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
July 7,2020

Washington DC, Jul 7: With US President Donald Trump promoting re-opening the economy, the country has now four epicentres of coronavirus instead of one -- Los Angeles, cities in Texas, cities in Florida and Arizona. This has led to the governors fearing that their hospitals could be overrun with patients.

"We are right back where we were at the peak of the epidemic during the New York outbreak...The difference now is that we really had one epicentre of spread when New York was going through its hardship. Now, we really have four major epicentres of spread -- Los Angeles, cities in Texas, cities in Florida and Arizona. Florida looks to be in the worst shape," Scott Gottlieb, former Food and Drug Administration commissioner was quoted by The Washington Post as saying in an interview.

As per the latest data, Florida, New York and California have crossed the 200,000 mark of coronavirus cases.

After Texas continued to break its own record of registering the highest number of coronavirus cases, Austin Mayor Steve Adler (D) was quoted as saying in an interview, "If we do not change this trajectory, then I am within two weeks of having our hospitals overrun."

He further said that intensive care units in the city will start overflowing within 10 days.

Echoing similar sentiments, Judge Lina Hidalgo, the top elected official in Harris County, said, "As long as we're doing as little as possible and hoping for the best, we are always going to be chasing this thing. We are always going to be behind and the virus will always outrun us...And so what we need right now is to do what works, which is a stay-home order."

She was stripped of authority to issue stay-at-home orders after Governor Greg Abbott decided to move forward with the reopening plan.

"It is clear that the (coronavirus) growth is exponential at this point...We have been breaking record after record after record... the last couple of weeks," Miami Mayor Francis Suarez was quoted as saying in an interview.

"The city of Miami was the last city in the entire state of Florida to open. I was criticized for waiting so long. But there is no doubt that the fact that when we reopened, people started socialising as if... the virus didn't exist."

He further said that if the numbers do not begin to fall "more drastic measures" will be taken in the coming week.

As per the latest update by the Johns Hopkins University, a total of 2,938,625 people in the US have tested coronavirus positive and 130,306 deaths have been reported so far.

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
April 15,2020

Seoul, Apr 15: Wearing masks and gloves, South Korean voters cast their ballots on Wednesday to elect 300 parliamentary lawmakers amid the coronavirus outbreak.

Voting kicked off at 6 am (local time) and was to run until 6 pm (local time) at 14,330 polling stations across the country, according to the National Election Commission (NEC). The number of eligible voters is 44 million, according to Yonhap news agency.

The once-in-four-years legislative election is widely seen as a referendum on President Moon Jae-in, whose five-year term will end in mid-2022, as well as a test of the country's fight against COVID-19 under the leadership of Moon, The Strait Times reported.

South Korea has received international praise for its massive testing capability and other innovative measures, such as drive-through testing and high-tech contact tracing.

Experts, therefore, expect the ruling Democratic Party (DP) to extend its lead in Parliament, given that the government's handling of the virus outbreak is viewed positively both at home and abroad, as per The Strait Times.

At least 10,564 people in the country have been infected by coronavirus, which has claimed 222 lives. About 2,800 patients are undergoing treatment.

The number of new cases has fallen from a high of 813 on February 29 to below 50 for six days in a row as an intensive social distancing campaign that started on March 21 remained in place.

Several surveys cited by the newspaper also showed that voters consider the pandemic as the biggest factor in their decision. A recent poll showed that 72.6 per cent of respondents rated the government's response to the outbreak as positive.

The NEC has said that public safety at polling stations will be a priority to prevent any possible spread of the virus.

All 14,330 polling stations and 251 counting stations will be disinfected on polling day, the NEC was quoted.

Voters will undergo temperature screening and those registering temperatures of 37.5 degrees Celsius or higher or display respiratory symptoms will have to exercise their franchise at a separate booth.

Tuesday was the last of 13 days of campaigning, which saw most candidates reducing their ground activities and face-to-face encounters with voters. Instead, the candidates boosted their online presence with videos and social media engagements in a bid to win votes, according to The Strait Times.

In addition, the government has also decided to temporarily lift quarantine rules to permit self-isolators to vote in the elections. Some 50,000 people in self-isolation who have no symptoms and expressed a willingness to vote will be allowed to cast ballots after the regular voting ends in the evening.

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
January 27,2020

Kabul, Jan 27: A passenger plane crashed on Monday in a Taliban-held area of Afghanistan's Ghazni province, local officials said.

Arif Noori, spokesman for the provincial governor, said the plane went down around 1:10 p.m. local time in Deh Yak district, which is held by the Taliban. Two provincial council members also confirmed the crash.

The number of people on board and their fate was not immediately known, nor was the cause of the crash.

Ariana Airlines, Afghanistan's national carrier, dismissed the claim that one of their planes had crashed in a statement on their website, saying all their aircraft were operational and safe.

The mountainous Ghazni province sits in the foothills of the Hindu Kush mountains and is bitterly cold in winter.

The last major commercial air crash in Afghanistan occurred in 2005 when a Kam Air flight from western Herat to the capital Kabul crashed into the mountains as it tried to land in snowy weather.

The war however has seen a number of deadly crashes of military aircraft. One of the most spectacular occurred in 2013 when an American Boeing 747 cargo jet crashed shortly after takeoff from Bagram air base north of Kabul en route to Dubai in the United Arab Emirates. All seven crew member were killed.

Afghanistan's aviation industry suffered desperately during the rule of the Taliban when its only airline Ariana was subject to punishing sanctions and allowed to fly only to Saudi Arabia for Hajj flights.

Since the overthrow of the religious regime smaller private airlines have emerged but the industry is still a nascent one.

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.