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
May 1,2020

Washington, May 1: The United States on Thursday recorded 29,625 new coronavirus cases, and 2,035 deaths in the last 24 hours, according to Johns Hopkins University.

The total number of coronavirus cases has reached 1,069,534 and the death toll stands at 63,001, CNN reported.

The novel coronavirus has infected more than 3.2 million people and killed at least 233,000 globally, according to Johns Hopkins University.

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Agencies
July 2,2020

Moscow, Jul 2: Russian voters approved changes to the constitution that will allow President Vladimir Putin to hold power until 2036, but the weeklong plebiscite that concluded Wednesday was tarnished by widespread reports of pressure on voters and other irregularities.

With most of the nation's polls closed and 20% of precincts counted, 72% voted for the constitutional amendments, according to election officials.

For the first time in Russia, polls were kept open for a week to bolster turnout without increasing crowds casting ballots amid the coronavirus pandemic a provision that Kremlin critics denounced as an extra tool to manipulate the outcome.

A massive propaganda campaign and the opposition's failure to mount a coordinated challenge helped Putin get the result he wanted, but the plebiscite could end up eroding his position because of the unconventional methods used to boost participation and the dubious legal basis for the balloting.

By the time polls closed in Moscow and most other parts of Western Russia, the overall turnout was at 65%, according to election officials. In some regions, almost 90% of eligible voters cast ballots.

On Russia's easternmost Chukchi Peninsula, nine hours ahead of Moscow, officials quickly announced full preliminary results showing 80% of voters supported the amendments, and in other parts of the Far East, they said over 70% of voters backed the changes.

Kremlin critics and independent election observers questioned the turnout figures.

We look at neighboring regions, and anomalies are obvious there are regions where the turnout is artificially (boosted), there are regions where it is more or less real, Grigory Melkonyants, co-chair of the independent election monitoring group Golos, told The Associated Press.

Putin voted at a Moscow polling station, dutifully showing his passport to the election worker. His face was uncovered, unlike most of the other voters who were offered free masks at the entrance.

The vote completes a convoluted saga that began in January, when Putin first proposed the constitutional changes.

He offered to broaden the powers of parliament and redistribute authority among the branches of government, stoking speculation he might seek to become parliamentary speaker or chairman of the State Council when his presidential term ends in 2024.

His intentions became clear only hours before a vote in parliament, when legislator Valentina Tereshkova, a Soviet-era cosmonaut who was the first woman in space in 1963, proposed letting him run two more times.

The amendments, which also emphasize the primacy of Russian law over international norms, outlaw same-sex marriages and mention a belief in God as a core value, were quickly passed by the Kremlin-controlled legislature.

Putin, who has been in power for more than two decades longer than any other Kremlin leader since Soviet dictator Josef Stalin said he would decide later whether to run again in 2024.

He argued that resetting the term count was necessary to keep his lieutenants focused on their work instead of darting their eyes in search for possible successors.

Analyst Gleb Pavlovsky, a former Kremlin political consultant, said Putin's push to hold the vote despite the fact that Russia has thousands of new coronavirus infections each day reflected his potential vulnerabilities.

Putin lacks confidence in his inner circle and he's worried about the future, Pavlovsky said.

He wants an irrefutable proof of public support.

Even though the parliament's approval was enough to make it law, the 67-year-old Russian president put his constitutional plan to voters to showcase his broad support and add a democratic veneer to the changes.

But then the coronavirus pandemic engulfed Russia, forcing him to postpone the April 22 plebiscite.

The delay made Putin's campaign blitz lose momentum and left his constitutional reform plan hanging as the damage from the virus mounted and public discontent grew.

Plummeting incomes and rising unemployment during the outbreak have dented his approval ratings, which sank to 59%, the lowest level since he came to power, according to the Levada Center, Russia's top independent pollster.

Moscow-based political analyst Ekaterina Schulmann said the Kremlin had faced a difficult dilemma: Holding the vote sooner would have brought accusations of jeopardizing public health for political ends, while delaying it raised the risks of defeat.

Holding it in the autumn would have been too risky, she said.

In Moscow, several activists briefly lay on Red Square, forming the number 2036 with their bodies in protest before police stopped them.

Some others in Moscow and St. Petersburg staged one-person pickets and police didn't intervene.

Several hundred opposition supporters rallied in central Moscow to protest the changes, defying a ban on public gatherings imposed for the coronavirus outbreak. Police didn't intervene and even handed masks to the participants.

Authorities mounted a sweeping effort to persuade teachers, doctors, workers at public sector enterprises and others who are paid by the state to cast ballots. Reports surfaced from across the vast country of managers coercing people to vote.

The Kremlin has used other tactics to boost turnout and support for the amendments.

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News Network
June 25,2020

London, Jun 25: British Prime Minister Boris Johnson has called on India and China to engage in dialogue to sort out their border issues as he described the escalation in eastern Ladakh as "a very serious and worrying situation" which the UK is closely monitoring.

The first official statement of Mr Johnson came during his weekly Prime Minister's Questions (PMQs) in the House of Commons on Wednesday.

Responding to Conservative Party MP Flick Drummond on the implications for British interests of a dispute between a "Commonwealth member and the world's largest democracy on the one side, and a state that challenges our notion of democracy on the other," he described the escalation in eastern Ladakh as "a very serious and worrying situation", which the UK is "monitoring closely".

"Perhaps the best thing I can say... is that we are encouraging both parties to engage in dialogue on the issues on the border and sort it out between them," the Prime Minister said.

In a statement in New Delhi on Wednesday, the Ministry of External Affairs (MEA) said India and China have agreed that expeditious implementation of the previously agreed understanding on disengagement of troops from standoff points in eastern Ladakh would help ensure peace and tranquillity in the border areas.

During the diplomatic talks between India and China, the situation in the region was discussed in detail and the Indian side conveyed its concerns over the violent face-off in Galwan Valley on June 15. Twenty Indian Army personnel were killed in the clash. There were reports of several casualties for the Chinese army too, but China hasn't declared any official number yet.

The talks were held in the midst of escalating tension between the two countries following the violent clashes in Galwan Valley on June 15.

The Indian and Chinese armies are engaged in the standoff in Pangong Tso, Galwan Valley, Demchok and Daulat Beg Oldie in eastern Ladakh. A sizable number of Chinese Army personnel even transgressed into the Indian side of the Line of Actual Control in several areas including Pangong Tso.

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