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.


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
January 28,2020

New Delhi, Jan 28: Kolkata Metro Rail Corp expects to complete its East-West project, which runs partly under the city’s iconic Hooghly river, by March 2022 after a delay of several years doubled costs.

The authority is awaiting a final installment of Rs 20 crore ($2.8 million) over the next two years from the Indian Railway Board, said Manas Sarkar, managing director at KMRC. A soft loan of Rs 4,160 crore from Japan International Cooperation Agency helps fund 48.5% of the project.

India’s oldest metro, which started in 1984 with a North-South service, was due to expand by 2014 but faced problems including squatters on the planned route. These issues have contributed to the total project cost rising to about Rs 8,600 crore for some 17 kilometers from Rs 4,900 crore for 14 km.

“About 40% of total transport demand will be tackled by these two metro services,” Sarkar said in an interview at his office in Kolkata. “It will be a relief for environmental pollution and the city should be much more decongested.”

The new line is expected to carry about 900,000 people daily, -- roughly 20% of the city’s population -- and will take less than a minute to cross a 520-meter underwater tunnel. Depending on the time of day, it takes some 20 minutes to use the ferry and anywhere upward of an hour to cross the Howrah bridge.

KMRC will repay the JICA loan over 30 years after an initial six-year moratorium. The interest rate is between 1.2% to 1.6%. The East-West metro project is 74% owned by the railway ministry and 26% by the ministry of housing and urban affairs.

“We don’t anticipate any further cost escalation now,” Sarkar said.

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
June 12,2020

New Delhi, Jun 13: Ten days after recording two lakh COVID-19 cases, India surpassed the three lakh-mark on Saturday with the worst daily spike of 11,458 infections, while the death toll too climbed to 8,884 with 386 new fatalities, the Union Health Ministry said.

India took 64 days to cross the 1 lakh-mark from 100 cases, then in another fortnight it reached the grim milestone of two lakh cases. It has now become the fourth worst-hit nation by the pandemic with a caseload of 3,08,993, according to coronavirus statistics website Worldometer.

However, the Health Ministry said on Friday the doubling time of coronavirus cases has improved to 17.4 days from 15.4 days. And its data updated at 8 am on Saturday showed active cases at 1,45,779 and those who have recovered at 1,54,329; one patient has migrated.

"Thus, around 49.9 per cent patients have recovered so far," a ministry official said.

The total number of confirmed cases include foreigners.

Of the 386 new deaths, Delhi accounted for the highest 129 fatalities followed by Maharashtra 127. The virus is moving rapidly in Delhi, which for the first time reported over 2,000 cases on Friday, and Maharashtra, where the number of cases has crossed one lakh.

Gujarat reported 30 deaths, Uttar Pradesh 20, Tamil Nadu 18, West Bengal, Telangana and Madhya Pradesh 9 each, Karnataka and Rajasthan 7 each, Haryana and Uttarakhand 6 each, Punjab 4, Assam 2, Kerala, Jammu and Kashmir and Odisha 1 each.

Of the total 8,884 deaths, Maharashtra tops the tally with 3,717 fatalities followed by Gujarat with 1,415, Delhi with 1,214, West Bengal with 451, Madhya Pradesh with 440, Tamil Nadu with 367, Uttar Pradesh with 365, Rajasthan with 272 and Telangana with 174 deaths.

The death toll reached 80 in Andhra Pradesh, 79 in Karnataka, 70 in Haryana and 63 in Punjab. Jammu and Kashmir has reported 53 COVID-19 fatalities, Bihar 36 and Uttarakhand 21, Kerala 19, Odisha 10 and Jharkhand and Assam 8 each.

Chhattisgarh and Himachal Pradesh have registered 6 deaths each, Chandigarh 5, Puducherry 2, while Meghalaya, Tripura and Ladakh 1 each, according to the health ministry.

Maharashtra has reported the maximum number of cases at 1,01,141 followed by Tamil Nadu (40,698), Delhi (36,824), Gujarat (22,527), Uttar Pradesh (12,616), Rajasthan (12,068) and Madhya Pradesh (10,443).

The number of COVID-19 cases has gone up to 10,244 in West Bengal, 6,516 in Karnataka, 6,334 in Haryana and 6,103 in Bihar. It has risen to 5,680 in Andhra Pradesh, 4,730 in Jammu and Kashmir, 4,484 in Telangana and 3,498 in Odisha and Assam each.

Punjab has reported 2,986 cases while Kerala has 2,322 cases.

A total of 1,724 people have been infected by the virus in Uttarakhand, 1,617 in Jharkhand, 1,424 in Chhattisgarh, 961 in Tripura, 486 in Himachal Pradesh, 463 in Goa, 385 from Manipur and 334 in Chandigarh.

Ladakh has registered 239 COVID-19 cases, Puducherry 157, Nagaland 156, Mizoram 104, Arunachal Pradesh 67, Sikkim 63, Meghalaya 44 while Andaman and Nicobar Islands has registered 38 cases.

Dadar and Nagar Haveli and Daman and Diu together have reported 30 cases.

The ministry said 7,984 cases are being reassigned to states and "our figures are being reconciled with the ICMR". State-wise distribution is subject to further verification and reconciliation, it added.

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
July 3,2020

New Delhi, Jul 3: In a significant step, ICMR has partnered with Bharat Biotech International Limited (BBIL) to fast-track clinical trials of the indigenous COVID-19 vaccine (BBV152 COVID Vaccine). It is the first indigenous vaccine being developed by India and is one of the top priority projects which is being monitored at the topmost level of the Government, says ICMR in a statement.

The vaccine is derived from a strain of SARS-CoV-z isolated by ICMR-National Institute of Virology, Pune. ICMR and BBIL are jointly working for the preclinical as well as clinical development of this vaccine.

In a letter to the institutes that will be involved in the trails of the vaccine, ICMR has said

"It is envisaged to launch the vaccine for public health use latest by 15th August 2020 after completion of all clinical trials. BBIL is working expeditiously to meet the target. However, final outcome will depend on the cooperation of all clinical trial sites involved in this project. you have been chosen as a clinical trial site of the BBV152 COVID vaccine. ln view of the public health emergency due to COVID-19 pandemic and urgency to launch the vaccine, you are strictly advised to fast track all approvals related to initiation of the clinical trial and ensure that the subject enrollment is initiated no later than 7th July 2020."

The ICMR also asked the institutes to comply with the order, "Kindly note that non-compliance will be viewed very seriously. Therefore, you are advised to treat this project on the highest priority and meet the given timelines without any lapse."

The ICMR has selected 12 institutes, including one from Odisha, for the clinical trial of the country's first indigenous COVID-19 vaccine.

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.