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 4,2020

London, Jun 4: Meghan, Britain's Duchess of Sussex, has spoken about events following the death of George Floyd saying she was sorry that children had to grow up in a world where racism still existed and that current events in the United States were "devastating".

"I know you know that black lives matter," Meghan said in a video she recorded for students graduating from her old high school in Los Angeles which was aired on Wednesday.

The death of Floyd has become the latest flashpoint for long-simmering rage over police brutality against African Americans and led to nationwide protests, some violent, with curfews imposed in some cities to quell the disorder.

"For the past couple of weeks I've been planning on saying a few words to you for your graduation and as we've all seen over the last week what is happening in our country, and in our state and in our home town of LA is absolutely devastating," said Meghan, whose mother is African American and father is white.

"First thing I want to say to you is that I'm sorry, I'm so sorry that you have to grow up in a world where this is still present," she said in her message to the girls at the Immaculate Heart High School.

The duchess, a former US actress and wife of Queen Elizabeth's grandson Prince Harry, said she wanted to say "the right thing" and was nervous her words would be "picked apart".

"The only wrong thing to say is to say nothing. Because George Floyd's life mattered, and Breonna Taylor's life mattered, and Philando Castile's life mattered and Tamir Rice's life mattered and so did so many other people whose names we know, and whose names we do not know," she said.

Britain's royal family by tradition does not comment on political issues. However, Meghan and Harry stepped down from their official royal roles at the end of March and are now living in Los Angeles with their baby son Archie.

In her message, the 38-year-old reflected on her own memories of the 1992 LA riots.

"Those memories don't go away and I can't imagine that at 17 or 18 years old, which is how old you are now, that you would have to have a different version of that same type of experience," she said.

"That's something you should have an understanding of, but an understanding of as a history lesson not as your reality. So I'm sorry that in a way we have not gotten the world to the place you deserve it to be."

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May 22,2020

May 22: A Pakistan International Airlines (PIA) flight on its way from Lahore to Karachi, crashed in the area near Jinnah International Airport on Friday, according to Civil Aviation Authority officials.

Geo News reported that the plane crashed at the Jinnah Ground area near the airport as it was approaching for landing. There were more than 90 passengers on board the Airbus aircraft. Black smoke could be seen from afar at the crash site, say eye witnesses.

There were no immediate reports on the number of casualties. The aircraft arriving from the eastern city of Lahore was carrying 99 passengers and 8 crew members, news agency AP said, quoting Abdul Sattar Kokhar, spokesman for the country’s civil aviation authority.

Witnesses said the Airbus A320 appeared to attempt to land two or three times before crashing in a residential area near Jinnah International Airport.

Flight PK-303 from Lahore was about to land in Karachi when it crashed at the Jinnah Garden area near Model Colony in Malir, just a minute before its landing, Geo News reported.

Local television reports showed smoke coming from the direction of the airport. Ambulances were on their way to the airport.

News agency said Sindh’s Ministry of Health and Population Welfare has declared emergency in all major hospitals of Karachi due to the plane crash.

It’s the second plane crash for Pakistani carrier in less than four years. The airline’s chairman resigned in late 2016, less than a week after the crash of an ATR-42 aircraft killed 47 people. The incident comes as Pakistan was slowly resuming domestic flights in the wake of the coronavirus pandemic, Bloomberg reported.

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March 19,2020

Rome, Mar 19: Italy on Wednesday reported 475 new deaths from the novel coronavirus, the highest one-day official toll of any nation since the first case was detected in China late last year.

The total number of deaths in Italy has reached 2,978, more than half of all the cases recorded outside China, while the number of infections stood at 35,713.

The previous record high of 368 deaths was also recorded in Italy, on Sunday. The nation of 60 million has now recorded 34.2 percent of all the deaths officially attributed to COVID-19 across the world.

With the death rate still climbing despite the Mediterranean country entering a second week under an effective lockdown, officials urged Italians to have faith and to stay strong.

"They main thing is, do not give up," Italian National Institute of Health chief Silvio Brusaferro said in a nationally televised press conference.

"It will take a few days before we see the benefits" of containment measures, said Brusaferro. "We must maintain these measures to see their effect, and above all to protect the most vulnerable."

Imposed nationally on March 12, the shutdown of most Italian businesses and a ban on public gatherings are due to expire on March 25.

But school closures and other measures, such as a ban fan attendance at sporting events, are due to run on until April 3.

A top government minister hinted Wednesday that the school closure would be extended well into next month, if not longer.

The rates within Italy itself remained stable, with two-thirds of the deaths -- 1,959 in all -- reported in the northern Lombardy region around Milan, the Italian financial and fashion capital.

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