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.
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.
News Network
June 8,2020

Hundreds of thousands of people across the world are joining the anti-racism demonstrations days after the killing of George Floyd in United Sates. 

The protests are being held in cities including London, Manchester, Cardiff, Leicester and Sheffield.

Demonstrators attached ropes to the statue of Edward Colston before pulling it down to cheers and roars of approval from the crowd. Images on social media show the statue was eventually rolled into the city's harbour. 

It was not the only statue targeted on Sunday. In Brussels, protesters clambered onto the statue of former King Leopold II and chanted "reparations".

The word "shame" was also graffitied on the monument, reference perhaps to the fact that Leopold is said to have reigned over the mass death of 10 million Congolese.

In London, thousands of people congregated around the US embassy for the second day running.

While protests were mainly peaceful, there were some scuffles near the office of Prime Minister Boris Johnson and outside the Parliament gates.

In Hong Kong, about 20 people staged a rally in solidarity with the Black Lives Matter movement on Sunday outside the US consulate in the semi-autonomous Chinese city.

"It's a global issue," Quinland Anderson, a 28-year-old British citizen living in Hong Kong, told The Associated Press news agency.

"We have to remind ourselves despite all we see going on in the US and in the other parts of the world, Black lives do indeed matter."

Several dozen demonstrators took part in a Black Lives Matter protest held in Tel Aviv's central Rabin Square.

A rally in Rome's sprawling People's Square was noisy but peaceful, with the majority of protesters wearing masks to protect against coronavirus. Participants listened to speeches and held up handmade placards saying "Black Lives Matter" and "It's a White Problem".

In Spain, several thousand people gathered on the streets of Barcelona and at the US embassy in Madrid.

Many in Madrid carried homemade signs reading "Black Lives Matter", "Human rights for all" and "Silence is pro-racist".

"We are not only doing this for our brother George Floyd," said Thimbo Samb, a spokesman for the group that organised the events in Spain mainly through social media. "Here in Europe, in Spain, where we live, we work, we sleep and pay taxes, we also suffer racism."

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
July 24,2020

The total number of global coronavirus cases has topped 15.4 million, while the deaths have increased to over 631,000, according to the Johns Hopkins University.

As of Friday morning, the total number of cases stood at 15,439,456, while the fatalities rose to 631,926, the University's Center for Systems Science and Engineering (CSSE) revealed in its latest update.

The US accounted for the world's highest number of infections and fatalities at 4,034,831 and 144,242, respectively, according to the CSSE.

Brazil came in the second place with 2,287,475 infections and 84,082 deaths.

In terms of cases, India ranks third (1,238,798), and is followed by Russia (793,720), South Africa (408,052), Peru (371,096), Mexico (370,712), Chile (334,683), the UK (298,721), Iran (284,034), Spain (270,166), Pakistan (269,191), Saudi Arabia (260,394), Italy (245,338), Turkey (223,315), Colombia (218,428), France (216,667), Bangladesh (216,110), Germany (204,881), Argentina (148,027), Canada (114,398), Qatar (108,244) and Iraq (102,226), the CSSE figures showed.

The other countries with over 10,000 deaths are the UK (45,639), Mexico (41,908), Italy (35,092), France (30,185), India (29,861), Spain (28,429), Iran (15,074), Peru (17,654) and Russia (12,873).

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.