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.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
March 25,2020

Moscow, Mar 25: An earthquake measuring 7.5 on the Richter scale struck off Russia's Kuril Islands on Wednesday, the United States Geological Survey (USGS) said.

The magnitude of the quake, which occurred at 2:49 am (UTC), was registered at a depth of 56.7 kilometres, about 219 kilometres southeast of the Russian town of Severo-Kuril'sk, the USGS said.

There were no immediate reports of casualties or damage to the property as a result of the quake.
Further details are awaited.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
June 2,2020

Washington, Jun 2: US President Donald Trump said that peaceful protests following the death of African-American man George Floyd in police custody were derailed by acts of domestic terrorism.

"These are not acts of peaceful protests, these are acts of domestic terror - the destruction of innocent life, and the spilling of innocent blood is an offence to humanity and a crime against God," Trump said during a press briefing on Monday.

Trump also added that the chaos is the work of professional agitators and provocateurs - anarchists and the far-left movement Antifa, among others - and put them on notice, vowing to enforce law and order.

He further said, "Those who threaten innocent life and property will be arrested, detained and prosecuted to the fullest extent of the law. I want the organizers of this terror to be on notice that you will face severe criminal penalties and lengthy sentences in jail. This includes Antifa and others who are leading instigators."

The US president also that he is invoking an 1807 law to mobilize the military around the country to "quickly solve the problem."

"I am also taking swift and decisive action to protect our capital Washington DC. As we speak, I am dispatching thousands and thousands of heavily armed soldier, military personnel and enforcement officers to stop the rioting," Trump said during a press briefing.

"I am mobilizing all available federal resources, civilian and military, to stop the rioting and looting, to end the destruction and arson. And to protect the rights of law-abiding Americans, including your Second Amendment rights," he added.

Trump said mayors and governors must establish an "overwhelming law enforcement presence until the violence has been quelled." If the city or state refuses to take the actions, Trump said he would deploy the US military.

Trump on Monday also said that all Americans are rightly 'sickened by the brutal death' of George Floyd and his administration is fully committed to providing justice to George and his family.

"All Americans were rightly sickened and revolted by the brutal death of George Floyd. My administration is fully committed, the justice will be fully served for George and his family and He will not have died in vain," Trump said.

"My first and highest duty as president is to defend and protect the great country and the American people. I have sworn an oath to uphold the laws of our nation and that is exactly what I will do," he added.

After the media address, Trump made a surprise visit to the damaged St Johns church near White House, walking through park violently cleared of protesters. He walked to the church across the street from the White House after tear gas was fired at protesters in the area.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
February 12,2020

Saint Martin's Island, Feb 12: At least 15 women and children drowned and more than 50 others were missing after a boat overloaded with Rohingya refugees sank off southern Bangladesh as it tried to reach Malaysia Tuesday, officials said.

Some 138 people -- mainly women and children -- were packed on a trawler barely 13 metres (40 feet) long, trying to cross the Bay of Bengal, a coast guard spokesman told news agency.

"It sank because of overloading. The boat was meant to carry maximum 50 people. The boat was also loaded with some cargo," another coast guard spokesman, Hamidul Islam, added.

Nearly one million Rohingya live in squalid camps near Bangladesh's border with Myanmar, many fleeing the neighbouring country after a 2017 brutal military crackdown.

With few opportunities for jobs and education in the camps, thousands have tried to reach other countries like Malaysia and Thailand by attempting the hazardous 2,000-kilometre journey.

In the latest incident, 71 people have been rescued including 46 women. Among the dead, 11 were women and the rest children.

Anwara Begum said two of her sons, aged six and seven, drowned in the tragedy.

"We were four of us in the boat... Another child (son, aged 10) is very sick," the 40-year-old told news agency.

Fishermen tipped off the coast guard after they saw survivors swimming and crying for help in the sea.

The boat's keel hit undersea coral in shallow water off Saint Martin's Island, Bangladesh's southernmost territory, before it sank, survivors said.

"We swam in the sea before boats came and rescued us," said survivor Mohammad Hossain, 20.

Coast guard commander Sohel Rana said three survivors, including a Bangladeshi, were detained over human trafficking allegations.

An estimated 25,000 Rohingya left Bangladesh and Myanmar on boats in 2015 trying to get to Thailand, Malaysia and Indonesia. Hundreds drowned when overloaded boats sank.

Begum said her family paid a Bangladeshi trafficker $450 per head to be taken to Malaysia.

"We're first taken to a hill where we stayed for five days. Then they used three small trawlers to take us to a large trawler, which sank," she said.

Shakirul Islam, a migration expert whose group works with Rohingya to raise awareness against trafficking, said desperation in the camps was making refugees want to leave.

"It was a tragedy waiting to happen," he said.

"They just want to get out, and fall victim to traffickers who are very active in the camps."

Islam said in the past two months dozens of Rohingya reported approaches from traffickers to his OKUP migration rights group.

"Human smuggling and trafficking in the Bay of Bengal is particularly difficult to address as it requires concerted effort from multiple states," the Bangladesh head of UN agency the International Organization for Migration, Giorgi Gigauri, told news agency.

"The gaps in coordination are easily exploited by criminal networks."

Since last year, Bangladeshi authorities have picked up over 500 Rohingya from rickety fishing trawlers or coastal villages as they waited to board boats.

Trafficking often increases during the November-March period when the sea is safest for the small trawlers used by traffickers.

Bangladesh and Myanmar signed a repatriation deal to send back some Rohingya to their homeland, but none have agreed to return because of safety fears.

The charity Save the Children called on Myanmar to "take all necessary steps to ensure the Rohingya community can return to their homes in a safe and dignified manner".

"The tragic drowning of women and children... should be a wake-up call for us all," the group's Athena Rayburn said in a statement.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.