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 28,2020

Washington, Feb 28: US intelligence agencies are monitoring the global spread of coronavirus and the ability of governments to respond, sources familiar with the matter said on Thursday, warning that there were concerns about how India would cope with a widespread outbreak.

While there are only a few known cases in India, one source said the country's available countermeasures and the potential for the virus to spread given India's dense population was a focus of serious concern.

US intelligence agencies are also focusing on Iran, where the country's deputy health minister has fallen ill during a worsening outbreak.

US Secretary of State Mike Pompeo said on Tuesday the United States was "deeply concerned" Tehran may have covered up details about the spread of coronavirus. A US government source said Iran's response was considered ineffective because the government only has minimal capabilities to respond to the outbreak.

Another source said US agencies were also concerned about the weak ability of governments in some developing countries to respond to an outbreak.

The US House of Representatives Intelligence Committee has received a briefing on the virus from the spy agencies. "The Committee has received a briefing from the IC (intelligence community) on coronavirus, and continues to receive updates on the outbreak on a daily basis," an official of the House Intelligence Committee told Reuters.

"Addressing the threat has both national security and economic dimensions, requiring a concerted government-wide effort and the IC is playing an important role in monitoring the spread of the outbreak, and the worldwide response," the official added.

A source familiar with the activities of the Senate Intelligence Committee, led by Republican Senator Richard Burr and Democratic Senator Mark Warner, said the panel was receiving daily updates. The role of US intelligence agencies in responding to the coronavirus epidemic at this point principally involves monitoring the spread of the illness around the world and assessing the responses of governments.

They are working closely with health agencies, such as the US Center for Disease Control, in sharing information they collect and targeting further intelligence gathering.

One source said US agencies would use a wide range of intelligence tools, ranging from undercover informants to electronic eavesdropping tools, to track the virus' impact.

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
June 13,2020

Washington, Jun 13: America's first-ever Hindu lawmaker Tulsi Gabbard has said that in this chaotic time, one can find certainty, strength, and peace in Bhagavad Gita.

In her message during a virtual commencement address, the 39-year-old Congresswoman from Hawaii said that it is a chaotic time and no one can say with certainty what tomorrow looks like.

"... but we find certainty, strength, and peace in the practice of Bhakti Yoga and Karma Yoga taught to us by Krishna in the Bhagavad Gita," Tulsi Gabbard told the 'Class of 2020 for Hindu students''.

Her address came amidst protests in the US against the killing of African-American George Floyd by a white police officer in Minneapolis.

The country has been swept by protests since George Floyd's custodial death on May 25 with thousands of people mounting pressure for changes to the law enforcement practices.

The first-ever virtual Hindu commencement was organised by the Hindu Students Council on June 7, which drew thousands of viewers on Facebook and YouTube Live, all coming together in solidarity during the ongoing COVID-19 crisis.

According to Johns Hopkins Coronavirus Resource Center, the contagion has infected over 76,00,000 people and killed more than 4,25,000 across the world. The US is the worst affected country with over 2.04 million cases and more than 1,14,000 deaths.

The COVID-19, which originated in China''s Wuhan city in December last year, has also battered the world economy with the International Monetary Fund saying that the global economy is bound to suffer a "severe recession".

Scientists are racing against time to find a vaccine or medicine for its treatment.

Hundreds of graduates from the US, Canada, the UK, India and Australia attended to commemorate their graduation in a unique way - by celebrating their shared Hindu values.

Professor Subhash Kak served as the ceremony's Grand Marshall.

"As you think about this new chapter in your lives, ask yourself what is my purpose in life? It is a deep question that if you can recognise now that your purpose is to serve God and God''s children, practicing Karma Yoga, then you can lead a truly successful life," Tulsi Gabbard said.

"Success is not defined by temporary material things, trinkets, glittery objects or accomplishments - but a deeply successful and happy life centered around service," she added.

The Iraq war veteran ended her presidential campaign in March and offered her full support to former vice president Joe Biden, 77, who is all set to challenge Republican incumbent Donald Trump, 73, in November elections.

The commencement address focused heavily on themes from the Bhagavad Gita, a timeless historical text that many Hindus consider their moral framework.

Professor Kak, Regent Professor at Oklahoma State University and 2019 Padma Shri recipient, read out the names of the graduating students.

"I exhort you - the graduating students - to be the leaders of the new world where education is less of the mind of a vessel to be filled with information (usually forgotten after the semester is over), and more of a flame that is lit as envisioned by our Vedic sages," he said.

The student speakers were from many university campuses, including the Massachusetts Institute of Technology, Princeton, and Stanford.

Listen to the latest songs, only on JioSaavn.com

The programme included offerings of Hindu prayers, recitation of a traditional graduation message from the Upanishads, and a symbolic conferral of degrees to high school and college graduate.

Founded in 1990, Hindu Students Council is North America''s largest pan-Hindu youth organisation. 

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 17,2020

Beijing, Jun 17: Beijing's airports cancelled more than 1,200 flights and schools in the Chinese capital were closed again on Wednesday as authorities rushed to contain a new coronavirus outbreak linked to a wholesale food market.

The city reported 31 new cases on Wednesday while officials urged residents not to leave Beijing, with fears growing about a second wave of infections in China, which had largely brought its outbreak under control.

Tens of thousands of people linked to the new Beijing virus cluster -- believed to have started in the sprawling Xinfadi wholesale food market -- are being tested, with almost 30 residential compounds in the city now under lockdown.

At least 1,255 scheduled flights were cancelled Wednesday morning, state-run People's Daily reported, nearly 70 percent of all trips to and from Beijing's main airports.

The outbreak had already forced authorities to announce a travel ban for residents of "medium- or high-risk" areas of the city, while requiring other residents to take nucleic acid tests in order to leave Beijing.

Meanwhile, several provinces were quarantining travellers from Beijing, where all schools -- which had mostly reopened -- have been ordered to close again and return to online classes.

"The epidemic situation in the capital is extremely severe," Beijing city spokesman Xu Hejian warned Tuesday.

Mass testing under way

Officials have closed 11 markets and disinfected thousands of food and beverage businesses in Beijing after the outbreak was detected.

The city has now reported 137 infections over the last six days, with six new asymptomatic cases and three suspected cases on Wednesday, according to the municipal health commission.

An additional two domestic cases, one in neighbouring Hebei province and another in Zhejiang, were reported by national authorities on Wednesday, while there were 11 imported cases.

Authorities have so far banned group sports, ordered people to wear masks in crowded enclosed spaces, and suspended inter-provincial group tours in response to the outbreak.

Officials said that since May 30, more than 200,000 people had visited Xinfadi market, which supplies more than 70 percent of Beijing's fruit and vegetables.

More than 8,000 workers there were tested and quarantined.

Until the new outbreak, most of China's recent cases were nationals returning from abroad as COVID-19 spread globally, and the government had all but declared victory against the disease.

China's Center for Disease Control and Prevention said Monday that the virus type found in the Beijing outbreak was a "major epidemic strain" in Europe.

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.