India celebrates the man who 'knew' infinity

http://www.atimes.com/atimes/South_Asia/NA10Df02.html

Jan 10, 2012

India celebrates the man who 'knew' infinity

By Raja Murthy

So the soul of immensity dwells in minutia.

And in narrowest limits no limits in here.

What joy to discern the minute in infinity!

The vast to perceive in the small, what divinity!

- Mathematician Jakob Bernoulli (1654-1705), quoted in Five Fingers to Infinity

MUMBAI - India has declared 2012 as "National Year of Mathematics" as tribute to Srinivasa Ramanujan, an enigmatic maths maverick who despite dying aged just 32 had already achieved enough to still be spoken of alongside Isaac Newton, Euclid and Archemedes.

"Men and women of such dazzling brilliance and deep intellect are born but rarely," declared Prime Minister Manmohan Singh in Chennai at a function on December 26, to celebrate the 125th birth anniversary of Ramanujan (December 22, 1887-April 26, 1920). The Indian government has also announced Ramanujan's birthday would be celebrated every year as "National Mathematics Day".

Mathematics, as Manmohan pointed out, is the "mother science", the universal language of truth through numbers, touching daily use, technology and life - working out time, distance, calendar, the grocery prices and passenger air craft navigation, from algorithms in Internet search engines, to creating secure credit card transactions and planning national budgets.

Where there is a civilization, there are numbers. And whatever happens in this world and to this world, two plus two will always equal four, and will be so for infinity remain as a truth verifiable in the five fingers of one hand.

Celebrating Ramanujan and reviving mathematics is part of India's greater plan to invest more in science training. Countries like China have overtaken India in science, said Manmohan while inaugurating the 99th Indian Science Congress on January 3, in the eastern coast city of Bhubaneswar.

Ramanujan is part of a rich, 1,500 years-old Indian heritage of mathematics and astronomy. Luminaries like Brahmagupta in the 6th century AD, Bhaskara (600-680 AD) Sankara Narayana (840-900 AD) and Vijayanandi (940-1010 AD) created and built upon the foundations of science as we know it today.

Perhaps the greatest of them all was Aryabhata (476- 550 AD), who gave the world the concept and number "zero". He was just 23 years old when the first of his works became known. He calculated the circumference of the Earth, found that the Earth spins on its axis and revolves round the sun. He also realized that the moon was a satellite of the Earth.

India named its first satellite launched in April 1975 "Aryabhata". Like Ramanujan, many of his findings were lost and some that survived continue to baffle scientists. [1].

Ramanujan carried on Aryabhata's work. Aryabhata approximated the value of "pi" - the circumference of a circle divided by the diameter. They mystical value of pi, beyond the decimal point after 3, is said to stretch to infinity, and to contain unknown significance.

American astronomer Carl Sagan in his bestseller Contact had an extra terrestrial civilization transmitting a message to Earth encoded in the value of pi. Ramanujan continued Aryabhata's work in his 1914/1916 paper on Modular Equations and Approximations to pi, or computing pi to a billion digits [2] - on the journey of numbers to infinity.

The legend of Ramanujan is heading for more international exposure through two commercial movies in the making. British film maker Roger Spottiswoode, director of the 1997 James Bond movie Tomorrow Never Dies, has started work on Ramanujan film titled A First Class Man, with American scriptwriter David Freeman.

Robert Kanigal, author of the acclaimed Ramanujan biography The man who knew Infinity, is working with director Matt Brown in a film of the same title as the book. New York-based film maker Mira Nair is executive producer.

Like many others in the genius tribe, Ramanujan was a child prodigy. Nothing comes from nowhere, and genius is nature at work across lifetimes. Extraordinary genius is the long-term effect of a cause at work. Each person is not just the sum total of all one's work in this lifetime, but of previous lifetimes.

Which is why geniuses are not merely born or made, but they continue from where they left off. Those succeeding dazzlingly in this lifetime are those have continued to work very hard work to build, hone their talents and merits accumulated in the past. Ramanujan had a day job as a clerk, but slogged all night with his numbers until 6.00 am.

The genius of the man was seen in the child. By age 12, when kids develop a deadly dread for arithmetic class, Ramanujan was creating theorems of his own. In college in 1904, he was redefining mathematical concepts in fields such as numbers theory and analysis, including in the related Bernoulli numbers - the work of 17th century Swiss mathematician Jakob Bernoulli.

The boy Ramanujan taught himself from advanced text books such as G S Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics, and also added his own discoveries to the 6,165 theorems in the tome.

Ramanujan's new concepts like mock theta functions [3] continue to influence and fascinate 21st-century mathematicians. To them, exploring Ramanujan's works, found in loosely collected "notebooks", is a Holy Grail of numbers.

Bruce Berndt is one such explorer of Ramanujan's genius. A leading mathematician from the College of Liberal Arts and Sciences, University Illinois,, Berndt and G E Andrews - who discovered the "Lost Notebook" in Britain's Trinity College, Cambridge University, in 1976 - have published multiple volumes containing proofs of over 600 mathematical formulas Ramanujan left as legacy.

Berndt told the College of Liberal Arts Alumni newsletter, "The discovery of this 'Lost Notebook' [in Cambridge University] caused roughly as much stir in the mathematical world as the discovery of Beethoven's 10th symphony would cause in the musical world."

It was in Cambridge University that Ramanujan first came to the notice of the Western world, through G H Hardy, a well-known mathematician at Trinity College. In 1913, Hardy received a letter from Ramanujan containing 120 theorems as a representative sample of his work. Hardy recognized some of the formulas, but many baffled him.

It took Hardy over five hours of analyzing the theorems to realize that the letter writer from faraway India was not some nutcase, but a rare genius. "They [theorems] must be true," Hardy reasoned, "because if they were not true, no one would have had the imagination to invent them.'' Hardy arranged for Ramanujan to travel to England and work at Trinity College.

"Thus began one of the most productive and unusual scientific collaborations in history," wrote Professor Kanigel of the Massachusetts Institute of Technology, "that of an English don and an impoverished Hindu genius whose like has never been seen again."

The life of the genius lasted only for seven more years. Ramanujan died in 1920 from a suspected stomach infection. His wife Janaki said he was working with numbers even on his death bed.

Ramanujan's work lives on. "Many scientists from around the world have testified that they gained inspiration from the life of Ramanujan," said Ram Murty and Kumar Murty, senior mathematics professors from the Queen's University and University of Toronto, Canada, in the Chennai-based daily Hindu. "As long as the spirit of inquiry is alive, his legacy will pass from one generation to the next."

Notes

1. Brief biography of Aryabhata, School of Mathematics and Statistics, University of St Andrews, Scotland.

2. Ramanujan, Modular Equations, and Approximations to Pi - article by David H Bailey, Jonathan M Borwein, Peter B Borwein. Published by Mathematics Association of America, 1993.

3. Puzzle Solved: Ramanujan's Mock Theta Conjectures, Mathematical Association of America.

(Copyright 2012 Asia Times Online (Holdings) Ltd. All rights reserved. Please contact us about sales, syndication and republishing

Jan 10, 2012

India celebrates the man who 'knew' infinity

By Raja Murthy

So the soul of immensity dwells in minutia.

And in narrowest limits no limits in here.

What joy to discern the minute in infinity!

The vast to perceive in the small, what divinity!

- Mathematician Jakob Bernoulli (1654-1705), quoted in Five Fingers to Infinity

MUMBAI - India has declared 2012 as "National Year of Mathematics" as tribute to Srinivasa Ramanujan, an enigmatic maths maverick who despite dying aged just 32 had already achieved enough to still be spoken of alongside Isaac Newton, Euclid and Archemedes.

"Men and women of such dazzling brilliance and deep intellect are born but rarely," declared Prime Minister Manmohan Singh in Chennai at a function on December 26, to celebrate the 125th birth anniversary of Ramanujan (December 22, 1887-April 26, 1920). The Indian government has also announced Ramanujan's birthday would be celebrated every year as "National Mathematics Day".

Mathematics, as Manmohan pointed out, is the "mother science", the universal language of truth through numbers, touching daily use, technology and life - working out time, distance, calendar, the grocery prices and passenger air craft navigation, from algorithms in Internet search engines, to creating secure credit card transactions and planning national budgets.

Where there is a civilization, there are numbers. And whatever happens in this world and to this world, two plus two will always equal four, and will be so for infinity remain as a truth verifiable in the five fingers of one hand.

Celebrating Ramanujan and reviving mathematics is part of India's greater plan to invest more in science training. Countries like China have overtaken India in science, said Manmohan while inaugurating the 99th Indian Science Congress on January 3, in the eastern coast city of Bhubaneswar.

Ramanujan is part of a rich, 1,500 years-old Indian heritage of mathematics and astronomy. Luminaries like Brahmagupta in the 6th century AD, Bhaskara (600-680 AD) Sankara Narayana (840-900 AD) and Vijayanandi (940-1010 AD) created and built upon the foundations of science as we know it today.

Perhaps the greatest of them all was Aryabhata (476- 550 AD), who gave the world the concept and number "zero". He was just 23 years old when the first of his works became known. He calculated the circumference of the Earth, found that the Earth spins on its axis and revolves round the sun. He also realized that the moon was a satellite of the Earth.

India named its first satellite launched in April 1975 "Aryabhata". Like Ramanujan, many of his findings were lost and some that survived continue to baffle scientists. [1].

Ramanujan carried on Aryabhata's work. Aryabhata approximated the value of "pi" - the circumference of a circle divided by the diameter. They mystical value of pi, beyond the decimal point after 3, is said to stretch to infinity, and to contain unknown significance.

American astronomer Carl Sagan in his bestseller Contact had an extra terrestrial civilization transmitting a message to Earth encoded in the value of pi. Ramanujan continued Aryabhata's work in his 1914/1916 paper on Modular Equations and Approximations to pi, or computing pi to a billion digits [2] - on the journey of numbers to infinity.

The legend of Ramanujan is heading for more international exposure through two commercial movies in the making. British film maker Roger Spottiswoode, director of the 1997 James Bond movie Tomorrow Never Dies, has started work on Ramanujan film titled A First Class Man, with American scriptwriter David Freeman.

Robert Kanigal, author of the acclaimed Ramanujan biography The man who knew Infinity, is working with director Matt Brown in a film of the same title as the book. New York-based film maker Mira Nair is executive producer.

Like many others in the genius tribe, Ramanujan was a child prodigy. Nothing comes from nowhere, and genius is nature at work across lifetimes. Extraordinary genius is the long-term effect of a cause at work. Each person is not just the sum total of all one's work in this lifetime, but of previous lifetimes.

Which is why geniuses are not merely born or made, but they continue from where they left off. Those succeeding dazzlingly in this lifetime are those have continued to work very hard work to build, hone their talents and merits accumulated in the past. Ramanujan had a day job as a clerk, but slogged all night with his numbers until 6.00 am.

The genius of the man was seen in the child. By age 12, when kids develop a deadly dread for arithmetic class, Ramanujan was creating theorems of his own. In college in 1904, he was redefining mathematical concepts in fields such as numbers theory and analysis, including in the related Bernoulli numbers - the work of 17th century Swiss mathematician Jakob Bernoulli.

The boy Ramanujan taught himself from advanced text books such as G S Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics, and also added his own discoveries to the 6,165 theorems in the tome.

Ramanujan's new concepts like mock theta functions [3] continue to influence and fascinate 21st-century mathematicians. To them, exploring Ramanujan's works, found in loosely collected "notebooks", is a Holy Grail of numbers.

Bruce Berndt is one such explorer of Ramanujan's genius. A leading mathematician from the College of Liberal Arts and Sciences, University Illinois,, Berndt and G E Andrews - who discovered the "Lost Notebook" in Britain's Trinity College, Cambridge University, in 1976 - have published multiple volumes containing proofs of over 600 mathematical formulas Ramanujan left as legacy.

Berndt told the College of Liberal Arts Alumni newsletter, "The discovery of this 'Lost Notebook' [in Cambridge University] caused roughly as much stir in the mathematical world as the discovery of Beethoven's 10th symphony would cause in the musical world."

It was in Cambridge University that Ramanujan first came to the notice of the Western world, through G H Hardy, a well-known mathematician at Trinity College. In 1913, Hardy received a letter from Ramanujan containing 120 theorems as a representative sample of his work. Hardy recognized some of the formulas, but many baffled him.

It took Hardy over five hours of analyzing the theorems to realize that the letter writer from faraway India was not some nutcase, but a rare genius. "They [theorems] must be true," Hardy reasoned, "because if they were not true, no one would have had the imagination to invent them.'' Hardy arranged for Ramanujan to travel to England and work at Trinity College.

"Thus began one of the most productive and unusual scientific collaborations in history," wrote Professor Kanigel of the Massachusetts Institute of Technology, "that of an English don and an impoverished Hindu genius whose like has never been seen again."

The life of the genius lasted only for seven more years. Ramanujan died in 1920 from a suspected stomach infection. His wife Janaki said he was working with numbers even on his death bed.

Ramanujan's work lives on. "Many scientists from around the world have testified that they gained inspiration from the life of Ramanujan," said Ram Murty and Kumar Murty, senior mathematics professors from the Queen's University and University of Toronto, Canada, in the Chennai-based daily Hindu. "As long as the spirit of inquiry is alive, his legacy will pass from one generation to the next."

Notes

1. Brief biography of Aryabhata, School of Mathematics and Statistics, University of St Andrews, Scotland.

2. Ramanujan, Modular Equations, and Approximations to Pi - article by David H Bailey, Jonathan M Borwein, Peter B Borwein. Published by Mathematics Association of America, 1993.

3. Puzzle Solved: Ramanujan's Mock Theta Conjectures, Mathematical Association of America.

(Copyright 2012 Asia Times Online (Holdings) Ltd. All rights reserved. Please contact us about sales, syndication and republishing