Friday, March 10, 2017

Math genius from India, Cambridge U. (video); Dhr. Seven, Ashley Wells (eds.), Wisdom Quarterly; Bhikkhu Dipa (video)

(Bhikkhu Dipa) Srinivasa Iyengar Ramanujan (Dec. 22, 1887-April 26, 1920) was an Indian mathematician and autodidact who lived during the time of the British Raj. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions.
Srinivasa Ramanujan (wiki)
The movie The Man Who Knew Infinity is about the Indian genius Srinivasa Ramanujan, who is generally viewed by mathematicians as one of the two most romantic figures in the discipline.

Ramanujan (1887-1920) was born and died in Southern India, passing away at the age of 32. [Suicide?] But in one of the most extraordinary events in mathematical history, he spent World War I at Trinity College Cambridge at the invitation of the leading British mathematician Godfrey Harold (G. H.) Hardy (1877-1947) and his great collaborator John E. Littlewood.
Brahmin wisdom comes from space
As a boy he refused to learn anything but mathematics, almost entirely self-taught, and his pre-Cambridge work is contained in a series of notebooks
The work he did after returning to India in 1919 is contained in the misleadingly named Lost Notebook. It was lost and later found in the Wren library of the leading college for mathematics of the leading University in England. While in England Ramanujan became the first Indian Fellow both of Trinity and of the Royal Society.
A Man of Numbers
Ramanujan had an extraordinary ability to see patterns. While he rarely proved his results, he left a host of evaluations of sums and integrals. He was especially expert in a part of number theory called modular forms which is of even more interest today than when he died.
The lost notebook initiated the study of mock theta functions that are only now being fully understood. Fleshing out his notebooks has only recently been completed principally by American mathematicians Prof. Bruce Berndt and Prof. George Andrews. It comprises thousands of printed pages.
An old Indian friend, Swami Swaminathan, oversaw the Ramanujan Library in Madras (modern Mumbai, India) over half a century ago. He commented that had Ramanujan been born ten years earlier, he would not have been able to receive the education and financial assistance that made his pre-Cambridge work possible.
Swaminathan went on to say that had Ramanujan been born just ten years later, he would probably have received a more robust and more ordinary education. In either case, this version of Ramanujan would not exist.
Ramanujan and Me
Ramanujan has been part of my life for as long as I can remember. My father David was a student of one of Hardy’s students. In our house “the Bible” referred to Hardy’s masterpiece Divergent Series.
In 1962 on the 75th anniversary of Ramanujan’s birth the envelope (below) arrived at my parents' home. A kind stranger had put the franked stamps on the back.

In 1987 I was fortunate enough to speak with my brother at the major centennial conference on Ramanujan, held at the University of Illinois. We had become experts on and had extended Ramanujan’s work on Pi.
Highlights at the conference included the Nobel prize winning astronomer Subrahmanyan Chandrasekhar, who described how important Ramanujan’s success in England had been to the self-confidence of himself and the co-founders (along with Mahatma Gandhi) of modern India including Jawaharlal Nehru, who became the first prime minister of independent India in 1947.
In 2008 David Leavitt published a novelized version of Ramanujan’s life entitled the Indian Clerk. While Leavitt captures much beautifully, as a novelist, he takes some considerable liberties. I prefer my novels as fables and my biographies straight.
In 2012 on the 125th anniversary of Ramanujan’s birth the Notices of the American Mathematical Society published eight articles on his work. This suite forcibly showed how Ramanujan’s reputation and impact continue to grow.
Gifted with Numbers
There is one famous anecdote about Ramanujan that even a non-mathematician can appreciate. In 1917 Ramanujan was hospitalized in London. He was said to have tuberculosis, but it is more likely this was to cover a failed suicide attempt.
Hardy took a cab to visit him. Not being very good at small talk, all Hardy could think to say was that the number of his cab, 1729, was uninteresting.
Ramanujan replied that quite to the contrary it was the smallest number expressible as a sum of two cubes in two distinct ways:
1,729 = 123 + 13 = 103 + 93
This is now known as Ramanujan’s taxi-cab number.
Mathematicians in the Movies
There has been a recent spate of books, plays, movies, and TV series about mathematicians and theoretical physicists: A Beautiful Mind (2001), Copenhagen (2002), Proof (2005) and last year’s Oscar winning movies The Imitation Game about Alan Turing, and The Theory of Everything on Stephen Hawking. More

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