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 9,2020

Beijing, Feb 9: After making sure everyone's face mask is on and sanitizer is to hand, the Qiao family heads out to Jingshan Park, a former royal sanctuary beside the Forbidden City in China's capital Beijing.

Snow has fallen for a second day, a rare event in the city of 21.5 million that would normally bring hundreds of thousands of people out to take photos and play. But the streets are empty and the parks are so quiet the only sound is of birds chirping.

It's not just Beijing. Shanghai, China's financial hub, and other cities in the world's most populous nation have turned into ghost towns after the government extended a holiday and asked residents not to go out because of the coronavirus.

"We know the situation of the coronavirus is severe. But the epicentre is far away, so we think it should be fine here ... It's a God-given chance to enjoy this family moment with snow and without work," said Mr Qiao, who has an 11-year-old daughter.

The epidemic has killed 722 people and infected nearly 32,000 in China as of February 8. More than three-quarters of the cases are in the central Hubei province where the virus originated - more than 1,000 km (620 miles) from Beijing.

Only a few people are brave enough to come out. A security guard at Jingshan Park said there were less than a third of the number of tourists than usual, even with the rare snowfall.

Even at one of the best spots for snapping photos of snowy Beijing just outside the Forbidden City, there's barely a crowd, while the usual tour buses and groups of people speaking different dialects are nowhere to be seen.

"Last year when it snowed, I took a few hours off work to come down here to take a picture and the crowd was several layers deep," said a man in his 30s who gave his surname as Yang. "But this year, I am not at all worried about finding a space to take a photo. The virus is keeping people indoors."

Security guards along Wangfujing street, a popular pedestrianised shopping area in downtown Beijing, said it was normally so crowded during the holiday period that it was hard to move around.

"Look at it now, there are more security guards and street cleaners than tourists!" said one of the guards.

Businesses, including shops, bars and restaurants, have been severely hit by the epidemic as the government has banned mass gatherings and even group meals in an effort to curb the spread of the coronavirus.

"You would have to wait outside for a table on a normal day," said a waitress at a restaurant with more than 50 tables. Just five were taken at the peak lunch hour.

Only a handful of the more than 100 restaurants along Beijing's famous food street, Guijie, were open, and the remaining outlets were wondering how long they can hold out.

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 24,2020

Jun 24: The coronavirus tally in Pakistan reached 188,926 with the detection of 3,892 new cases in the last 24 hours, the health ministry said on Wednesday.

Sixty more people died due to the viral infection, taking the death toll to 3,755.

As many as 3,337 patients are in critical condition across the country, the ministry said.

With the detection of 3,892 new cases in the last 24 hours, the coronavirus tally in the country now stands at 188,926, it said.

Sindh reported the maximum number of 72,656 cases, followed by 69,536 in Punjab, 23,388 in Khyber-Pakhtunkhwa, 11,483 in Islamabad, 9,634 in Balochistan, 1,337 in Gilgit-Baltistan and 892 in Pakistan-occupied Kashmir (Pok).

Health authorities have so far conducted 1,150,141 coronavirus tests, including 23,380 in the last 24 hours.

A total of 77,754 patients have recovered so far from the disease.

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
July 20,2020

Islamabad, Jul 20: Six advisors of Pakistan Prime Minister Imran Khan posses dual citizenships and several of top 20 aides have admitted of owning movable and immovable assets worth millions of dollars abroad.

The list was published on the official website of Pakistan government's cabinet division.
All the dual nationals were working as special assistants to the prime minister (SAPM). 

These people include SAPM on Overseas Pakistanis Syed Zulfiqar Abbas Bukhari (UK), SAPM on Power Division Shahzad Qasim (US), SAPM on Petroleum Nadeem Babar (US), SAPM on Political Affairs Shahbaz Gill (US), SAPM on Parliamentary Coordination Nadeem Afzal Gondal (Canada) and SAPM on Digital Pakistan Tania Aidrus (Canadian citizenship by birth).

According to Gulf News report, the wealthiest SAPM is Power Division and Mineral Resources Assistant Shahzad Syed Qasim who has assets worth over Rs 4 billion followed by SAPM on Petroleum Nadeem Babar with assets worth Rs 2.75 billion. Meanwhile, Adviser for Overseas Pakistanis Syed Zulfiqar Abbas Bukhari's net assets is estimated over Rs 2 billion.

Giving further details of the wealthiest SAPM, the official website stated that the PM's aide on Power Division and Coordination of Marketing and Development of Mineral Resources owns assets in Pakistan, UAE and US. His three properties in UAE include two villas in Jumeirah Golf Estates and Sienna Lakes, Jumeirah Golf Estates and an apartment at Park Towers, DIFC - all worth Dh20,688,000. He has three cars in the UAE worth Dh400,000 and in the US, he has property worth US$865,000 while he has Rs 4 billion in various local and foreign bank accounts and retirement funds including $2.1 million in US.

Meanwhile, Nadeem Babbar, who is Special Assistant on Petroleum Division, owns assets worth over Rs 2.7 billion, including several properties in Pakistan and abroad and stakes in more than 30 local and foreign companies.

The Gulf News further reported that in the list Dr Moeed Yusuf's, Special Assistant to the Prime Minister on National Security Division and Strategic Policy Planning, the name was also included but was later withdrawn as it was clarified that he had the US residency and only holds the citizenship of Pakistan as per the affidavit submitted to the government. "I have not returned to the US since I took up my current responsibility, have no employment or income in the US nor do I have any millions worth properties abroad" Dr Yusuf was quoted as saying.

The latest list on PM Imran Khan's advisors possessing dual nationalities has sparked strong criticisms by the Opposition leaders.

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.