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
April 15,2020

Seoul, Apr 15: Wearing masks and gloves, South Korean voters cast their ballots on Wednesday to elect 300 parliamentary lawmakers amid the coronavirus outbreak.

Voting kicked off at 6 am (local time) and was to run until 6 pm (local time) at 14,330 polling stations across the country, according to the National Election Commission (NEC). The number of eligible voters is 44 million, according to Yonhap news agency.

The once-in-four-years legislative election is widely seen as a referendum on President Moon Jae-in, whose five-year term will end in mid-2022, as well as a test of the country's fight against COVID-19 under the leadership of Moon, The Strait Times reported.

South Korea has received international praise for its massive testing capability and other innovative measures, such as drive-through testing and high-tech contact tracing.

Experts, therefore, expect the ruling Democratic Party (DP) to extend its lead in Parliament, given that the government's handling of the virus outbreak is viewed positively both at home and abroad, as per The Strait Times.

At least 10,564 people in the country have been infected by coronavirus, which has claimed 222 lives. About 2,800 patients are undergoing treatment.

The number of new cases has fallen from a high of 813 on February 29 to below 50 for six days in a row as an intensive social distancing campaign that started on March 21 remained in place.

Several surveys cited by the newspaper also showed that voters consider the pandemic as the biggest factor in their decision. A recent poll showed that 72.6 per cent of respondents rated the government's response to the outbreak as positive.

The NEC has said that public safety at polling stations will be a priority to prevent any possible spread of the virus.

All 14,330 polling stations and 251 counting stations will be disinfected on polling day, the NEC was quoted.

Voters will undergo temperature screening and those registering temperatures of 37.5 degrees Celsius or higher or display respiratory symptoms will have to exercise their franchise at a separate booth.

Tuesday was the last of 13 days of campaigning, which saw most candidates reducing their ground activities and face-to-face encounters with voters. Instead, the candidates boosted their online presence with videos and social media engagements in a bid to win votes, according to The Strait Times.

In addition, the government has also decided to temporarily lift quarantine rules to permit self-isolators to vote in the elections. Some 50,000 people in self-isolation who have no symptoms and expressed a willingness to vote will be allowed to cast ballots after the regular voting ends in the evening.

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News Network
January 31,2020

Wuhan, Jan 31: The World Health Organization declared a global emergency over the new coronavirus, as China reported Friday the death toll had climbed to 213 with nearly 10,000 infections.

The UN health agency based in Geneva had initially downplayed the threat posed by the disease, but revised its risk assessment after crisis talks.

suspended or reduced service to China include British Airways, German flag carrier Lufthansa, American Airlines, KLM and United.

Chinese efforts to halt the virus have included the suspension of classes nationwide and an extension of the Lunar New Year holiday.

All football matches across the country also will be postponed, the Chinese Football Association said on Thursday, including games in the top-tier Chinese Super League.

World stock markets tumbled again Thursday on fears that trouble in the "world's factory" would upset global supply chains and dent profits.

Toyota, IKEA, Starbucks, Tesla, McDonald's and tech giant Foxconn were among the corporate giants temporarily freezing production or closing large numbers of outlets in China.

Volkswagen announced Thursday its China joint-venture plants would not start production again before February 9.

US Federal Reserve Chairman Jerome Powell said the coronavirus posed a fresh risk to the world economy.

Throughout China, signs of paranoia multiplied, with residents of some Beijing residential compounds erecting makeshift barriers to their premises.

In one of many similar photos posted online, a man wearing a surgical mask and brandishing a traditional martial arts weapon squatted on a barricade outside a Chinese village, near a sign saying: "Outsiders forbidden from entering".

The crisis has caused food prices to spike, and the central government on Thursday blamed this partly on overzealous preventive measures, issuing a directive banning any roadblocks or other hindrances to food shipments.

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News Network
April 26,2020

Seoul, Apr 26: A train presumed to belong to North Korean's Kim Jong-un has been spotted at a station in the state's eastern coastal town of Wonsan amid speculation about the leader's health, a US monitor said on Sunday, citing commercial satellite imagery on the region, Yonhap news agency reported.

According to 38 North-- a website devoted to analysis about North Korea, the imagery showed a train "probably belonging to Kim Jong Un parked at the Leadership Railway Station servicing his Wonsan compound since at least April 21."

"The approximately 250-metre long train, although partially covered by the station's roof, can be seen at a railway station reserved for use by the Kim family. It was not present on April 15 but was present on both April 21 and 23," it said.

"The train's presence does not prove the whereabouts of the North Korean leader or indicate anything about his health, but it does lend weight to reports that Kim is staying at an elite area on the country's eastern coast," it added.

The report came as rumours about his health have spread as Kim apparently skipped an important annual visit to the Kumsusan Palace of the Sun on the occasion of the April 15 birthday of late state founder and his grandfather, Kim Il-sung.

CNN intensified the speculation by reporting earlier last week that the United States is looking into intelligence that Kim is "in grave danger" after surgery.

Seoul officials have disputed recent media reports about Kim, saying there have been no unusual signs from the North. Some said that Kim is presumed to be staying in Wonsan for unspecified reasons.

Washington has also dismissed the reports, with US President Donald Trump calling such reports "incorrect" in a press briefing late last week.

On Saturday, other media reports stated that China has dispatched a team of medical doctors and officials to North Korea "to advise on" Kim, citing multiple unnamed people familiar with the situation.

North Korea's state media, however, has not made any mention of Kim's public activity for two weeks since he was last seen in April 11 presiding over a major party meeting, though it has reported on his handling of routine state affairs, such as sending diplomatic letters.
But not all speculation has proven to be false.

When he was absent from public for about a month in 2014, speculation arose about his health and a political crisis in the secretive state. He later reemerged with a cane and a limp reportedly after having a cyst removed from his ankle.

The 36-year-old leader is known to have various health problems apparently caused by obesity and heavy smoking. He took office as leader of the communist state after his father, Kim Jong-il, died of a heart attack in late 2011.

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