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
June 15,2020

Stockholm, Jun 15: Nuclear powers continue to modernise their arsenals, researchers said Monday, warning that tensions were rising and the outlook for arms control was "bleak".

"The loss of key channels of communication between Russia and the USA... could potentially lead to a new nuclear arms race," said Shannon Kile, director of the nuclear arms control programme at the Stockholm International Peace Research Institute (SIPRI) and co-author of the report.

Russia and the US account for more than 90 percent of the world's nuclear weapons.

Kile was referring to the future of the New START treaty between the US and Russia, which is set to expire in February 2021.

It is the final nuclear deal still in force between the two superpowers, aimed at maintaining their nuclear arsenals below Cold War levels.

"Discussions to extend New START or to negotiate a new treaty made no progress in 2019," the SIPRI researchers noted.

At the same time, nuclear powers continue to modernise their weapons while China and India are increasing the size of their arsenals.

"China is in the middle of a significant modernisation of its nuclear arsenal. It is developing a so-called nuclear triad for the first time, made up of new land- and sea-based missiles and nuclear-capable aircraft," SIPRI said.

The country has repeatedly rejected Washington's insistence that it join any future nuclear arms reduction talks.

The number of nuclear warheads declined in the past year.

At the start of 2020, the United States, Russia, Britain, China, India, Pakistan, Israel and North Korea together had 13,400 nuclear arms, according to SIPRI's estimates, 465 fewer than at the start of 2019.

The decline was attributed mainly to the United States and Russia.

While the future of the New START treaty remains uncertain, Washington and Moscow have continued to respect their obligations under the accord.

"In 2019, the forces of both countries remained below the limits specified by the treaty," the report said. But both nations "have extensive and expensive programmes underway to replace and modernise their nuclear warheads, missile and aircraft delivery systems, and nuclear weapon production facilities," it added.

"Both countries have also given new or expanded roles to nuclear weapons in their military plans and doctrines, which marks a significant reversal of the post-Cold War trend towards the gradual marginalisation of nuclear weapons."

The Treaty on the Non-Proliferation of Nuclear Weapons (NPT), a cornerstone of the global nuclear non-proliferation regime, celebrates its 50th anniversary this year.

The number of nuclear arms worldwide has declined since hitting a peak of almost 70,000 in the mid-1980s.

The five original nuclear powers -- Washington, Beijing, Moscow, Paris and London -- in March reiterated their commitment to the treaty.

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 22,2020

Davos, Jan 22: President Donald Trump has said that the US is watching the developments between India and Pakistan over Kashmir "very closely" and repeated his offer to "help" resolve the longstanding dispute between the two neighbours as he met Prime Minister Imran Khan on the sidelines of the World Economic Forum here in the Swiss ski resort.

Addressing the media with the Pakistan Prime Minister prior to their private meeting on Tuesday, President Trump asserted that trade and borders were both critical points for discussion, while Khan said that for him, Afghanistan was the top priority.

Trump told Khan, whom he referred to as "my friend", that he would speak to Prime Minister Narendra Modi about the ongoing Kashmir issue. The US president is expected to visit India in the coming weeks, marking his first visit after taking up his post in the White House.

"What's going on between Pakistan and India … if we can help, we certainly will be willing to. We have been watching it very closely and it's an honour to be here with my friend," he said.

"The Pakistan-India conflict is a very big issue for us in Pakistan and we expect the US to always play its part in deescalating the tensions, because no other country can," Khan said.

President Trump has repeatedly offered to mediate following India's August 5 decision to revoke the special status to Jammu and Kashmir and bifurcate the state into two Union Territories, evoking strong reaction from Pakistan which has been trying to internationalise the Kashmir issue.

New Delhi has defended the move, saying Jammu and Kashmir is an integral part of India and the issue was strictly internal to the country, and the special status provisions only gave rise to terrorism in Jammu and Kashmir.

"The country took the decision of abrogation of Article 370, which had only given separatism and terrorism to that state," Prime Minister Narendra Modi said at a function in October last year.

This is the third meeting between Trump and Khan since Pakistan premier assumed office in 2018 and it came against the backdrop of Pakistan Foreign Minister Shah Mehmood Qureshi's recent trip to the US, amid reports that the US and Afghan Taliban were close to striking a peace deal.

"There are issues we want to talk about. The main issue is Afghanistan because it concerns the US and Pakistan. Fortunately, we are on the same page. Both of us are interested in peace there and an orderly transition in Afghanistan with talks with Taliban and the government," Khan said.

When a reporter asked Trump if he would visit Pakistan considering he was already set to visit India, the US president said he was meeting the Pakistan premier in Davos.

"Well, we're visiting right now. So we don't really have to. I wanted to say that from a relationship standpoint, we got a great relationship. From the standpoint our two countries, we're getting along very well. I would say we've never been closer with Pakistan the way we're right now. And this is a big statement," Trump said.

Khan left for Switzerland to attend the World Economic Forum and meet the world leaders, including President Trump, on the sidelines of the annual event which kicked off at the ski resort town of Davos on Tuesday.

The four-day summit marks the 50th anniversary of the forum.

A total of 53 heads of State are on the guest list. Nearly 3,000 participants from 118 countries are expected to attend the event during which political leaders, business executives, heads of international organisations and civil society representatives are set to deliberate on contemporary economic, geopolitical, social and environmental issues.

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 21,2020

New Delhi, Feb 21: Global terror financing watchdog FATF on Friday decided continuation of Pakistan in the "Grey List" and warned the country that stern action will be taken if it fails to check flow of money to terror groups like the LeT and the JeM, sources said.

The decision has been taken at the Financial Action Task Force's plenary in Paris.

The FATF decided to continue Pakistani in the "Grey List". The FATF also warned Pakistan that if it doesn't complete a full action plan by June, it could lead to consequences on its businesses, a source said.

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.