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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Agencies
July 17,2020

Washington, Jul 17: US President Donald Trump's economic adviser Larry Kudlow has said that TikTok may cut off ties to its Chinese parent and become a 100 per cent American company to circumvent demands to ban it as India has done.

"I think TikTok is going to pull out of the holding company which is China-run and operate as an independent American company," he told reporters at the White House on Thursday.

The US has not made a final decision on whether to ban it - which has been suggested by Secretary of State Mike Pompeo, he said.

TikTok being divested by ByteDance Technology Company "is a much better solution than banning or pushing away", said Kudlow, who is the Director of the National Economic Council.

He said that its services will be located in the US and "it will become an hundred per cent American company".

If it becomes a US company without Chinese links, India may have to reconsider the ban on the short video app wildly popular in the country.

India banned TikTok along with 58 other Chinese apps on June 29 citing threats to its defence and national security.

The ban came after a deadly clash between Indian and Chinese troops along the Line of Actual Control in Ladakh.

Under Beijing's National Security Law, all Chinese companies have to provide intelligence requested by the government, creating risks for users and their countries.

India was TikTok's biggest market outside of China, where it operates as Douyin.

There were about 200 million users in India and over 300 million downloads.

The US comes next with over 30 million users for the app.

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News Network
July 11,2020

Istanbul, Jul 11: Turkish President Recep Tayyip Erdogan announced Friday that the Hagia Sophia, one of the architectural wonders of the world, would be reopened for Muslim worship, sparking fury in the Christian community and neighbouring Greece.

His declaration came after a top Turkish court revoked the sixth-century Byzantine monument's status as a museum, clearing the way for it to be turned back into a mosque.

The UNESCO World Heritage site in historic Istanbul, a magnet for tourists worldwide, was first constructed as a cathedral in the Christian Byzantine Empire but was converted into a mosque after the Ottoman conquest of Constantinople in 1453.

The Council of State, Turkey's highest administrative court, unanimously cancelled a 1934 cabinet decision to turn it into a museum and said Hagia Sophia was registered as a mosque in its property deeds.

The landmark ruling could inflame tensions not just with the West and Turkey's historic foe Greece but also Russia, with which Erdogan has forged an increasingly close partnership in recent years.

'Millions of Christians not heard'

Greece swiftly branded the move by Muslim-majority Turkey an "open provocation to the civilised world".

"The nationalism displayed by Erdogan... takes his country back six centuries," Culture Minister Lina Mendoni said in a statement.

The Russian Orthodox Church was equally scathing.

"The concern of millions of Christians were not heard," Church spokesman Vladimir Legoida told Interfax news agency.

The decision "shows that all pleas regarding the need to handle the situation extremely delicately were ignored," he said.

UNESCO chief Audrey Azoulay said she "deeply regrets" the decision made without prior dialogue with the UN's cultural agency.

The move was also condemned by the US Commission on International Religious Freedom, which said it was an "unequivocal politicisation" of the monument.

Hagia Sophia, which stands opposite the impressive Sultanahmet Mosque -- often called the Blue Mosque, has been a museum since 1935 and open to believers of all faiths.

Transforming it from a mosque was a key reform under the new republic born out of the ashes of the Ottoman Empire.

Sharing a presidential decree which named Hagia Sophia as a "mosque", Erdogan announced its administration would be handed over to Turkey's religious affairs directorate known as Diyanet.

"May we be blessed," he commented. The decree was published on the official gazette.

Erdogan has in recent years placed great emphasis on the battles which resulted in the defeat of Byzantium by the Ottomans, with lavish celebrations held every year to mark the conquest.

Muslim clerics have occasionally recited prayers in the museum on key anniversaries or religious holidays.

"The decision is intended to score points with Erdogan's pious and nationalist constituents," said Anthony Skinner of the risk assessment firm Verisk Maplecroft.

"Hagia Sophia is arguably the most conspicuous symbol of Turkey's Ottoman past -- one which Erdogan is leveraging to strengthen his base while snubbing domestic and foreign rivals," he told AFP.

'Chains broken'

A few hundred Turks carrying Turkish flags gathered outside Hagia Sophia shouting "Chains broken, Hagia Sophia reopened".

Police heightened security measures around the building, according to AFP journalists.

"It's been a dream since we were kids," said Erdal Gencler, an Istanbul resident.

"(Hagia Sophia) finds its true purpose again. We are very excited, proud, and hopeful that there will be beautiful services here," he added.

Fatma, a woman with tearful eyes, said: "Of course I am crying. (Hagia Sophia) belongs to us."

Ahead of the court decision, Justice Minister Abdulhamit Gul shared a picture of Hagia Sophia on his official Twitter account, with a message: "Have a good Friday."

Finance Minister Berat Albayrak, Erdogan's son-in-law, tweeted that Hagia Sophia would be reopened to Muslim worship "sooner or later", referring to a quote from Turkish poet Necip Fazil Kisakurek.

The Council of State had on July 2 debated the case brought by a Turkish group -- the Association for the Protection of Historic Monuments and the Environment, which demanded Hagia Sophia be reopened for Muslim prayers.

Since 2005, there have been several attempts to change the building's status. In 2018, the Constitutional Court rejected one application.

Despite occasional protests outside the site by Islamic groups, Turkish authorities had until now kept the building as a museum.

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News Network
March 31,2020

Washington, Mar 31: The United States has performed over one million coronavirus tests so far, said President Donald Trump on Monday.

"Today, we reached a historic milestone in our war against coronavirus. Over 1 million Americans have now been tested, more than any other country by far, not even close," Trump said during a press briefing.

US Health Secretary Alex Azar said that approximately 100,000 samples are tested for coronavirus daily.

The number of novel coronavirus (COVID-19) cases within the United States surpassed 150,000 and the death toll has reached 2828, according to Johns Hopkins University. 

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