American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

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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.

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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.

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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. 

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News Network
April 12,2020

London, Apr 12: British Prime Minister Boris Johnson has thanked the medics and staff of the state-funded National Health Service (NHS) for saving his life after he tested positive for the coronavirus, saying he owed them his life.

In his first public statement since being moved out of the intensive care at St. Thomas’ Hospital in London on Saturday, the 55-year-old Johnson said, “I can't thank them enough, I owe them my life.”

Downing Street has said that Johnson, who completes a week in hospital on Sunday after being shifted there with persistent COVID-19 symptoms, continues to make “very good progress” while on the ward.

Coronavirus India update: State-wise total number of confirmed cases, deaths on April 12

He has been able to take short walks as his doctors monitor his recovery after being moved out of the intensive care and has been watching films and doing puzzles in his hospital bed.

Johnson's fiancee Carrie Symonds, who is pregnant with their first child, is said to have sent him letters and baby scans to lift his spirits during his time in the hospital.

Thousands of get-well-soon cards have also poured in for the prime minister since he went into self-isolation after testing positive for coronavirus over two weeks ago.

Asked about plans for his return to work, UK Home Secretary Priti Patel said on Saturday that the UK PM needed "time and space to rest, recuperate and recover".

The Indian-origin Cabinet minister, who led the daily Downing Street update on the pandemic on Saturday, revealed that the UK had recorded 917 new coronavirus deaths, taking the total deaths in the country to 9,875.

According to the Johns Hopkins University data, the country has nearly 80,000 coronavirus cases.

Patel urged people to stay at home over the Easter weekend to curb the spread of the virus, despite warm and sunny weather across parts of the UK.

“We have given the police powers to enforce the necessary measures we have put in place, including through enforcement fines," said Patel.

"If you don't play your part... our selfless police will be unafraid to act. You will be endangering the lives of your own family, friends and loved ones," she said.

Meanwhile, an Easter message posted on the official 10 Downing Street Twitter account on behalf of the prime minister also urged people to stay at home to save lives.

It read: “Wishing everyone a very happy Easter from Downing Street.

“This year across the country churches will remain closed, and families will spend the day apart. But by staying home, remember, you are protecting the NHS and saving lives.” 

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News Network
March 16,2020

New Delhi, Mar 16: Due to the coronavirus pandemic, most airlines in the world will be bankrupt by the end of May and only a coordinated government and industry action right now can avoid the catastrophe, said global aviation consultancy firm CAPA in a note on Monday.

"As the impact of the coronavirus and multiple government travel reactions sweep through our world, many airlines have probably already been driven into technical bankruptcy, or are at least substantially in breach of debt covenants," it stated.

Across the world, airlines have announced drastic reduction in their operations in the wake of the coronavirus outbreak. For example, Atlanta-based Delta Air Lines stated on Sunday that it would be grounding 300 aircraft in its fleet and reduce flights by 40 per cent.

The US has suspended all tourist visas for people belonging to the European Union, the UK and Ireland. Similarly, the Indian government has suspended all tourist visas and e-visas granted on or before March 11.

CAPA, in its note on Monday, said, "By the end of May-2020, most airlines in the world will be bankrupt. Coordinated government and industry action is needed - now - if catastrophe is to be avoided."

Cash reserves are running down quickly as fleets are grounded and "what flights there are operate much less than half full", it added.

"Forward bookings are far outweighed by cancellations and each time there is a new government recommendation it is to discourage flying. Demand is drying up in ways that are completely unprecedented. Normality is not yet on the horizon," it said.

India's largest airline IndiGo -- which has around 260 planes in its fleet -- said on Thursday that it has seen a decline of 15-20 per cent in daily bookings in the last few days.

The low-cost carrier had stated that it expects its quarterly earnings to be materially impacted due to such decline.

CAPA said the failure to coordinate the future will result in protectionism and much less competition.

"The alternative does not bear thinking about. An unstructured and nationalistic outcome will not be survival of the fittest.

"It will mostly consist of airlines that are the biggest and the best-supported by their governments. The system will reek of nationalism. And it will not serve the needs of the 21st century world. That is not a prospect that any responsible government should be prepared to contemplate," the consultancy firm said.

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