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
June 11,2020

Jun 11: The total death toll in the US from the novel coronavirus pandemic could hit the grim figure of 200,000 by September and expecting a dramatic decrease in COVID-19 cases in the country will be a "wishful thinking , an eminent Indian-American professor has warned.

Ashish Jha, the head of Harvard's Global Health Institute, told CNN on Wednesday that he is not trying to scare people to stay at home rather urged everyone to wear masks, adhere to the social distancing rules and called for ramping up testing and tracing infrastructure.

Anybody who's expecting a dramatic decrease in cases is almost surely engaging in wishful thinking. And if it (COVID numbers) stays just flat for the next three months, we're going to hit 200,000 deaths sometime in September and that is just awful, Jha said.

Jha said the 200,000 death toll is not just a guess . Currently 800-1000 people are dying daily in America from the virus and all data suggest that the situation is going to get worse.

We're gonna have increases, but even if we assume that it's going to be flat all summer, that nothing is going to get worse... even if we pick that low number of 800 a day, that is 25,000 (deaths) a month in three and a half months. We're going to add another 88,000 people and we will hit 200,000 sometime in September, Jha said.

The United States is by far the hardest-hit country in the global pandemic, in terms of both confirmed infections and deaths.

According to data by the Johns Hopkins University, the number of coronavirus cases in the US currently is nearly two million and about 112,900 people have died in the country, the most in the world.

When asked about an improvement in states like New York, which had been the epicenter of the COVID19 pandemic in the US, Jha said while coronavirus cases are declining in New York, New Jersey, Connecticut and Massachusetts, the numbers are increasing in states such as Arizona, Florida, Texas, North and South Carolina while the country as a whole is pretty flat.

He said, people should take measures as that will help suppress the virus and ensure people could get back outside safely but he voiced concern that this was not the situation in reality.

We're not doing that and so we're going to unfortunately have another 25,000 deaths a month until September, and then it'll keep going. It's not going to magically disappear. We've got a turn around. This is not the future I want, he said.

Jha said he had expected the situation to improve in the summer months but on the contrary the numbers have continued to rise even in the warm weather.

Summer was supposed to be our better months - warmer weather, people outside, a little less transmission. This is not the time (summer) I was expecting a lot more cases. We're seeing a lot more cases, especially in states like Arizona where the numbers look really scary, he said.

Jha added that he was hopeful that maybe the summer months would give us more of a break. I think I may have been too optimistic on that.

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Agencies
May 4,2020

Washington, May 4: Anxious for an economic recovery, President Donald Trump fielded Americans' questions about decisions by some states to allow nonessential businesses to reopen while other states are on virtual lockdown due to the coronavirus.

After more than a month of being cooped up at the White House, Trump returned from a weekend at the Camp David presidential retreat in Maryland and participated in a “virtual” town hall, hosted Sunday night by Fox News Channel, from inside the Lincoln Memorial.

He pushed for an economic reopening, one his advisers believe will be essential for his reelection chances this November.

“We have to get it back open safely but as quickly as possible," Trump said.

The president acknowledged fear on both sides of the issue, some Americans worried about getting sick while others are concerned about losing jobs.

Though the administration's handling of the pandemic, particularly its ability to conduct widespread testing, has come under fierce scrutiny, the president defended the response and said the nation was ready to begin reopening.

“I'll tell you one thing. We did the right thing and I really believe we saved a million and a half lives,” the president said.

But he also broke with the assessment of his senior adviser and son-in-law, Jared Kushner, saying it was “too soon to say" if the federal government was overseeing a “success story."

Trump's impatience also flashed. While noting that states would go at their own pace in returning to normal, with ones harder hit by the coronavirus going slower, he said that “some states frankly I think aren't going fast enough" and singled out Virginia, which has a Democratic governor and legislature.

And he urged the nation's schools and universities to return to classes this fall.

But many public health experts believe that cannot be done safely until a vaccine is developed.

Trump declared Sunday that he believed one could be available by year's end although his own pandemic task force has predicated it could be another 18 months.

Federal guidelines that encouraged people to stay at home and practice social distancing expired late last week.

Debate continued over moves by governors to start reopening state economies that tanked after shopping malls, salons and other nonessential businesses were ordered closed in attempt to slow a virus that has killed more than 66,000 Americans, according to a tally of reported deaths by Johns Hopkins University.

The U.S. economy has suffered, shrinking at a 4.8 per cent annual rate from January through March, the government estimated last week. It was the sharpest quarterly drop since the 2008 financial crisis.

Roughly 30.3 million people have filed for unemployment aid in the six weeks since the outbreak forced employers to shut down and slash their workforces. It was the worst string of layoffs on record.

Larry Kudlow, Trump's top economic adviser, on Sunday predicted a “spectacular 2021” — with “the right set of policies” — on top of a rebound from July through December of this year.

He said on CNN's "State of the Union" that the administration would "pause” to review the effectiveness of trillions in economic relief spending before making any decision on whether additional aid is needed.

House Speaker Nancy Pelosi, D-Calif., said Thursday that state and local governments are seeking up to USD 1 trillion for coronavirus costs, The Senate planned to reopen Monday, despite the Washington area's continued status as a virus hot spot and with the region still under stay-at-home orders.

The House remains shuttered. The pandemic is forcing big changes at the tradition-bound Supreme Court: The justices will hear arguments, beginning Monday, by telephone for the first time since Alexander Graham Bell patented his invention in 1876.

Congressional Republicans are resisting calls by Democrats for emergency spending for states and local governments whose revenue streams all but dried up in recent weeks.

The GOP is counting on the country's reopening and the rebound promised by Trump as their best hope to forestall another big round of virus aid.

The leaders of California and Michigan are among governors under public pressure over lockdowns still in effect while states such as Florida, Georgia and Ohio are reopening.

Michigan Governor Gretchen Whitmer, a Democrat, said Sunday that the armed protesters who demonstrated inside her state's Capitol “depicted some of the worst racism” and “awful parts” of US history by showing up with Confederate flags, nooses and swastikas.

Trump had tweeted “LIBERATE” and named Michigan and other states in mid-April. In a new tweet Friday, he urged Whitmer to “make a deal” with the protesters. “These are very good people, but they are angry.

They want their lives back again, safely!” Trump said.

Despite the opposition of Michigan's Republican-controlled Legislature, Whitmer has extended a state of emergency declaration and directed most businesses statewide to remain closed.

Some people participating in other public protests across the US have not kept their distance from one another and have rallied without masks, not heeding public health recommendations.

Deborah Birx, coordinator of the White House coronavirus task force, called that behavior “devastatingly worrisome.”

She said people will feel guilty for the rest of their lives if they end up infected and unwittingly spread the virus to vulnerable family members.

“We need to protect each other at the same time we're voice our discontent,” she told CNN's “State of the Union.”

An overwhelming majority of Americans support stay-at-home orders and other efforts to slow the virus' spread, according to a recent survey from The Associated Press-NORC Center for Public Affairs Research.

Asked about states that are reopening before they meet benchmarks laid out in federal guidelines she helped write, Birx said the guidelines “are a pretty firm policy of what we think is important from a public health standpoint.”

She added that she and others have made it clear that people must continue practising social distancing, “scrupulous” hand washing and other measures to protect themselves and others.

Fox News Channel said it asked viewers to submit questions about reopening the country on the network's Twitter, Facebook and Instagram accounts for a chance to appear on the rare broadcast from the Lincoln Memorial. Trump spoke from the memorial's steps last July Fourth.

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News Network
January 8,2020

Sydney, Jan 8:  Authorities in Australia will begin five-day campaign to kill thousands of camels in the country as they drink too much water amid the wildfires.  The government will send helicopters to kill up to 10,000 camels in a five-day campaign starting Wednesday, The Hill reported citing The Australian.

Marita Baker, an Anangu Pitjantjatjara Yankunytjatjara (APY) (large, sparsely-populated local government area for Aboriginal Australians) executive board member, said that the camels were causing problems in her community of Kanypi.

"We have been stuck in stinking hot and uncomfortable conditions, feeling unwell, because the camels are coming in and knocking down fences, getting in around the houses and trying to get to water through air conditioners,'' she said.

The planned killing of the camels comes at a time the country is ravaged by wildfires since November. The disaster has killed more than a dozen people and caused the displacement or deaths of 480 million animals, according to University of Sydney researchers.

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