American mathematicians solve Ramanujan's “deathbed” puzzle

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

sr


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
May 21,2020

Canberra, May 21: Australian Prime Minister Scott Morrison and his Indian counterpart, Narendra Modi, are looking forward to deepening the countries' strategic relationship, with both sides expected to sign a range of pacts from defence to trade in strategic sectors amid heightened tensions with China over Beijing's response to coronavirus pandemic.

During a virtual summit, scheduled to take place on June 4, both leaders are expected to ramp up efforts to diversify Australia's export markets and find trusted suppliers of vital products and components, a local newspaper, The Australian reported on Tuesday.

The new agreements will focus on reliable supply chains in key strategic sectors, including medical goods, technology and critical minerals, amid heightened tensions with China over Beijing's response to coronavirus pandemic.

The leaders will seal a new defence agreement allowing reciprocal access to bases and co-operation on military technology projects, while a new education partnership will be on the table to help overcome Australian university reliance on Chinese students.

The talks in terms of strategic convergence, now have greater significance as COVID-19 exacerbates the strategic contest between the US and China, and forces like-minded countries to seek out reliable partners.

Australian farmers could also benefit, with talks underway on expanding agricultural exports to India, including barley, as China throws up new trade barriers, media reports stated.

The virtual summit follows the cancellation of Morrison's planned state visit to India in January due to the bushfires.

Morrison said last year, ahead of his planned visit, that India was "a natural partner for Australia", referring to the countries' "shared values" -- a point of differentiation with China.

Former Department of Foreign Affairs and Trade secretary Peter Varghese, who wrote a landmark report on the bilateral relationship in 2018, was quoted by the newspaper as saying that India would be even more important to Australia in the post-COVID world. "If one of the lessons from COVID is that countries need to spread their risk, then finding new markets or building up existing markets is a crucial part of that," he added.

Varghese noted that India, a member of the Quadrilateral Security Dialogue along with Australia, Japan and the US, was a vital strategic partner to Australia in helping "constrain China's ambitions to be the predominant power".

"That shared objective between Australia and India of not wanting to see the region dominated by China is a key component of building up our geopolitical relationship," he told The Australian.

The summit also follows recent talks between Australian Foreign Minister Marise Payne and Indian counterpart Subrahmanyam Jaishankar on the pandemic response and Australia's call for an independent inquiry, which was overwhelmingly backed at the World Health Assembly on Tuesday.

Australia wants to support India to develop a domestic critical minerals processing industry, which would provide Western nations with an alternative to sourcing the materials from China.

Meanwhile, India has strong expertise as a manufacturer of drugs and medical equipment, while Australia is a centre of biomedical research, opening the possibility for closer co-operation in the key sector, the media reported further.

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News Network
February 18,2020

Washington, Feb 18: The upcoming visit of President Donald Trump to India later this month has the potential to usher in a new era of bilateral ties between the two countries, a top American business advocacy group has said.

President Trump will pay a state visit to India on February 24 and 25 at the invitation of Prime Minister Narendra Modi. He would be accompanied by First Lady Melania Trump.

This would be the president's first bilateral visit in the third decade of the 21st century and also the first after his acquittal by the Senate in the impeachment trial.

"I believe President Trump's upcoming visit to India has the potential to usher in a new era of our bilateral ties," Mukesh Aghi, President of the US India Strategic and Partnership Forum (USISPF) said in a statement on Monday.

On the sidelines of the visit, the USISPF, in collaboration with the Federation of Indian Chambers of Commerce and Industry (FICCI) and the ORF, has announced to organise a program entitled "US-India Forum: Partners for Growth".

The full-day discussion will focus on the key pillars defining India and the US' strategic, economic, and cultural partnership over the next decade.

"We have an opportunity before us to make real progress on multiple aspects of the relationship— whether it is upholding peace and security in the Indo-Pacific region; building upon an already strong energy partnership; developing co-production and co-development opportunities in the defense space; or strengthening bilateral trade," Aghi said.

"We look forward to an extremely successful visit and some concrete outcomes from the visit," he said.

The day-long programme on February 25 in New Delhi, will bring together over 500 senior business executives, members of the US-India think tank community and leading figures of the Indian diaspora to set the agenda for this strategic partnership.

Discussions during the day will touch upon areas, including the Indo-Pacific Strategy and Maritime Security; the US-India Defence Partnership, the US-India Energy Partnership, Elevating US-India Trade and Investment and Role of the Indian Diaspora in US-India Relations.

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News Network
March 6,2020

Mar 6: UK stocks fell again on Friday as growing economic risks from the coronavirus outbreak shattered investor confidence, with Britain recording its first death from the pathogen.

A 1.5% fall for the FTSE 100 erased the blue-chip index's gains from earlier this week. Export-heavy companies have now lost over $230 billion in value since the epidemic sparked a worldwide rout last week.

The domestically focussed mid-cap index was down 1.9%.

Cruise operator Carnival dropped 4.2% to its lowest level since 2012, a day after its Grand Princess ocean liner was barred from returning to its home port of San Francisco on virus fears.

Britain said an older person with underlying health problems had succumbed to the flu-like virus on Thursday, while the number of infections jumped to 115.

In company news, drug maker AstraZeneca fell 1% after it said its treatment for a form of bladder cancer failed to meet the main goal of improving overall survival in patients in a late-stage study.

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