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
April 11,2020

Washington, Apr 11: China is considered a developing country, make the United States too a developing one, US President Donald Trump said on Friday, alleging that Beijing has taken advantage of his country.

"China has been unbelievably taken advantage of us and other countries. You know, for instance, they are considered a developing nation. I said well then make us a developing nation too,” Trump told reporters at his daily White House news conference on coronavirus.

The president was responding to a question on China.

“They get big advantages because they are a developing nation. India, a developing nation. The United States is a big developed nation. Well, we have plenty of development to do,” he said.

Reiterating that United States was taken advantage of by the World Trade Organization, Trump said the Chinese economy started booming after it joined WTO with the help of the US.

“If you look at the history of China, it was only since they went into the WTO that they became a rocket ship with their economy. They were flatlined for years and years,” he said.

“Frankly, for many, many decades. And it was only when they came into the WTO that they became a rocket ship because they took advantage of all -- I'm not even blaming them. I'm saying how stupid were the people that stood here and allowed it to happen,” he said.

For latest updates on coronavirus outbreak, click  here

The Trump Administration will now allow that to happen, he said.

“If they don't treat us fairly, will leave. But now we're starting to win cases,” he said.

Alleging that China has taken advantage of the United States for 30 years, he said, China has taken advantage of the US through WTO and using rules that are unfair to the United States.

"They should have never been allowed it, this should have never been allowed to happen", he added.

“When China joined and was allowed to join under those circumstances the WTO, that was a very bad day for the United States because they have rules and regulations that were far different and far easier than our rules and regulations,” he said.

“Plus. They took advantage of them down to the last. China took advantage of them like few people would even think to take advantage of them and again they are considered right a developing nation,” he added.

The United States, he rued, is not considered a developing nation.

“The were given advantages (for being a developing nation). For many years China has ripped off the United States. Then I came along and right now, as you know, China is paying 25 percent," said Trump, adding that the US is now gaining "billions and billions and billions of dollars in tariffs from China”.

The US is not paying, he asserted.

“Not every country is China but China would devalue their currency and they would also pour out money and they essentially were paying most of those tariffs not us,” he said.

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News Network
January 24,2020

Davos, Jan 24: Pakistan Prime Minister Imran Khan claimed that he met with a “brick wall” when he approached Indian Prime Minister Narendra Modi with a peace proposal, soon after assuming office.

In an interview to Foreign Policy magazine on the sidelines of WEF 2020 here, Khan also said he told Modi that Pakistan will act firmly if it was given evidence of any involvement in the Pulwama terror attack, but India instead “bombed” Pakistan.

Tensions have escalated between the two countries, following India withdrawing the special status of Jammu and Kashmir in August 2019. Even since, Khan has been trying to seek global intervention to de-escalate the tensions between the two countries.

On Thursday, India's External Affairs Ministry spokesperson Raveesh Kumar categorically ruled out any third party role on the Kashmir issue, asserting that any issue between the two countries should be resolved bilaterally.

In the interview, Khan said that he is a firm believer that military means are not a solution to ending conflicts. “After assuming office, I immediately reached out to Prime Minister Modi. I was amazed by the reaction I got, which was quite weird.

The subcontinent hosts the greatest number of poor people in the world, and the best way to fight poverty is to have a trading relationship between the two countries rather than spending money on arms. This is what I said to the Indian Prime Minister. But I was met by brick wall,” Khan said.

Khan took charge as Prime Minister in August 2018. Referring to the suicide attack in Pulwama, Khan said he immediately told Modi ,“if you can give us any actionable intelligence (that Pakistanis were involved), we will act on it. But rather than do so, they bombed us.”

Noting that the both countries are not close to conflict right now, Khan said that it is important that the UN and the US act.

When asked about US President Donald Trump’s close relationship with Modi, Khan said the relationship is understandable because India is a huge market. “My concern is not about the US-India relationship. My concern is the direction in which India is going,” Khan said.

Khan also sought to compare the events in India to what happened in Nazi Germany.

“Between 1930 and 1934, Germany went from a liberal democracy to a fascist, totalitarian, racist state. If you look at what is happening in India under the BJP in the last five years, look where it's heading, you'll see the danger. And you're talking about a huge country of 1.3 billion people that is nuclear-armed,” he said.

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News Network
July 11,2020

Geneva, Jul 11: The World Health Organization said Friday that it is still possible to bring coronavirus outbreaks under control, even though case numbers have more than doubled in the past six weeks.

WHO chief Tedros Adhanom Ghebreyesus said the examples of Italy, Spain, South Korea and India's biggest slum showed that however bad a outbreak was, the virus could still be reined in through aggressive action.

"In the last six weeks cases have more than doubled," Tedros told a virtual press conference in Geneva.

However, "there are many examples from around the world that have shown that even if the outbreak is very intense, it can still be brought back under control," said Tedros.

"And some of these examples are Italy, Spain and South Korea, and even in Dharavi -- a densely packed area in the megacity of Mumbai -- a strong focus on community engagement and the basics of testing, tracing, isolating and treating all those that are sick is key to breaking the chains of transmission and suppressing the virus."

The novel coronavirus has killed at least 555,000 people worldwide since the outbreak emerged in China last December, according to a tally from official sources compiled by AFP on Friday.

Nearly 12.3 million cases have been registered in 196 countries and territories.

"Across all walks of life, we are all being tested to the limit," Tedros said, "from countries where there is exponential growth, to places that are loosening restrictions and now starting to see cases rise.

"Only aggressive action combined with national unity and global solidarity can turn this pandemic around."

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