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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The wire
May 20,2020

Bhopal, May 20: Two months after Deepak Bundele, an advocate and former journalist, was brutally assaulted by the Madhya Pradesh’s Betul Police on March 23, an Assistant Sub-Inspector of Kotwali Police Station in Betul district, BS Patel, approached the victim to record his statement. However, he allegedly tried to convince Bundele to withdraw the case saying that the cops had mistaken him for a Muslim since he has a long beard and assaulted him. But, the cop added, they were ashamed of the incident after they came to know that they had beaten their ‘Hindu brother’.
Bundele was on his way to the government hospital for diabetes treatment, a day before the countrywide lockdown was announced, when the assault occurred. Miffed with the incident and after the district police denied to register the case, he wrote to the State Human Rights Commission; Chief Justice of Madhya Pradesh High Court; Chief Minister Shivraj Singh Chouhan; Vivek Johri, Director General of Police, Madhya Pradesh; and SP Betul to register an FIR against the police officials and take punitive action against them.
In the wake of COVID-19 pandemic outbreak, section 144 had been imposed in Betul district and public movement was restricted when the incident had occurred. 
Talking to Bundele, ASI Patel had said, “We seek an apology on behalf of those officials [who assaulted Bundele]. We are truly embarrassed because of the incident. If you want, I can bring those officials and make them apologise in person to you. They mistook you as a Muslim and assaulted you, since you had a long beard. And the man (who assaulted you) is a kattar (staunch) Hindu…In Hindu-Muslim riots whenever a Muslim is arrested, they beat them up brutally, always,” the police official can be heard saying in an audio recording shared by the victim.
In the 14 minutes long audio, he further said, “I request to you to withdraw the complaint. Please agree to our request; understand that we are living in Gandhi’s country; we are all Gandhi’s children…I have at least 50 friends from your caste.”
The cop continued, “All those people are ashamed that they did something like this to a Hindu brother without knowing his identity. We do not have any enmity against you. Whenever there is a Hindu-Muslim riot, police always supports the Hindus; even Muslims know this. But whatever happened with you was because of ignorance. For that, I have no words.” 
Refuting ASI Patel’s claim, Bundele claimed that there was no Hindu-Muslim riot that day, and asked whether he was beaten for being wrongly identified as a Muslim. The police officials agreed, and said: “Yes, exactly.”
“When I constantly declined to withdraw the compliant, he indirectly threatened me saying, ‘Agree to our request, else you and your advocate brother will face consequences’,” Bundele claimed. 
When contacted Betul SP DS Bhadoriya said, “I’m not aware of this audio clip. I will taken strict action, if I receive any such complain.”
Bundele said that he has written to the DGP and other senior police officials with details about the incident.   
THE ASSAULT
On March 23 evening, when Bundele was on his way to a hospital for the treatment, Betul Police allegedly thrashed him. The 32-year-old advocate had worked as a journalist for various dailies in Madhya Pradesh’s state capital for a decade. He moved to Betul in 2017 and started practising in the district court with his brother. “I have been a patient of diabetes and blood pressure for the last 15 years. On March 23, since I was not feeling well, I decided to visit the hospital and get some medicines. But I was stopped by the police midway,” Bundele had said. 
Even though the advocate, who sports a beard, said that he explained to police personnel that he had to get his medicines but one of them slapped him without trying to listen to what he was saying. “When I protested and said that police have no right to beat the public, they got anxious and within no time, many police officials came and started beating me up with sticks,” he added. 
"I need constant medication and lifesaving medicines to survive and I told the policemen everything while they were assaulting me. But, they kept hitting me, even after I fell,” he said, adding, "I bled for almost a 2-3 days after the incident.”
Bundele, sustained multiple injuries and his ear bled for almost two days after the incident, but, Betul police denied to file an FIR in the incident.
‘WILL MOVE TO THE HIGH COURT’
“Even after two months of the incident, no FIR has been registered and it seems that police is trying to sweep the matter under the carpet,” Bundele said, adding, “I have talked to the Supreme Court’s veteran advocate Vivek Tankha and Etasham Hashmi and will take this matter to the court.”
He also raised serious concerns about the communal angle of the incident, saying, “It’s a matter of grave concern that the police is turning communal and targeting a particular community.”

Source: https://www.google.com/amp/s/m.thewire.in/article/communalism/madhya-pr…

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Agencies
April 14,2020

Mumbai, Apr 14: The Shiv Sena and NCP said Prime Minister Narendra Modis address to the nation on Tuesday lacked substance as he did not suggest ways to strengthen the economy or a relief package for the poor and those worst hit by the lockdown.

Shiv Sena spokesperson Manisha Kayande also took a dig at the prime minister, saying he thankfully did not give any activity to people this time like clanging utensils or lighting lamps.

Modi on Tuesday announced that the lockdown across the country will be extended till May 3, saying the measure has produced a significant outcome in containing the infection.

He said implementation of the lockdown will be strictly ensured in its second phase and detailed guidelines will be brought out on Wednesday to ensure that outbreak does not spread to new areas.

Some relaxations may be allowed after April 20 in places where there are no hotspots, he said.

Kayande said Modi could have announced extension of the lockdown on Wednesday itself along with the new guidelines, instead of declaring it separately.

"He could have elaborated steps to be taken to tackle the coronavirus, relaxing restrictions on movements in different areas (depending upon threat posed by the disease)," she said.

"His speech normally is more of a rhetoric than substance. Thankfully, he did not give any other event to the people like lighting up lamps or clanging utensils. There was nothing substantial (in the address), the only takeaway was that the lockdown has been extended, she added.

Maharashtra Minister and NCP national spokesman Nawab Malik noted that Modi talked about helping the poor.

"But, he could have announced a package on behalf of the central government to help the poor, those working in the unorganised sector who are the worst hit due to the lockdown.

There was no mention of it anywhere," Malik said.

Another NCP spokesman Mahesh Tapase said it was expected that the prime minister would address the economic concerns being faced by the country.

"The least to expect was the announcement of a slew of measures to kick-start the economy in a phased manner as and when the restrictions are lifted, he added.

Tapase said the employers and employees wanted to know from the government how recession and unemployment will be tackled in the time to come.

"Access to capital for business, especially for MSMEs and agriculture, is a big concern. Supply and logistics is the cornerstone of economic activity which has come to a virtual standstill," he said.

The 2020-21 fiscal looks grim and hence, the right stimulus from the government coupled with a renewed zeal by the industry will only bring the economy back on track, he suggested.

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News Network
February 4,2020

New Delhi, Feb 4: Leader of Congress in Lok Sabha, Adhir Ranjan Chowdhury, on Tuesday attacked the BJP over Anantkumar Hegde's controversial remark on Mahatma Gandhi and termed the party as "Ravan ke aulad" (children of Ravana). "Aaj ye Mahatma Gandhi ko gaali dete hain. Ye Ravan ke aulad hain. Ram ke pujari ka ye apmaan kar rahe hain (Today, they abuse Mahatma Gandhi. They are children of Ravan. They are insulting Lord Ram's devotee)," Chowdhury said.

Later, BJP lawmakers object to Chowdhury's statement. Hegde, who is a Lok Sabha MP from Uttara Kannada, had on Saturday said that the freedom struggle led by Mahatma Gandhi was a "drama".

"None of these so-called leaders were beaten up by the cops even once. Their independence movement was one big drama. It was staged by these leaders with the approval of the British. It was not a genuine fight. It was an adjustment freedom struggle," Hegde had said while addressing a public event in Bengaluru. While several Congress leaders, including Karti Chidambaram and BK Hariprasad, have condemned Hegde's remark, BJP leaders too have distanced themselves from it.

Top leadership in BJP is unhappy with Anantkumar Hegde over his controversial remark on Mahatma Gandhi, party sources had said on Monday, adding that he has been asked to issue an unconditional apology.

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