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
January 24,2020

Beijing, Jan 24: As China stepped up measures to control the spread of coronavirus, locking down Wuhan and Huanggang cities in the Hubei province where several Indians live, the Indian Embassy here has set up hotlines for their assistance.

Chinese officials assured all assistance, including food supply, to the Indians who stayed put in the province, the Indian Embassy here said in a press release on Thursday.

Wuhan and its surrounding area became the epicentre of the coronavirus outbreak as the confirmed cases climbed to over 600 mostly from the city and the province with 17 deaths so far.

China has virtually sealed Wuhan and Huanggang cities, halting all public transport, including flight services, and advised people to stay at home and follow the precautions. The two cities put together have a population of over 17 million people.

Chinese officials said the measures have been taken to prevent the spread of the virus to other cities and the world.

Concerns arose for India too as about 700 Indian students, mostly studying medicine in different Chinese universities, resided in Wuhan and its neighbouring areas.

While many of them were believed to have left home for the Chinese New Year holidays, others remained in the city to complete their academic work. However, the exact number is not yet known.

“The Embassy of India has been receiving queries from Indians in Hubei province as well as their relatives in India in connection with the evolving situation of coronavirus infection in China,” the embassy press release said.

The embassy is in touch with relevant Chinese authorities in Beijing and Wuhan as well as Indians in Hubei Province, especially in Wuhan, it said.

“We are closely monitoring the evolving situation in China, including the advisories issued by the World Health Organisation (WHO),” the embassy said.

According to the embassy, Chinese authorities have assured all assistance to residents of Wuhan, including food supply.

“At present, it is reported that supermarkets (particularly those that are government-run) and e-commerce services, including food delivery, continue to remain operational in Wuhan,” it said.

The embassy has started two hotlines for those who wish to get in touch with the Mission in this regard in the following phone numbers:              +8618612083629 and +8618612083617.

“All are advised to also keep track of the embassy's social media accounts (Twitter:@EoIBeijing; Facebook: India in China) for updates on this evolving situation,” the release said.

Meanwhile, the Chinese Foreign ministry said all assistance would be provided to consular officials of the foreign missions to ensure the safety of the foreigners in the country.

Asked whether China would consider any request from the respective countries to move their citizens out of Wuhan, Chinese Foreign Ministry spokesman Geng Shuang said, “We always help foreign consular officials in China in their official jobs, we offer them all the assistance and convenience necessary and we work to guarantee foreign citizens' legitimate rights and interest in China.”

He said while specific detailed would be provided by local officials, China in principle, has always handled issues according to domestic laws, international laws and bilateral consular agreements.

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Agencies
May 17,2020

Washington, May 17: The overall number of global coronavirus cases has increased to over 4.6 million, while the death toll has surpassed 311,000, according to the Johns Hopkins University.

As of Sunday morning, the total number of cases stood at 4,634,068, while the death toll increased to 311,781, the University's Center for Systems Science and Engineering (CSSE) revealed in its latest update.

The US currently accounts for the world's highest number of cases and deaths at 1,467,796 and 88,754, respectively.

In terms of cases, Russia has the second highest number of infections at 272,043, followed by the UK (241,461), Brazil (233,142), Spain (230,698), Italy (224,760), France (179,630), Germany (175,752), Turkey (148,067) and Iran (118,392), the CSSE figures showed.

Meanwhile, the UK accounted for the second highest COVID-19 deaths worldwide at 34,546.

The other countries with over 10,000 deaths are Italy (31,763), Spain (27,563), France (27,532), and Brazil (15,662).

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News Network
February 9,2020

Beijing, Feb 9: After making sure everyone's face mask is on and sanitizer is to hand, the Qiao family heads out to Jingshan Park, a former royal sanctuary beside the Forbidden City in China's capital Beijing.

Snow has fallen for a second day, a rare event in the city of 21.5 million that would normally bring hundreds of thousands of people out to take photos and play. But the streets are empty and the parks are so quiet the only sound is of birds chirping.

It's not just Beijing. Shanghai, China's financial hub, and other cities in the world's most populous nation have turned into ghost towns after the government extended a holiday and asked residents not to go out because of the coronavirus.

"We know the situation of the coronavirus is severe. But the epicentre is far away, so we think it should be fine here ... It's a God-given chance to enjoy this family moment with snow and without work," said Mr Qiao, who has an 11-year-old daughter.

The epidemic has killed 722 people and infected nearly 32,000 in China as of February 8. More than three-quarters of the cases are in the central Hubei province where the virus originated - more than 1,000 km (620 miles) from Beijing.

Only a few people are brave enough to come out. A security guard at Jingshan Park said there were less than a third of the number of tourists than usual, even with the rare snowfall.

Even at one of the best spots for snapping photos of snowy Beijing just outside the Forbidden City, there's barely a crowd, while the usual tour buses and groups of people speaking different dialects are nowhere to be seen.

"Last year when it snowed, I took a few hours off work to come down here to take a picture and the crowd was several layers deep," said a man in his 30s who gave his surname as Yang. "But this year, I am not at all worried about finding a space to take a photo. The virus is keeping people indoors."

Security guards along Wangfujing street, a popular pedestrianised shopping area in downtown Beijing, said it was normally so crowded during the holiday period that it was hard to move around.

"Look at it now, there are more security guards and street cleaners than tourists!" said one of the guards.

Businesses, including shops, bars and restaurants, have been severely hit by the epidemic as the government has banned mass gatherings and even group meals in an effort to curb the spread of the coronavirus.

"You would have to wait outside for a table on a normal day," said a waitress at a restaurant with more than 50 tables. Just five were taken at the peak lunch hour.

Only a handful of the more than 100 restaurants along Beijing's famous food street, Guijie, were open, and the remaining outlets were wondering how long they can hold out.

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