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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News Network
June 17,2020

Washington, Jun 17: The United States is closely monitoring the situation following a fierce clash between Indian and Chinese forces in eastern Ladakh and hopes that the differences will be resolved peacefully, officials said here.

Twenty Indian Army personnel including a colonel were killed in the clash with Chinese troops in the Galwan Valley in eastern Ladakh on Monday night, the biggest military confrontation in over five decades that has significantly escalated the already volatile border standoff in the region.

"We are closely monitoring the situation between Indian and Chinese forces along the Line of Actual Control," a State Department spokesperson said.

"We note the Indian military has announced that 20 soldiers have died, and we offer our condolences to their families," the official said.

Both India and China have expressed their desires to de-escalate and the US supports a peaceful resolution of the current situation, the spokesperson said.

"During their phone call on June 2, 2020, President Donald Trump and Prime Minister Narendra Modi had discussed the situation along the India-China border," the official added.

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News Network
April 25,2020

Bueno Aires, Apr 25: Dozens of prisoners at a jail in Argentina's capital Buenos Aires rioted on Friday demanding urgent health measures after confirmation of a coronavirus case inside the facility.

Police surrounded the prison, which holds around 2,200 inmates, as explosions were heard, news agency reporters at the scene said.

A group of prisoners managed to climb onto a roof, burn mattresses and throw objects at security guards trying to quell the uprising.

Authorities have yet to comment on the riot or whether there are any injuries.

Inmates could be heard shouting demands for a judge to hear their case and for better protection against the pandemic, just a few days after a warden at the Villa Devoto prison was confirmed to have contracted the novel coronavirus.

"COVID-19 in Devoto, genocidal judges," read a banner hung from the prison roof. "We refuse to die in prison," read another.

The inmates are demanding, among other things, that releases that were pending before the pandemic be processed.

Several other riots broke out in prisons last week, including in Florencio Varela in Buenos Aires province where one inmate died and 20 were injured.

Argentina has been in lockdown since March 20 and has recorded more than 3,400 coronavirus cases and 167 deaths.

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March 28,2020

London: Italy on Friday recorded the most daily deaths of any country since the start of the coronavirus pandemic and Spain had its deadliest day, as British Prime Minister Boris Johnson became the first major world leader to test positive.

Italy reported 969 new deaths, Spain 769 and France 299 as Europe reeled from a crisis that has put millions at risk around the world and threatened a global economic meltdown.

In other grim milestones, AFP tallies showed a total of 300,000 cases now recorded in Europe with more than 26,000 deaths worldwide, and the United States overtook China as the country with the most infections.

Italy showed infection rates continuing a downward trend and Spain said its rate of new infections appeared to be slowing, but other countries were bracing to feel the full impact of the virus's spread.

The World Health Organization's regional director for Africa warned the continent faced a "dramatic evolution" of the pandemic, as South Africa became the latest nation to start life under lockdown and reported its first COVID-19 deaths.

Johnson, whose country has seen more than 14,000 declared coronavirus cases and 759 deaths, said he had developed mild symptoms over the previous 24 hours and was self-isolating after testing positive.

Britain's Health Secretary Matt Hancock also tested positive with mild symptoms.

Europe has suffered the brunt of the coronavirus crisis in recent weeks, with millions across the continent on lockdown and the streets of Paris, Rome and Madrid eerily empty.

In France — where nearly 2,000 people have died -- the government announced it was extending its stay-at-home order until at least April 15. While severe, the 299 new deaths it recorded on Friday was lower than the 365 reported the previous day.

The death of a 16-year-old girl from the virus has particularly shaken France, and shattered the belief of many young people that they are immune.

The girl's mother Sabine told AFP that Julie "just had a cough" at first but deteriorated quickly. She died on Wednesday, less than a week after showing her first symptoms.

"It's unbearable," Sabine said. "We were supposed to have a normal life."

Focus was also turning to the United States, where the number of known infections jumped by 18,000 on Friday, reaching more than 97,000 -- higher than both China and Italy. The US also recorded 345 deaths over the past 24 hours, with a total toll of 1,478.

In New York City, health workers are battling a surging toll of dead and infected at the US epicentre of the crisis, including an increasing number of younger patients.

"Now it's 50-year-olds, 40-year-olds, 30-year-olds," said one respiratory therapist at the Jewish Medical Center in Queens.

They "didn't listen about not going out or protecting themselves and washing their hands", he said.

- 'Afraid and lost' -

The coronavirus first emerged in China late last year before spreading globally, with more than half a million declared cases in 183 countries and territories.

Over the last six days, as many new cases have been diagnosed around the world as in the previous 80 days.

Beijing managed to contain its spread with lockdowns and quarantines and its epicentre Wuhan is in the process of easing severe movement restrictions in place for two months.

Three billion people around the world have been told to stay indoors.

In a historic first, Pope Francis performed the rarely recited "Urbi et Orbi" blessing to an empty Saint Peter's Square.

"Thick darkness has gathered over our squares, our streets and our cities; it has taken over our lives, filling everything with a deafening silence and a distressing void, that stops everything as it passes by," he said.

"We find ourselves afraid and lost," he said, describing the coronavirus as a "tempest".

Health care systems even in the most developed nations are stretched to breaking point and medical workers have been having to make difficult choices.

"If I've got five patients and only one bed, I have to choose who gets it," Sara Chinchilla, a paediatrician at a hospital near Madrid, told AFP.

The WHO's chief Tedros Adhanom Ghebreyesus said the dire lack of protective gear for frontline health workers was one of the most pressing problems in the fight to prevent deaths.

"The chronic global shortage of personal protective equipment is now one of the most urgent threats to our collective ability to save lives," he told a virtual news conference in Geneva.

Lockdowns and other measures are wreaking havoc on the global economy, with fears of a downturn worse than the Great Depression of the 1930s.

"It is clear that we have entered a recession" that will be worse than in 2009 following the global financial crisis, International Monetary Fund chief Kristalina Georgieva said Friday.

Unprecedented stimulus measures have helped markets bounce back after a brutal month, but people around the world are bracing for economic hardship.

The United States reported that 3.3 million people applied for unemployment benefits last week -- by far the highest number ever recorded.

Retail workers in particular have suffered as many countries shutter non-essential business, while airlines and the global tourism industry have been dealt devastating blows.

The fashion industry was the latest hit on Friday, with Paris men's fashion week and haute couture shows cancelled along with Milan men's fashion week.

- Armies of volunteers -

The World Tourism Organization said Friday it expected tourist arrivals to fall by 20-30 percent this year, with losses of $300 billion-450 billion in international tourism receipts.

But there have been rays of hope in the midst of the crisis.

Armed groups in Cameroon, the Philippines and Yemen have moved in recent days to reduce violence after UN Secretary General Antonio Guterres issued an appeal for ceasefires.

And armies of volunteers have emerged in many countries to bring help to the needy, with food deliveries for the elderly, free taxi rides, accommodation for health workers, and even home-sewn face masks.

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