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
March 3,2020

Wayanad, Mar 3: Anguished over the alleged delay in receiving flood relief from the Kerala government, a 42-year-old man committed suicide in Wayanad district, police said on Tuesday. Sanal Kumar, a native of Thrikaipatta in Meppadi near here was found hanging inside the temporary shelter built by his friends and local people on Monday. He was among the hundreds who had lost their homes in the August 2019 floods.

His home, built on a three cent plot, had been damaged partially in 2018 floods and completely in the 2019 deluge. Family members of the deceased alleged that it was due undue delay on the part of the authorities in allotting funds for rebuilding his house that drove Kumar to take the extreme step. Kumar was hoping to get a house under the Life Mission project, sources said.

A relative said Kumar had only 3 cent of land and had lot of debts. Even the Rs 10,000 assistance promised by the state government for the flood affected, had not reached him. Since the past two years he had filed several applications for assistance and apporached many revenue authroties for the promised government assistance, but it never came, the locals alleged.

According to K K Sahad, president of Meppadi Panchayat the deceased had some other financial issues and it was not the delay in rehabilitation that made him commit suicide. "It is true that he was not included in the first list of beneficiaries under the LIFE project as he had to have "pattayam" (land records) for his land.

However, he was included in the second list, thanks to the dilution in the norms that possession was enough for those who had no 'pattayam' for their property. The amount of Rs 4 lakhs was sanctioned for him, but was delayed a bit due to some technical issues."

Wayanad MLA C K Saseendran described it as an "extremely sad" development. As Kumar had some difficulties in producing the land recrods, the authroties had been unable to include his name in the LIFE housing scheme in the first phase.

The matter has been brought before the notice of the revenue authorities, he said. Vythiri Tahsildar, Abdul Hameed, visited Kumar's relatives this morning as the family members of the deceased wanted his presence before the body was taken for post-mortem.

"There was some technical issues with regard to the land as it falls within the adhivasi reserve. But they were occupying it for long. However, the issue has been sorted out and that his family members would be getting the eligibility amount of four lakhs," Hameed said.

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Agencies
June 11,2020

New Delhi, Jun 11: India on Thursday rejected a US government report that voiced concerns over alleged attacks and discrimination against religious and ethnic minorities in the country.

"Our principled position remains that we see no locus standi for a foreign entity to pronounce on the state of our citizens' constitutionally protected rights," Spokesperson in the Ministry of External Affairs Anurag Srivastava said.

He was replying to a question on the report at an online media briefing.

Mandated by the US Congress, the '2019 International Religious Freedom Report' that documents major instances of violation of religious freedom across the world was released by Secretary of State Mike Pompeo on Wednesday.

"India's vibrant democratic traditions and practices are evident to the world. The people and government of India are proud of our country's democratic traditions," the spokesperson said.

"We have a robust public discourse in India and constitutionally mandated institutions that guarantee protection of religious freedom and rule of law," he added.

The India section of the report said that US government officials underscored the importance of respecting religious freedom and promoting tolerance and mutual respect throughout the year with the ruling and opposition parties, civil society and religious freedom activists, and religious leaders belonging to various faith communities.

The report referred to the revocation of the special status of Jammu and Kashmir last August and the passage of the Citizenship Amendment Act (CAA) in Parliament in December as major highlights for India last year.

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Agencies
May 31,2020

New Delhi, May 31: Congress leader Kapil Sibal on Sunday questioned the Prime Minister on how much money has been given to labourers from the PM-CARES Fund.

"I would like to ask Prime Minister Modi, 'Can you tell us how much money did you give to labourers from your PM-CARES Fund?' I request him to answer this question. Many people died during this period, some died while walking, some died in the train, some died of hunger," Sibal said while addressing a virtual press conference.

The senior Congress leader further asked how much ex gratia did the Prime Minister give to the labourers who died in the corona crisis while negotiating the lockdown.

"I refer you to Section 12 of the Disaster Management Act. It says that ex gratia assistance on account of the loss of life and also assistance for the restoration of livelihood should be provided by the government. Did the government give ex gratia assistance to people who died in the crisis? The act also mentions special provisions for widows and orphans. The government should clarify how much assistance they gave to such people," he said.

Sibal said that the government should keep aside its agenda for the last six years and concentrate on making pro-poor policies.

"In the coming days, our economy is going to go into the negative territory as also confirmed by RBI. There are 45 crore labourers in our country. What will be their state? We have to look at our future. That is why we want to request the government that the agenda that they have run over the last six years should be kept aside and that government should care about the poor and draft policies for them," the Congress leader said.

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