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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Agencies
June 29,2020

Tehran, Jun 29: Iran has issued an arrest warrant and asked Interpol for help in detaining President Donald Trump and dozens of others it believes carried out the drone strike that killed a top Iranian general in Baghdad, a local prosecutor reportedly said Monday.

While Trump faces no danger of arrest, the charges underscore the heightened tensions between Iran and the United States since Trump unilaterally withdrew America from Tehran’s nuclear deal with world powers.

Tehran prosecutor Ali Alqasimehr said Trump and more than 30 others whom Iran accuses of involvement in the Jan. 3 strike that killed Gen. Qassem Soleimani in Baghdad face “murder and terrorism charges,” the semiofficial ISNA news agency reported.

Alqasimehr did not identify anyone else sought other than Trump, but stressed that Iran would continue to pursue his prosecution even after his presidency ends.

Interpol, based in Lyon, France, did not immediately respond to a request for comment.

Alqasimehr also was quoted as saying that Iran requested a “red notice” be put out for Trump and the others, which represents the highest level arrest request issued by Interpol. Local authorities end up making the arrests on behalf of the country that request it. The notices cannot force countries to arrest or extradite suspects, but can put government leaders on the spot and limit suspects’ travel.

After receiving a request, Interpol meets by committee and discusses whether or not to share the information with its member states. Interpol has no requirement for making any of the notices public, though some do get published on its website.

It is unlikely Interpol would grant Iran’s request as its guideline for notices forbids it from “undertaking any intervention or activities of a political” nature.

The U.S. killed Soleimani, who oversaw the Revolutionary Guard’s expeditionary Quds Force, and others in the January strike near Baghdad International Airport. It came after months of incidents raising tensions between the two countries and ultimately saw Iran retaliate with a ballistic missile strike targeting American troops in Iraq.

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News Network
July 1,2020

Washington, Jul 1: The United States has approved four coronavirus vaccine candidates for clinical trials, Food and Drug Administration (FDA) head Stephen Hahn told reporters.

"Four vaccines have been approved for moving into clinical trials... and another six are in the pipeline for us to review," Hahn said during a press briefing on Tuesday.

The US Administration launched in May Operation Warp Speed, a joint project of Health and Defense Departments, which aims to deliver 300 million doses of a vaccine for COVID-19 by January 2021.

The country's top pandemics expert Anthony Fauci warned on Tuesday, however, that there is no certainty the United States will be able to develop a vaccine against COVID-19 that works and will be safe.

Data on vaccine effectiveness, he added, may be available in the winter or early next year.

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Agencies
May 31,2020

Washington, May 31: US President Donald Trump said Saturday he will delay the G7 summit scheduled to take place in June and invite other countries -- including India and Russia -- to join the meeting.

"I don't feel that as a G7 it properly represents what's going on in the world. It's a very outdated group of countries," Trump told reporters on Air Force One.

He said he would like to invite Russia, South Korea, Australia and India to join an expanded summit in the fall.

It could happen in September, either before or after the UN General Assembly, Trump said, adding that "maybe I'll do it after the election."

Americans head to the polls in early November to choose a new president, with Trump keen for a return to normalcy after the coronavirus pandemic and a healthy economy as voters cast their ballots.

Describing the event as a "G-10 or G-11", Trump said he had "roughly" broached the topic with leaders of the four other countries.

Leaders from the Group of Seven, which the United States heads this year, had been scheduled to meet by videoconference in late June after COVID-19 scuttled plans to gather in-person at Camp David, the US presidential retreat outside Washington.

Trump created suspense last week, however, when he announced that he might hold the huge gathering in-person after all, "primarily at the White House" but also potentially parts of it at Camp David.

German Chancellor Angela Merkel became the first leader to decline the in-person invitation outright.

"Considering the overall pandemic situation, she cannot agree to her personal participation, to a journey to Washington," her spokesman said Saturday.

Her response followed ambivalent to positive reactions to the invitation from Britain, Canada and France.

The 65-year-old chancellor is the oldest G7 leader after Trump, who is 73. Japan's Shinzo Abe, also 65, is several months younger than Merkel. Their age puts them at higher risk from the coronavirus.

The G7 major advanced countries -- Britain, Canada, France, Germany, Italy, Japan and the United States -- hold annual meetings to discuss international economic coordination.

Russia was thrown out of what was the G8 in 2014 after it seized Ukraine's Black Sea peninsula of Crimea, an annexation never recognized by the international community.

The work of the G7 is now more important than ever as countries struggle to repair coronavirus-inflicted damage.

The White House had previously said the huge diplomatic gathering would be a "show of strength" when world economies are gradually reemerging from shutdowns.

The United States is the worst-hit country for COVID-19 infections, recording more than 1.7 million cases and over 103,680 deaths.

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