Tag Archives: GH Hardy

AI chills and thrills, climate pledges, a Nazi haven, children’s lit, and a film about a genius: Facts, and Opinions, that matter this week

U.S. Secretary of State John Kerry kisses his two-year-old granddaughter Isabelle Dobbs-Higginson after signing the Paris Agreement on climate change at United Nations Headquarters in Manhattan, New York, U.S., April 22, 2016. REUTERS/Mike Segar

U.S. Secretary of State John Kerry kisses his two-year-old granddaughter Isabelle Dobbs-Higginson after signing the Paris Agreement on climate change at United Nations Headquarters in Manhattan, New York, U.S., April 22, 2016. REUTERS/Mike Segar

Reports:

Ban Ki-moon (2nd from R), Secretary-General of the United Nations, delivers his opening remarks at the Paris Agreement signing ceremony on climate change as French President Francois Hollande (2nd from L) looks on at the United Nations Headquarters in Manhattan, New York, U.S., April 22, 2016. REUTERS/Mike SegarChina, US, among those pledging to ratify Paris Agreement. By Michelle Nichols & Valerie Volcovici  Report

China and the United States, the world’s top producers of greenhouse gas emissions, pledged to formally adopt by the end of the year a Paris deal to slow global warming, raising the prospects of it being enforced much faster than anticipated. The United Nations said 175 states took the first step of signing the deal on April 22, the biggest day one endorsement of a global agreement.

Focus on Artificial Intelligence

Figure-1The chilling significance of AlphaGo. By Sheldon Fernandez  Magazine

In March, a computer named AlphaGo played the human world champion in a five-game match of Go, the ancient board game often described as the ‘Far East cousin’ of chess. That AlphaGo triumphed provoked curiosity and bemusement in the public — but is seen as hugely significant in the artificial intelligence and computer science communities. Computer engineer Sheldon Fernandez explains why.

The Sunflower Robot is a prototype that can carry objects and provide reminders and notifications to assist people in their daily lives. It uses biologically inspired visual signals and a touch screen, located in front of its chest, to communicate and interact with users. Photo by Thomas Farnetti for Wellcome/Mosaic, Creative CommonsA one-armed robot will look after me until I die. By Geoff Watts Magazine

I am persuaded by the rational argument for why machine care in my old age should be acceptable, but find the prospect distasteful – for reasons I cannot, rationally, account for. But that’s humanity in a nutshell: irrational. And who will care for the irrational human when they’re old? Care-O-bot, for one; it probably doesn’t discriminate.

And from earlier this year:

Product and graphic designer Ricky Ma, 42, gives a command to his life-size robot ''Mark 1'', modelled after a Hollywood star, in his balcony which serves as his workshop in Hong Kong, China March 31, 2016. Ma, a robot enthusiast, spent a year-and-a half and more than HK$400,000 ($51,000) to create the humanoid robot to fulfil his childhood dream. REUTERS/Bobby Yip SEARCH "ROBOT STAR" FOR THIS STORY. SEARCH "THE WIDER IMAGE" FOR ALL STORIESBuilding a humanoid Hollywood Star. By Bobby Yip  Report

The rise of robots and artificial intelligence are among disruptive labor market changes that the World Economic Forum projects will lead to a net loss of 5.1 million jobs over the next five years. Where will they come from? Why, we can make them ourselves. Or at least some of us can, and do.

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Commentary:

By Brian McMorrow - http://www.pbase.com/bmcmorrow/image/45156182, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=833719This Week’s Other Birthday, by Jonathan Manthorpe, International Affairs  column

Until quite recently, while Queen Elizabeth and her family were celebrating her birthday every April 21, a group of elderly men in south-west Africa were nursing the effects of the birthday toasts they had drunk the night before, to Adolf Hitler,  born on April 20, 1889. The men had been senior  Nazi officials, and had managed to escape capture by the Allies at the end of the Second World War. What is now Namibia offered a lasting sanctuary.

Why Bernie Sanders need to fight on … and surrender, by Tom Regan, Summoning Orenda Column

It looks like the end is nigh for the Sanders campaign. But it is absolutely necessary that Bernie not give up running. Yes, he should start to encourage his supporters to support Clinton. I am, however, totally in favor of him building up his delegate total and going into Philadelphia in late July demanding that the party’s platform reflect his point of view.

Those Healthy Yankees: Graham and Alcott, by Jim McNiven, Thoughtlines Column

Sylvester Graham and William Andrus Alcott were men of their disease-ridden times, amongst the first American promoters of “health food,” “phys-ed” and temperate living for health in both the here and now — and the afterlife.

The crew of the U.S. Coast Guard Cutter Healy, in the midst of their ICESCAPE mission, retrieves supplies in the Arctic Ocean in this July 12, 2011 NASA handout photo. Kathryn Hansen/NASA via REUTERS/File PhotoAfter Paris climate pact, let’s get personal. By Gwynne Taraska and Shiva Polefka  Loose Leaf salon Column

Reengineering global economic dependence on carbon pollution requires conscious commitment and action from individuals as well as governments and corporations.

Arts:

image-20160421-30266-12jsnvsHow GH Hardy tamed Srinivasa Ramanujan’s genius. By Béla Bollobás   Report

Throughout the history of mathematics, there has been no one remotely like Srinivasa Ramanujan. There is no doubt that he was a great mathematician, but had he had simply a good university education and been taught by a good professor in his field, we wouldn’t have a film about him. Credit is due to GH Hardy.

Why children’s books are serious literature. By Catherine Butler Report

Once a generation, it seems, a cri de coeur goes out, in which a representative of the world of children’s literature speaks with revelatory authority to the literary establishment and makes it reassess the place of children’s books.

Last but not least: alongside the many musical tributes to the American artist Prince, who died this week at age 57, his appearance on the Muppets should not be missed:

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How GH Hardy tamed Srinivasa Ramanujan’s genius

By Béla Bollobás, University of Cambridge
April, 2016

Jeremy Irons as GH Hardy and Dev Patel as Srinivasa Ramanujan in The Man Who Knew Infinity. Warner Bros publicity photo

Jeremy Irons as GH Hardy and Dev Patel as Srinivasa Ramanujan in The Man Who Knew Infinity. Warner Bros publicity photo

Throughout the history of mathematics, there has been no one remotely like Srinivasa Ramanujan. There is no doubt that he was a great mathematician, but had he had simply a good university education and been taught by a good professor in his field, we wouldn’t have a film about him.

As the years pass, I admire more and more the astonishing body of work Ramanujan produced in India before he made contact with any top mathematicians. Not because the results he got at the time changed the face of mathematics, far from it, but because, working by himself, he fearlessly attacked many important and some not so important problems in analysis and, especially, number theory – simply for the love of mathematics.

It cannot be understated, however, the role played by Ramanujan’s tutor Godfrey Harold Hardy in his life story. The Cambridge mathematician worked tirelessly with the Indian genius, to tame his creativity within the then current understanding of the field. It was only with Hardy’s care and mentoring that Ramanujan became the scholar we know him as today.

In December 1903, at the age of 16, Ramanujan passed the matriculation exam for the University of Madras. But as he concentrated on mathematics to the exclusion of all other subjects, he did not progress beyond the second year. In 1909 he married a nine-year-old girl, but failed to secure any steady income until the beginning of 1912, when he became a clerk in the Madras Port Trust office on a meagre salary.

All this time, Ramanujan remained obsessed with mathematics and kept working on continued fractions, divergent series, elliptic integrals, hypergeometric series and the distribution of primes. By 1911, Ramanujan was desperate to gain recognition from leading mathematicians, especially those in England. So, at the beginning of 1913, when he was just past 25, he dispatched a letter to Hardy in Cambridge with a long list of his discoveries –- a letter which changed both their lives.

Although only 36 when he received Ramanujan’s letter, Hardy was already the leading mathematician in England. The mathematical scene in England in the first half of the 20th century was dominated by Hardy and another titan of Trinity College, J.E. Littlewood. The two formed a legendary partnership, unique to this day, writing an astounding 100 joint papers. They were instrumental in turning England into a superpower in mathematics, especially in number theory and analysis.

Hardy was not the first mathematician to whom Ramanujan had sent his results, however the first two to whom he had written judged him to be a crank. But Hardy was not only an outstanding mathematician, he was also a wonderful teacher, eager to nurture talent.

After dinner in Trinity one evening, some of the fellows adjourned to the combination room. Over their claret and port Hardy mentioned to Littlewood some of the claims he had received in the mail from an unknown Indian. Some assertions they knew well, others they could prove, others they could disprove, but many they found not only fascinating and unusual but also impossible to resolve.

This toing and froing between Hardy and Littlewood continued the next day and beyond, and soon they were convinced that their correspondent was a genius. So Hardy sent an encouraging reply to Ramanujan, which led to a frequent exchange of letters.

It was clear to Hardy that Ramanujan was totally exceptional: however, in spite of his amazing feats in mathematics, he lacked the basic tools of the trade of a professional mathematician. Hardy knew that if Ramanujan was to fulfil his potential, he had to have a solid foundation in mathematics, at least as much as the best Cambridge graduates.

It was for Ramanujan’s good that Hardy invited him to Cambridge, then, and he was taken aback when, due to caste prejudices, Ramanujan did not jump at the chance. As a Brahmin, Ramanujan was not allowed to cross the ocean and his mother was totally opposed to the idea of the voyage. When, in early 1914, Ramanujan gained his mother’s consent, Hardy swang into action. He asked E.H Neville, another fellow of Trinity College, who was on a serendipitous trip to Madras, to secure Ramanujan a scholarship from the University of Madras. Neville’s wrote in a letter to the university that “the discovery of the genius of S. Ramanujan of Madras promises to be the most interesting event of our time in the mathematical world …”

Ramanujan sailed for England in the company of Neville, and arrived in Cambridge in April 1914.

I cannot but admire Hardy for his care in mentoring Ramanujan. His main worry was how to teach this astounding talent much mathematics without destroying his confidence. The last thing Hardy wanted was to dent Ramanujan’s fearless approach to the most difficult problems. To quote Hardy:

The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations, and theorems of complex multiplication, to orders unheard of, whose mastery of continued fractions was, on the formal side at any rate, beyond that of any mathematician in the world … It was impossible to ask such a man to submit to systematic instruction, to try to learn mathematics from the beginning once more.

On the other hand there were things of which it was impossible that he would remain in ignorance … so I had to try to teach him, and in a measure I succeeded, though I obviously learnt from him much more than he learnt from me.

For almost three years, things went extremely well. In 1916 Ramanujan got his BA from Cambridge and his research went from strength to strength. He published one excellent paper after another, with a great deal of Hardy’s help in the proofs and presentation. They also collaborated on several great projects, and published wonderful joint papers. Sadly, in the spring of 1917 Ramanujan fell ill, and was in and out of sanatoria for the rest of his stay in Cambridge.

By early 1919 Ramanujan seemed to have recovered sufficiently, and decided to travel back to India. Hardy was alarmed not to have heard from him for a considerable time, but a letter in February 1920 made it clear that Ramanujan was very active in research.

Ramanujan’s letter contained some examples of his latest discovery, mock theta functions, which have turned out to be very important. A main conjecture about them was solved 80 years later, and these functions are now seen as interesting examples of a much larger class of mock modular forms in mathematics, which have applications to elliptic curves, Borcherds products, Eichler cohomology and Galois representations – and the nature of black holes.

Sadly, Ramanujan’s recovery was short-lived. His illness returned and killed him, aged just 32, on April 26 1920, leaving him only a short time to benefit from his fellowship of the Royal Society and fellowship of Trinity.

Ramanujan’s death at the height of his powers was a tremendous blow to mathematics. His like may never be seen again, and certainly such a partnership as that which Hardy and Ramanujan built will not either.

The ConversationCreative Commons

Béla Bollobás is a Professor of Pure Mathematics  at the University of Cambridge. This article was originally published on The Conversation. Read the original article.

The trailer for Warner Bros. film The Man Who Knew Infinity, released in April.

 

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Facts and Opinions is a boutique journal of reporting and analysis in words and images, without borders. Independent, non-partisan and employee-owned, F&O is funded by our readers. It is ad-free and spam-free, and does not solicit donations from partisan organizations. To continue we require a minimum payment of .27 for one story, or a sustaining donation. Details here; donate below. Thanks for your interest and support.

F&O’s CONTENTS page is updated each Saturday. Sign up for emailed announcements of new work on our free FRONTLINES blog; find evidence-based reporting in Reports; commentary, analysis and creative non-fiction in OPINION-FEATURES; and image galleries in PHOTO-ESSAYS. If you value journalism please support F&O, and tell others about us.

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