman for avian flu at the agriculture department, said that while there is a possibility of transmission to humans through excretion and secretion, "the chances are very slim".

"There is also zero mortality rate," she said.

Dar said his department and the local government were jointly conducting an investigation and contact-tracing to determine the source of infection.

To ensure steady domestic supply of poultry, he said the transport of day-old chicks, hatching eggs and chicken meat will be allowed provided the source farms have tested negative for bird flu.

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