Ramanujan's 'genius' finally proven by mathematicians

November 10, 2012

ramanujam

London, November 10: Hence proved! A US scientist has finally proven the mathematical relation - discussed by great Indian mathematician Srinivasa Ramanujan with his mentor G H Hardy in one of his last letters.

Ramanujan, the young genius who died at the age of 32, often managed to leap from insight to insight without formally proving the logical steps in between.

Now proof has been found for a connection that he seemed to mysteriously intuit between two types of mathematical functions, the 'New Scientist' reported.

"His ideas as to what constituted a mathematical proof were of the most shadowy description," G H Hardy, Ramanujan's mentor and one of his few collaborators, had once said.

Ken Ono of Emory University in Atlanta, Georgia, who has previously unearthed hidden depths in Ramanujan's work, was prompted by Ramanujan's 125th birth anniversary, to look once more at his writings.

"I wanted to go back and prove something special," Ono said.

Ono settled on a discussion in the last known letter that Ramanujan wrote to Hardy, concerning a type of function now called a modular form.

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

The functions looked unlike any other modular forms, but Ramanujan wrote that their outputs would be very similar to those of modular forms when computed for the roots of 1 like the square root -1.

Characteristically, Ramanujan offered neither proof nor explanation for this conclusion.

It was only 10 years later that mathematicians formally defined this other set of functions, now known as mock modular forms.

However, still no one fathomed what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.

Now Ono and colleagues have exactly calculated one of Ramanujan's mock modular forms for values very close to -1, and said the difference in the value of the two functions, ignoring the functions signs, is tiny when computed for -1, just like Ramanujan said.

The result confirms Ramanujan's incredible intuition, says Ono.

Born in 1887 in Erode, Tamil Nadu, Ramanujan was self-taught and worked in almost complete isolation from the mathematical community of his time, the report said.


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News Network
April 8,2020

New Delhi, Apr 8: The number of confirmed coronavirus cases in the country have continued to rise even on the 15th day of the lockdown, and reached 5,274 cases on Wednesday evening, according to the Ministry of Health and Family Welfare.

The tally includes 4,714 active, 411, cured/discharged and migrated cases as well as deaths. A total of 149 deaths have been reported due to the infection so far in the country.

Maharashtra with 1,018 confirmed cases has the highest number of COVID-19 patients in the country, while Tamil Nadu (690) and Delhi (576) are the two next most affected regions.

Fresh cases were reported on Wednesday from Telangana, Tamil Nadu, West Bengal, Maharashtra, Rajasthan and the union territory of Andaman and Nicobar Islands, among other states and UTs.

Meanwhile, in an interaction between Prime Minister Narendra Modi and floor leaders of several parties held today via video conferencing, discussions were held on extending the lockdown even further after the 21-day period.

The 21-day lockdown was announced on March 24 by Prime Minister Narendra Modi.
At the regular media briefing at 4 pm, Lav Aggarwal, Joint Secretary in the Health Ministry said that the government has ensured that there is no shortage of hydroxychloroquine in the country at present as well as in the future.

In the wake of COVID-19 outbreak, the Ministry of Human Resource and Development (MHRD) has launched 'Integrated Government Online Training Portal' wherein required resources will be provided for capacity building of the frontline workers.

"MHRD's training portal will provide required resources to the doctors, paramedics, nurse, technicians and ANMs and state government officials and civil defence officials, volunteers of National Cadet Corps (NCC), National Surveillance teams, Red Cross society and other organisations to have a large skill workforce to combat the coronavirus outbreak," said Aggarwal at a press conference here.

Speaking on government's preparedness on dealing with the patients having mild, very mild and serious conditions, Aggarwal said, "For people who have mild or very mild symptoms we have temporary hospitals, ie COVID care hospitals. Work is now being done to develop the field level infrastructure to take care of the mild and very mild symptomatic patients.

Similarly, for serious patients, we have dedicated healthcare centre and dedicated hospitals."

With fresh COVID-19 cases being reported across the country, several states and union territories, including Uttar Pradesh and Chandigarh, on Wednesday made it compulsory for people to use masks while venturing out of their houses.

Here's a quick read on the COVID-19 related updates:

1. Prime Minister Narendra Modi hinted that the lockdown might be extended after the completion of the 21-day period.
2. Floor party leaders of various political parties from both the Rajya and Lok Sabha assured the government of their full support in the decisions needed to be taken in the coming days and also suggested taking various measures to help the people.
3. According to the Indian Council of Medical Research (ICMR), a total of 1,21,271 tests have been conducted in the country.
4. The Uttar Pradesh government has decided to strictly implement 100 per cent lockdown in hotspots located across 15 districts in the state till the morning of April 15. These areas will be completely cordoned off and civilian passes will stay suspended while essentials would be delivered to citizens at their doorsteps.
5. The Supreme Court suggested that all tests to identify coronavirus positive patients should be conducted free of cost in the identified private laboratories and said that the court will pass appropriate order on the matter. The SC bench also asked the central government to look into creating a mechanism for providing reimbursement for the same.
6. Prime Minister Narendra Modi urged people to take the responsibility of a poor family, at least till the COVID-19 crisis persists if they wanted to honour him.
7. Union Home Ministry announced that Rs 3000 crores have been distributed among two crore registered construction workers till now, according to Saheli Ghosh Roy, Joint Secretary.
8. The MHA official said that the Home Secretary has written to the state Chief Secretaries to ensure a continuous supply of essential commodities under the Essential Commodities Act, 1955. The states can use measures like fixing stock limits, capping of price and checking bank accounts of the dealers.
9. The Health Ministry has assured that there will be no shortage of Hydroxychloroquine in the country. This came after India lifted the ban on the export of the anti-malarial drug being sued to treat COVID-19
10. The Maharashtra government too has issued an order to compulsorily wear masks while entering any government offices in Mumbai Metropolitan Region and Pune Metropolitan Region.

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Agencies
May 25,2020

New Delhi, May 25: Union Home Minister Amit Shah on Monday extended his greetings on the occasion of Eid-ul-Fitr and wished that the festival will bring peace and happiness to all.

"Extend my warm greetings on the occasion of Eid-ul-Fitr. May this festival bring peace and happiness in everyone's life," Shah tweeted.

Eid-ul-Fitr is being celebrated across the country on Monday.

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News Network
March 10,2020

New Delhi, Mar 10: Minutes after Jyotiraditya Scindia submitted his resignation to the party membership to Congress chief Sonia Gandhi, the Congress expelled him for anti-party activities after reports emerged that he had met PM Modi and Amit Shah.

Disgruntled Congress leader Jyotiraditya Scindia met Prime Minister Narendra Modi on Tuesday amid indications that he might join hands with the BJP to topple the Madhya Pradesh government.

Sources said Scindia first met Union Home Minister Amit Shah, and then the two leaders met Modi at the prime minister's residence.

Legislators loyal to Scindia, who has been upset with the Congress leadership with his marginalisation in the affairs of the Madhya Pradesh Congress, are likely to quit the party to reduce the Kamal Nath-led government to a minority.

It is likely to be followed by the Bharatiya Janata Party staking claim to form the government in the state.

The Congress President has approved the expulsion of Jyotiraditya Scindia from the Indian National Congress with immediate effect for "anti-party activities," said KC Venugopal, General Secretary Congress.

No person is, nor will be greater than the party: Congress youth wing chief

Indian Youth Congress (IYC) chief Srinivas B V on Tuesday slammed Jyotiraditya Scindia, who has announced his resignation from the primary membership of the Congress, and thanked party chief Sonia Gandhi for expelling the former Guna MP "who was promoting anti-party activities and factionalism".

"The history of 1857 and 1967 was once again repeated," Srinivas B V said, referring to the 1857 Revolt against East India Company and the role of the Scindia royals back then as well as Vijayaraje Scindia's switch from the Congress to the Jana Sangh in 1967.

"I would like to thank Congress president Sonia Gandhiji for taking the strong steps to expel the leader who was promoting anti-party activities and factionalism," the IYC chief said.

"No person is, nor will be greater than the party," he added.

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