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.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
January 20,2020

Wuhan, Jan 20: A 45-year-old Indian woman has become the first foreigner in China to have contracted a mysterious virus, which is suspected to be Severe Acute Respiratory Syndrome (SARS)-like corona virus.

In 2002-2003, the SARS corona virus killed around 650 people in China and Hong Kong. This time, a new strain of virus with 62 cases have been reported in Wuhan and two in Shenzhen so far. 19 patients have been already cured and discharged, as per the Chinese media.

Official sources in Beijing said that the patient, Preeti Maheshwari, a school teacher at an international school, is undergoing treatment for the new strain of pneumonia outbreak, which has been spreading in two major cities of China - Wuhan and Shenzen. She has been on a ventilator in the intensive care unit.

Maheshwari was admitted to a local hospital after she seriously fell ill last Friday. Her husband, a businessman from Delhi, is allowed to visit her daily.

Following a second death due to the outbreak of the virus in Wuhan, India on Friday issued an advisory to its nationals travelling to China. Over 500 Indian medical students are studying in Wuhan.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
June 29,2020

Karachi, Jun 29: Four heavily-armed militants attacked the busy Pakistan Stock Exchange on Monday morning, killing four security guards and a police sub-inspector before being shot dead in an exchange of fire, media reports said.

The unidentified militants opened indiscriminate fire and lobbed hand grenades at the main gate of the building as they tried to storm it, Geo News reported.

Police said that all the terrorists have been killed while five persons injured in the attack.

Four security guards and a police sub-inspector were also killed in the attack.

"An unfortunate incident took place at the Pakistan Stock Exchange. They made their way from our parking area and opened fire on everyone," said Abid Ali Habib, Director of Pakistan Stock Exchange.

The firing by militants caused panic among the people in the building.

Sindh province Governor Imran Ismail condemned the incident.

"Strongly condemn the attack on PSX aimed at tarnishing our relentless war on terror. Have instructed the IG & security agencies to ensure that the perpetrators are caught alive & their handlers are accorded exemplary punishments. We shall protect Sindh at all costs," he said on Twitter.

Police and rangers have arrived on the spot and surrounded the area.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
August 7,2020

Russia boasts that it's about to become the first country to approve a Covid-19 vaccine, with mass vaccinations planned as early as October using shots that are yet to complete clinical trials -- and scientists worldwide are sounding the alarm that the headlong rush could backfire.

Moscow sees a Sputnik-like propaganda victory, recalling the Soviet Union's launch of the world's first satellite in 1957.

But the experimental Covid-19 shots began first-in-human testing on a few dozen people less than two months ago, and there's no published scientific evidence yet backing Russia's late entry to the global vaccine race, much less explaining why it should be considered a front-runner.

“I'm worried that Russia is cutting corners so that the vaccine that will come out may be not just ineffective, but also unsafe,” said Lawrence Gostin, a global public health law expert at Georgetown University. “It doesn't work that way... Trials come first. That's really important.”

According to Kirill Dmitriev, head of Russia's Direct Investment Fund that bankrolled the effort, a vaccine developed by the Gamaleya research institute in Moscow may be approved in days, before scientists complete what's called a Phase 3 study.

That final-stage study, usually involving tens of thousands of people, is the only way to prove if an experimental vaccine is safe and really works.

Health Minister Mikhail Murashko said members of “risk groups,” such as medical workers, may be offered the vaccine this month.

He didn't clarify whether they would be part of the Phase 3 study that is said to be completed after the vaccine receives “conditional approval.”

Deputy Prime Minister Tatyana Golikova promised to start “industrial production” in September, and Murashko said mass vaccination may begin as early as October.

Dr Anthony Fauci, the top US infectious disease specialist, questioned the fast-track approach last week.

“I do hope that the Chinese and the Russians are actually testing a vaccine before they are administering the vaccine to anyone, because claims of having a vaccine ready to distribute before you do testing I think is problematic at best," he said.

Questions about this vaccine candidate come after the US, Britain and Canada last month accused Russia of using hackers to steal vaccine research from Western labs.

Delivering a vaccine first is a matter of national prestige for the Kremlin as it tries to assert the image of Russia as a global power capable of competing with the US and China.

The notion of being “the first in the world” dominated state news coverage of the effort, with government officials praising reports of the first-step testing.

In April, President Vladimir Putin ordered state officials to shorten the time of clinical trials for a variety of drugs, including potential coronavirus vaccines.

According to Russia's Association of Clinical Trials Organizations, the order set “an unattainable bar” for scientists who, as a result, "joined in on the mad race, hoping to please those at power.”

The association first raised concern in late May, when professor Alexander Gintsburg, head of the Gamaleya institute, said he and other researchers tried the vaccine on themselves.

The move was a “crude violation of the very foundations of clinical research, Russian law and universally accepted international regulations" the group said in an open letter to the government, urging scientists and health officials to adhere to clinical research standards.

But a month later, the Health Ministry authorized clinical trials of the Gamaleya product, with what appeared to be another ethical issue.

Human studies started June 17 among 76 volunteers. Half were injected with a vaccine in liquid form and the other half with a vaccine that came as soluble powder.

Some in the first half were recruited from the military, which raised concerns that servicemen may have been pressured to participate.

Some experts said their desire to perform well would affect the findings. “It's no coincidence media reports we see about the trials among the military said no one had any side effects, while the (other group) reported some," said Vasily Vlassov, a public health expert with Moscow's Higher School of Economics.

As the trials were declared completed and looming regulatory approval was announced last week, questions arose about the vaccine's safety and effectiveness.

Government assurances the drug produced the desired immune response and caused no significant side effects were hardly convincing without published scientific data describing the findings.

The World Health Organization said all vaccine candidates should go through full stages of testing before being rolled out.

“There are established practices and there are guidelines out,” WHO spokesman Christian Lindmeier said Tuesday.

“Between finding or having a clue of maybe having a vaccine that works, and having gone through all the stages, is a big difference.”

Offering an unsafe compound to medical workers on the front lines of the outbreak could make things worse, Georgetown's Gostin said, adding: “What if the vaccine started killing them or making them very ill?”

Vaccines that are not properly tested can cause harm in many ways — from a negative impact on health to creating a false sense of security or undermining trust in vaccinations, said Thomas Bollyky, director of the global health program at the Council on Foreign Relations. 

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.