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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Agencies
February 4,2020

The Seattle City Council, one of the most powerful city councils in the U.S., on Monday unanimously passed a resolution condemning India’s recently-enacted Citizenship Amendment Act (CAA) and the National Register of Citizens (NRC).

Reaffirming Seattle as a welcoming city and expressing solidarity with the city’s South Asian community regardless of religion and caste, the resolution “resolves that the Seattle City Council opposes the National Register of Citizens and the Citizenship Amendment Act in India, and finds these policies to be discriminatory to Muslims, oppressed castes, women, indigenous, and LGBT people“.

Introduced by Indian American City Council member Kshama Sawant, the resolution urges the Parliament of India to uphold the Indian Constitution by repealing the CAA, and to stop the National Register of Citizens, and take steps towards helping refugees by ratifying various UN treaties on refugees.

“Seattle City’s decision to condemn CAA should be a message to all who wish to undermine pluralism and religious freedom. They cannot peddle in hate and bigotry, and expect to have international acceptability at the same time,” said Ahsan Khan, president of Indian American Muslim Council.

Thenmozhi Soundararajan of Equality Labs, which organised the community in support of the resolution, welcomed its passage. “We are proud of the Seattle City Council for standing on the right side of history today. Seattle is leading the moral consensus in the global outcry against the CAA, she said.

Soundararajan said that thousands of organizers across the country have called, e-mailed, and visited Seattle City Council members to amplify this resolution, and it sets an example to cities across the United States.

“At a time when members of the Indian ruling party sided Trump, the Muslim ban, and his war on immigrants as justification for targeting hundreds of millions of Indian minorities, Americans have a unique responsibility to stand up and speak about this human rights crisis. We are glad that Seattle is leading the way on this,” she said.

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News Network
February 27,2020

Washington, Feb 27: President Donald Trump has said that the US' relationship with India is "extraordinary" right now and a lot of progress was made in bilateral ties during his maiden official visit to the country where America will be doing a lot of business.

Talking to reporters, after his return from India on Wednesday, Trump said, "He (Prime Minister Narendra Modi) is a great gentleman, a great leader. It's an incredible country."

President Trump visited India from February 24 to 25. He was accompanied by first lady Melania Trump, daughter Ivanka Trump, son-in-law Jared Kushner and the top brass of his administration, including national security advisor Robert O'Brien.

They visited Ahmedabad, Agra and New Delhi before leaving for Washington on Tuesday.

During his stay, he addressed a massive rally in Ahmedabad, visited Agra and held official meetings in New Delhi.

The US President was feted at the world's largest cricket stadium in the "Namaste Trump" event in Ahmedabad and was cheered by tens of thousands of people.

"We were treated very, very well and we really enjoyed it. A lot of tremendous progress was made in terms of relationship - our relationship with India is extraordinary right now," he said.

"We are going to be doing a lot of business with India, they are sending billions and billions of dollars now to the United States," Trump said in response to a question.

In a tweet, his daughter Ivanka said that, Trump announced that US international development finance corporation "will establish a permanent presence in India to strengthen our economic ties, improve development plus further women's economic empowerment through WGDP (Women's Global Development and Prosperity Initiative)!"

On her arrival from India, she thanked PM Modi for "your warm hospitality as we visited your beautiful country and celebrated the strength, spirit and unity of the US and India!"

"Throughout our visit we saw monumental achievements of human creativity and proof of the infinite capacity of the human heart!" she said.

The first lady tweeted two pictures of her with Trump facing the Taj Mahal in Agra.

"One of the Seven Wonders of the World, the breathtaking Taj Mahal!" she said.

President Trump "reaffirmed the strong strategic partnership, vibrant economic ties and expanding security relationship between our two countries. Wonderful trip, but glad to be home! Thank you India!" said White House press secretary Stephanie Grisham.

During the visit, India and the US on Tuesday finalised defence deals worth $3 billion under which 30 military helicopters will be procured from two American defence majors for Indian armed forces.

The deals will include procurement of 24 MH-60 Romeo helicopters by India from the US at a cost of $2.6 billion. Another contract to acquire six AH-64E Apache helicopters for $800 million from the US is also on the table.

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Agencies
January 6,2020

The Cambridge Analytica scandal is far from over. New explosive details leaked by a whistleblower shows that the extent of the rot is far deeper than previously thought.

An anonymous Twitter account, @HindsightFiles, has started releasing the documents, apparently on behalf of Brittany Kaiser, a former employee of the now defunct British data analytics and consulting company Cambridge Analytica.

"Democracies around the world are being auctioned to the highest bidder. We release the documents that explain how," reads the biography of the @HindsightFiles.

The document will reveal previously unreleased emails, project plans, case studies, negotiations and more spanning over 60 countries.

"Over the past two years I have given evidence to investigators, journalists and academics to analyse what happened at Cambridge Analytica, and how our data was used to influence democracies around the world. In the name of shedding light on these dark practices, I am releasing documents and emails in full for the public good," Kaiser, who worked with Cambridge Analytica from 2014 to 208, was quoted as saying.

"I do this to strengthen the case for data rights and enforcement of our electoral laws online globally. We should all be seeking more ethical digital future for ourselves and our children," added Kaiser who starred in the Oscar-shortlisted Netflix documentary "The Great Hack".

The details released so far includes links to material on the firm's activities in Malaysia, Kenya, Brazil and Iran, an addition to the John Bolton archive.

Over the next months, more than 100,000 documents relating to work in 68 countries are set to be released, according to a report in The Guardian.

More than one and a half year after the Cambridge Analytica scandal first became public, US regulators last month said that the now-defunct British data analytics and consulting company engaged in deceptive practices to harvest personal information from tens of millions of Facebook users for voter profiling and targeting.

According to Kaiser, the Facebook data scandal was part of a much bigger global operation designed to manipulate people in collaboration with governments, intelligence agencies, commercial companies and political campaigns.

The unpublished documents contain material that suggests the firm collaborated with a political party in Ukraine in 2017 even while under investigation as part of Robert Mueller's investigation into Russian interference in the 2016 US presidential election, said The Guardian report.

"There are emails between these major Trump donors discussing ways of obscuring the source of their donations through a series of different financial vehicles. These documents expose the entire dark money machinery behind US politics," Kaiser was quoted as saying.

Similar tactics were deployed in other countries that Cambridge Analytica operated in, including Britain, she claimed.

The files released by Kaiser suggest that Cambridge Analytica offered to help United Malays National Organisation (Umno), the party of Malaysia's Former Prime Minister Najib Razak, to influence the voting of 40 parliamentary constituencies in the 14th General Election (GE14) in 2013.

Umno, according to the leaks, requested the company to prepare a proposal to regain 13 seats, The South China Morning Post reported on Saturday.

In 2018, Razak claimed that he had never engaged Cambridge Analytica in any way.

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