American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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

Jan 23: Pakistan's Prime Minister Imran Khan called on Wednesday for the United Nations to help mediate between nuclear armed India and Pakistan over the disputed territory of Kashmir.

"This is a potential flashpoint," Khan said during a media briefing at the annual meeting of the World Economic Forum in Davos, Switzerland, adding that it was time for the "international institutions ... specifically set up to stop this" to "come into action".

The Indian government in August revoked the constitutional autonomy of Indian-administered Kashmir, splitting the Muslim-majority region into two federal territories in a bid to integrate it fully with the rest of the country.

Kashmir is claimed in full by both India and Pakistan. The two countries have gone to war twice over it, and both rule parts of it. India's portion has been plagued by separatist violence since the late 1980s.

Khan said his biggest fear was how New Delhi would respond to ongoing protests in India over a citizenship law that many feel targets Muslims.

"We're not close to a conflict right now ... What if the protests get worse in India, and to distract attention from that, what if ..."

The prime minister said he had discussed the prospect of war between his country and India in a Tuesday meeting with US President Donald Trump. Trump later said he had offered to help mediate between the two countries.

Khan said Pakistan and the United States were closer in their approach to the Taliban armed rebellion in Afghanistan than they had been for many years. He said he had never seen a military solution to that conflict.

"Finally the position of the US is there should be negotiations and a peace plan."

In a separate on-stage conversation later on Wednesday, Khan said he had told Trump in their meeting that a war with Iran would be "a disaster for the world". Trump had not responded, Khan said.

Khan made some of his most straightforward comments when asked why Pakistan has been muted in defence of Uighurs in China.

China has been widely condemned for setting up complexes in remote Xinjiang province that Beijing describes as "vocational training centres" to stamp out ""extremism and give people new skills.

The United Nations says at least one million ethnic Uighurs and other Muslims have been detained.

When pressed on China's policies, Khan said Pakistan's relations with Beijing were too important for him to speak out publicly.

"China has helped us when we were at rock bottom. We are really grateful to the Chinese government, so we have decided that any issues we have had with China we will handle privately."

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News Network
January 12,2020

Washington, Jan 12: US president Donald Trump said Saturday the United States was monitoring Iranian demonstrations closely, warning against any new “massacre” as protests broke out after Tehran admitted to shooting down a passenger plane.

Iran said earlier it unintentionally downed a Ukrainian jetliner outside Tehran, killing all 176 people aboard, in an abrupt about-turn after initially saying that it had crashed due to mechanical failure. The firing came shortly after Iran launched missiles at bases in Iraq housing American forces.

President Hassan Rouhani said a military probe into the tragedy had found that “missiles fired due to human error” brought down the Boeing 737, calling it an “unforgivable mistake.”

Trump told Iranians -- in tweets in both English and Farsi -- that he stands by them and is monitoring the demonstrations.

“To the brave, long-suffering people of Iran: I've stood with you since the beginning of my Presidency, and my Administration will continue to stand with you,” he tweeted.

“There can not be another massacre of peaceful protesters, nor an internet shutdown. The world is watching,” he added, apparently referring to an Iranian crackdown on street protests that broke out in November.

“We are following your protests closely, and are inspired by your courage," he said.

The new demonstrations follow an Iranian crackdown on street protests that broke out in November. Amnesty International has said it left more than 300 people dead. Internet access was reportedly cut off in multiple Iranian provinces ahead of memorials planned a month after the protests.

On Saturday evening, police dispersed students who had converged on Amir Kabir University in Tehran to pay tribute to the victims, after some among the hundreds gathered shouted "destructive" slogans, Fars news agency said.

State television reported that students shouted "anti-regime" chants, while the news agency Fars reported that posters of Soleimani had been torn down.

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News Network
June 10,2020

Jun 10: Indian-origin California Senator Kamala Harris has joined former vice president and 2020 Democratic presidential nominee Joe Biden to raise USD 3.5 million for the upcoming November elections.

Tuesday's fundraiser is the second-largest single event haul so far for the Biden campaign, which raised USD 4 million at one event earlier this month.

Harris' presence during the virtual mega fund raiser assumes significance as the Democratic Party leaders consider her to be one of the front-runners to be the nominee for vice president. The 55-year-old lawyer-politician was once considered to be a strong opponent of Biden in the 2020 Democratic primaries.

Introducing Harris to the 1,400 supporters present at the event, Biden underlined the history-breaking nature of her past electoral wins.

"For much of her career, she was the only person in the room who looked like she did," he said.

At the start of the campaign last year, Harris was very critical of Biden. She later endorsed him, months after she decided to withdraw herself from the race to the White House.

During the fundraiser, Harris was effusive in her praise for Biden.

Referring to Biden's meeting with George Floyd's family, she said, "He (Biden)is someone who whether one on one or speaking to the nation always has a sense of how people are experiencing this world, and what their needs are...This moment in the history of our country really represents an extraordinary exercise in contrast."

"On the other hand, we have a Donald Trump who had the gall to dispatch the US military to clear the streets so that he could prance down and then, like a prop, hold up the bible for a photo op," Harris said.

The death of African-American Floyd during police confinement in Minneapolis on May 25 has resulted in widespread protests not only in the US but across the world.

"There are so many contrasts between Joe Biden and Donald Trump that really point to the choice that we as Americans have today," Harris said.

California Lt Governor Eleni Kounalakis also joined the fund raiser.

In his remarks, Biden, 77, said the US is reeling in anguish and anger over the brutal killing of Floyd or the systemic racism that still infects every part of the society. "Harris knows better than anybody," he said.

"At the same time, we're facing the worst economic disaster since the Great Depression. American history is not a fairy tale with a guaranteed ending, a happy ending. This is a battle for the soul of the country.

"It's been a constant tug of war between the American ideal that we all are created equal -- and the harsh reality that racism has long torn us apart...I'm going to ask every American to look where we are now and to think, is this who we are? Is this who we want to be?" Biden asked.

Participating in the questions and answers session, Harris said America has still not fully embraced, acknowledged or addressed its history of racism and its current history of racism.

"One can think of this moment as an inflection moment, and it will require bold action and it will require immediate action...This stresses the importance and the immediacy and the urgency of electing Joe Biden," she said.

Replying to a question, Biden said, "Did you see today where the President of the United States while George Floyd was being buried, was condemning the older man who was knocked down with his head bleeding and everyone walking by. Did you see that? I mean, my lord. What have we become if we abide by this? So much we can do and must do."

Harris said the election is going to be rough and tumble.

"There are very powerful forces that thrive off of the hate and division that Donald Trump has been sowing. This is not going to be easy. And we have about just a few months to get this thing done," she said.

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