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
March 21,2020

Beijing, Mar 21: China reported no domestically transmitted coronavirus cases for the third consecutive day even as seven more fatalities have been confirmed, taking the death toll in the country to 3255.

No new domestically transmitted cases of COVID-19 were reported on the Chinese mainland for the third day in a row on Friday, China's National Health Commission (NHC) said on Saturday.

The overall confirmed cases on the mainland had reached 81,008 by the end of Friday, which included 3,255 who died, 6,013 patients still undergoing treatment, 71,740 patients who had been discharged after recovery, the NHC said.

The NHC said 41 new confirmed COVID-19 cases were reported on the Chinese mainland on Friday from the people arriving from abroad, taking the total number of imported cases to 269.

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News Network
July 2,2020

Washington, Jul 2: Former US Ambassador to the UN, Nikki Haley, on Wednesday (local time) hailed India's action to ban 59 apps linked to Chinese firms including Tik Tok and said New Delhi is continuing to show it will not back down from China's aggression.

"Good to see India banning 59 popular apps owned by Chinese firms, including TikTok, which counts India as one of its largest markets. India is continuing to show it won't back down from China's aggression," Haley tweeted.

The Indian government on Monday announced that it had decided to block 59 apps in view of the information available that "they are engaged in activities which are prejudicial to sovereignty and integrity of India, defence of India, the security of the state and public order".

Information Technology Minister, Ravi Shankar Prasad said that the government has banned the apps for the safety, security, defense, sovereignty, and integrity of India.

Haley'='s remarks come after US Secretary of State Mike Pompeo welcomed India''s ban on the Chinese apps and stressed that the move would "boost India''s integrity and national security".

"We welcome India''s ban on certain mobile apps. India''s clean app approach will boost India's sovereignty and boost integrity and national security," Pompeo said.

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Agencies
June 8,2020

China is aggressively pursuing a diverse range of tactics -- from cyber-attacks to recruiting insiders for economic espionage, Indian security agencies have warned. The specific alert circulated among key stakeholders suggests that Chinese operatives are not only planning to steal classified cutting-edge defense technology but also eyeing to recruit best academicians and researchers around the globe, especially from the US.

Sources said they have noticed that China has authorized an "aggressive program of stealing US science and technology information by recruiting Americans in the technology sector with access to trade secrets".

In the technology sector of the US, many Indians scientists are working at the forefront. "This is a serious matter for Indian government and security establishments," said a top source further adding that Chinese always pursue economic espionage because it suits their low cost manufacturing sector on the basis of stolen research and costly design developed by top companies across the globe.

"An alert was also issued in early January about Chinese cyber intrusion attempts at several companies where Indian researchers are working. The espionage attempt was to target UAV technology and certain top-end military equipment designs. After stealing the techniques and design, China starts producing these equipment domestically and sells at a cheaper rate, inflicting irreparable damage to the original equipment manufacturers," the sources in the security establishment observed.

Recently, the US accused China for targeting academia by sending researchers to American labs and using talent recruitment programme to steal scientific analysis. The US has also found that young recruits of the People's Liberation Army posing as students are entering into various universities across the globe to get research papers and recruit academia.

Earlier this year, the US charged a former Boston University student of visa fraud for failing to disclose the status as a lieutenant in the China's People's Liberation Army.

The US intelligence agencies have found that their "universities have become a soft target in the global espionage war with China".

In January this year, the US Department of Justice charged a leading academician at the Harvard University for hiding his alleged role in a Chinese government programme.

In July last year, the Federal Bureau of Investigation (FBI) Director Christopher Wray had revealed that the FBI is probing nearly 1,000 cases of economic espionage and attempted intellectual property theft, nearly all of them leading back to China.

Accordingly, Indian Missions have been informed about the threats being posed by Chinese spies and attempts to recruit Indian scientists and technologists working in the US and other parts of the world.

Sources further stated that security establishments in India have informed the scientist fraternity to be on alert amid threat posed by Chinese spies.

The Chinese had earlier recruited a personnel, Dongfan Chung, working at Boeing for economic espionage. Chung had stolen secret technology to benefit Chinese government and during the raid at his house more than 2.5 lakh classified pages related to Boeing were recovered.

"There has been intense debate on the international platforms regarding Chinese-sponsored theft of intellectual property. American agencies have gone on record to say that China was targeting trade secrets. In the backdrop of pandemic and global health crisis, Indian establishments in defence and technology sectors have been told to be extra cautious as China is planning to become the most advanced economy while the other countries are crippled by the highly contagious virus," the sources further added.

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