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 18,2020

Amsterdam, Jun 18: A statue of Mahatma Gandhi has been vandalised here in the capital of Netherlands by unknown miscreants with graffiti and spray painting, amid a wave of attacks on controversial figures following the protests around the world after the custodial killing of African-American George Floyd, according to media reports.

The statue of Gandhi on the Churchilllaan in Amsterdam was covered with red paint and the pedestal has 'racist' and an abbreviation for an expletive against the police chalked on it, Metro, the Dutch newspaper, reported.

According to alderman Rutger Groot Wassink, the municipality will file a declaration for daubing.

"Obviously, we are opposed to any form of vandalism and daubing of these things is completely unacceptable," the city official was quoted as saying by the AD.nl.

"It is logical that we will file a declaration, the image will be cleaned," Wassink said.

It is not yet known who is behind the daubing. An employee of the Kunstwacht, who provides maintenance and repairs, says that the cleaning work can take hours.

A 75-year-old man saw the daubs on Wednesday and called the municipality. “I have lived here for forty years and I have never experienced this. I have been watching the statue for years," the man said.

Since the death of 46-year-old Floyd on May 25 in Minneapolis, US, and subsequent worldwide Black Lives Matter protests, there has been much debate about street names and statues of people with a colonial past. All over the world, statues of controversial historical figures are brought down or defaced.

Recently, images and buildings have been defaced in various places that refer to the colonial past of the Netherlands, including the Tropenmuseum in Amsterdam and the statue of Piet Hein in Rotterdam. These are anti-racist expressions that follow the death of Floyd through a white police officer, Metro reported.

Gandhi was known as a champion of human rights and non-violence. But in his twenties, which he spent in South Africa, he still called black people “troublesome, very dirty and they live like beasts” and found that the white people were the “dominant race”. Later he renounced those ideas, the report added.

The statue was unveiled on the Churchillaan on October 2, 1990 in honour of Gandhi's 121st birthday.

The design was made by the sculptor Karel Gomes, who died in 2016. At the time, the plan for the statue came from the Hindu organisation Triveda.

Gandhi is depicted walking, featuring robes around the body, slippers on the feet, a book in one hand and a stick in the other.

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News Network
February 1,2020

Washington, Feb 1: The Indian economy experienced some abrupt slowdown in 2019 due to turbulence in non-banking financial institutions and major reform measures such as GST and demonetisation, but it is not in a recession, IMF Managing Director Kristalina Georgieva has said.

"The Indian economy indeed has experienced an abrupt slowdown in 2019. We had to revise our growth projections, downwards to four percent for last year. We are expecting 5.8 per cent (growth rate) in 2020 and then an upward trajectory to 6.5 percent in 2021," Georgieva told a group of foreign journalists here on Friday.

"It appears that the main reason for this slowdown was the non-banking financial institutions experiencing a turbulence," she said on the eve of Union Finance Minister Nirmala Sitharaman presenting the annual budget in Parliament on Saturday.

She said India had undertaken some important reforms that over the longer term would be beneficial for the country, but they do have some short-term impact.

"For example, coming with the unified tax system, and the demonetisation that took place. These are steps that over time are beneficial, but of course they might, might be somewhat disruptive over short term," Georgieva said in response to a question.

The International Monetary Fund (IMF) Managing Director said that there is not a lot of fiscal space in India. “But we also recognise that the policies of the government on that side, on the fiscal side have been prudent. We will see how the reading of the budget, the submission of the budget goes, tomorrow,” she said.

In the medium-term, she said, the IMF remains optimistic about India. “This is why we see that upswing potential for the growth in the country,” she said.

Georgieva said that the current economic slowdown cannot be described as a recession. "No.... You're far from that. But it is a significant slowdown, not the recession," she said.

The IMF managing Director noted that the consumption in India also slowed down and that contributed to the overall slowdown in the economy. The IMF would be keen to see what India does to get relatively sound macroeconomic fundamentals to pay off in terms of better growth trajectory, she said ahead of the budget.

One thing that is important for India is that budgetary revenue have been below target. "The country knows that. The finance minister knows it. They need to increase budgetary revenue collection so they can improve their fiscal position. I said it's tight on the spending side, but I also want to stress that there is room to improve collection on the revenue side," she said.

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News Network
March 6,2020

New York, Mar 6: A 23-year-old Indian with a student visa in the US has pleaded guilty to sexual enticement of a minor girl, prosecutors have said.

Sachin Aji Bhaskar faces a maximum penalty of life in prison.

He pleaded guilty before Senior US District Judge William M Skretny to sexual enticement of a minor.

The charge carries a minimum penalty of 10 years in prison, a maximum penalty of life in prison, a fine of USD 250,000 or both, US Attorney James P Kennedy said.

Prosecutors alleged that Bhaskar communicated by text and email with an 11-year-old girl for the purpose of engaging in sexual activity.

Through those communications, Bhaskar enticed the victim to engage in a sexual activity with him in August, 2018, they said.

The sentencing in the case is scheduled for June 17.

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