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
February 19,2020

Washington, Feb 19: Sri Srinivasan, a prominent Indian-American judge, has created history by becoming the first person of South Asian descent to lead a powerful federal circuit court considered next only to the US Supreme Court.

Srinivasan, 52, became the Chief Judge of the United States Court of Appeals for the DC Circuit.

An Obama appointee who has already been considered for a Supreme Court seat twice, donned the mantle of the chief judge of the DC federal court circuit on February 12.

Srinivasan succeeded Judge Merrick Garland, who has been a member of the DC Circuit since 1997 and Chief Judge since 2013. He will remain on the bench, a press release said.

Notably, Garland's nomination to the Supreme Court by the then president Barack Obama was blocked by Senate Republicans in 2016.

Srinivasan, was appointed to the US Court of Appeals for the District of Columbia Circuit in May 2013.

He was the first ever Indian-American to be appointed to the second most powerful court of the US.

Neomi Rao, nominated by President Donald Trump, is the second Indian American on this powerful judiciary bench.

History being made on the DC Court of Appeals. Congratulations, Judge Srinivasan! Senator Mark Warner said.

Congratulations to Judge Sri Srinivasan on becoming the Chief Judge of the U.S. Court of Appeals for the D.C. Circuit! A milestone for the Indian-American/Kansan community (and yet another piece of evidence my family can use that I'm underachieving), US Federal Communications Commission Chair Ajit Pai said.

According to The Washington Post, Srinivasan spoke recently about his path to the bench at an event celebrating women in the law, a field where men still dominate leadership positions.

"Everybody doubts their belonging and worthiness in some measure. I definitely did and still do. This is just going to be a part of the thing when you're looking out in the world in which everyone isn't like you. It's natural to doubt whether you belong and whether you're worthy, he said, "but you do belong and you are worthy.

Born in Chandigarh, and raised in Lawrence, Kansas, he received a B.A. from Stanford University, a J.D. from Stanford Law School, and an M.B.A. from the Stanford Graduate School of Business.

Following graduation, he served as a law clerk to Judge J. Harvie Wilkinson III of the US Court of Appeals for the Fourth Circuit, as a Bristow Fellow in the Office of the US Solicitor General, and as a law clerk to US Supreme Court Justice Sandra Day O'Connor.

From 2011 until his appointment to the US Court of Appeals, Judge Srinivasan served as the Principal Deputy Solicitor General of the United States.

He has argued 25 cases before the US Supreme Court. He has also taught appellate advocacy at Harvard Law School as well as a seminar on civil rights statutes and the Supreme Court at Georgetown University Law Center.

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News Network
February 27,2020

Dubai, Feb 27: Twenty two people have died so far from the new coronavirus in Iran, the official Iranian news agency IRNA reported in a chart it published on Thursday.

The number of people diagnosed with the disease is 141, the chart showed. It did not specify whether those who have died were included in the tally of those infected.

Iranian officials on Wednesday reported a total of 139 cases of coronavirus and 19 deaths.

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News Network
May 12,2020

London, May 12: British Prime Minister Boris Johnson has warned that a mass vaccine for the novel coronavirus may be over a year away and, in the worst-case scenario, may in fact never be found.

In his foreword to the government’s new 50-page guidance on a step by step easing of the lockdown measures in place to control the spread of the deadly virus, the UK prime minister lays out plans for businesses to gradually start reopening with “COVID-19 Secure” measures of social distancing and for the public to use “good solid British common sense” as the economy is unlocked.

“A mass vaccine or treatment may be more than a year away,” said Johnson, highlighting the work being done in the UK by scientists at Oxford University and Imperial College London towards this mission.

“Indeed, in a worst-case scenario, we may never find a vaccine. So our plan must countenance a situation where we are in this, together, for the long haul, even while doing all we can to avoid that outcome,” he said.

Admitting that a vaccine or drug-based treatment is the only “feasible long-term solution”, he said the UK has accelerated this with “promising” vaccine development programmes and a collaboration between Oxford University and pharma major AstraZeneca was a vital step that could help rapidly advance the manufacture of a Covid-19 vaccine when it is ready.

As part of global efforts, he flagged the GBP 388 million in aid funding for research into vaccines, tests and treatment, including GBP 250m to the Coalition for Epidemic Preparedness Innovations.

“But while we hope for a breakthrough, hope is not a plan,” he said, as he unveiled his plan for starting to lift lockdown restrictions from this week in phases.

Following a televised address to the nation on Sunday night and a statement in Parliament on Monday, the guidance comes into effect in public life across England from Wednesday when people will be allowed one-to-one contact with people other than those they live with, as long as they remain outside and two metres apart.

They are allowed to play sport with a friend or family member from outside their household or socialise with them in the open air for the first time in more than six weeks since the lockdown was imposed.

People are still advised to work from home where possible but start heading into work where necessary, in sectors such as construction and manufacturing, keeping the social distancing norms in place.

Under the step by step plan, by the start of next month non-essential shops will also reopen, with some hairdressers, pubs and cinemas to follow from July. However, as part of a Covid-19 Alert System, if infection rates are seen to be rising again, restrictions would be tightened “possibly at short notice”.

Fines for breaching the new rules will also be increased to GBP 100 and will double for each repeat offence, up to a maximum of GBP 3,200.

Johnson said: "I must ask the country to be patient with a continued disruption to our normal way of life, but to be relentless in pursuing our mission to build the systems we need. The worst possible outcome would be a return to the virus being out of control – with the cost to human life, and – through the inevitable re-imposition of severe restrictions – the cost to the economy. We must stay alert, control the virus, and in doing so, save lives.

“Then, as vaccines and treatment become available, we will move to another new phase, where we will learn to live with Covid-19 for the longer term without it dominating our lives.”

The devolved administrations of Scotland and Wales are putting their own measures in place and keeping the “stay at home” message in place, rather than switch to the new “stay alert” message.

The UK government’s latest messaging has come under attack from the Opposition and other sections of society over a feared lack of clarity for the general public.

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