Archive for the ‘MATHEMATICS’ Category

Srinivasa Ramanujan

Born: 22 Dec 1887 in Erode, Tamil Nadu state, India
Died: 26 April 1920 in Kumbakonam, Tamil Nadu state, India

The Man Who Knew Infinity – By Robert Kanigel

I think it was 1994 that I was introduced to this book by a dear friend Amit Nagar. I lived in Michigan and was about to move to NJ. Amit himself was relocating to NC. Being an avid fan of Ramanujam and a Pujari of Mathematics, thanks to my Guru in math for about 6 years – Shri Vijay Kumar, who not only instilled in me a passion for the subject, but also about the subject.

If I were to recall this book, I believe it is best done by visualizing this entire book as a documentary movie about the genius. I have captured the essence of my visualization aptly captured by these lines I found on the net. Why re-invent when most of the content captures the sentiments. Here you go….

If I were to script the movie, the initial credits would be superimposed on a high shot looking down on the delta of the river Cauvery in southeast India of a century ago. We slowly zoom down to a town; the sound track comes up with riverside noises, and we move with the camera to the life of a river market town in an exotic country. Of course the picture is incomplete; the audience will have to image the incredibly rich aromas—the spices in the market, the cooking odors. We would scan over to the quiet of the gigantic Hindu temple, foreign to western eyes in its architecture and its meaning. As the credits fade away, we would move down the street from the temple to the house of a poor, extremely devout, Brahmin family. This family is unremarkable in every way except for the intellectual talent of the boy studying on the porch. For purposes of our drama, his talent is also foreign and strange. He can play exotic mathematics in his mind. Numbers, symbols, series, functions. This is a play he must play alone, for there is no one else in India who has the talent to play on his level, or even to judge his skill. So he keeps a notebook of his play, sometimes writing over pencil with red ink to conserve paper.

In time, the scene shifts to another exotic location, a bowling green on the grounds of Trinity College, Cambridge, and focuses on one the premier mathematicians of his day. A powerful mathematician, member of the Royal Society; he is one of the main forces pulling British mathematics from the 200-year isolation it had imposed on itself after Newton into the modern subject seen on the continent. Confidant of Lytton Strachley, Leonard Woolf, Virginia Stephen. The camera loves his face. A graceful writer, rabid cricket fan, classic English athiest. A studied eccentric, gifted and barbed conversationalist, sophisticated and yet cloistered.

The drama is set, and the whole audience knows how it will unfold. Their subject will bring the two together. The Indian will go to England. Together, the two will produce wondrous mathematics, but the a price must be paid. The cultural difference is too much to overcome, and the Indian’s fidelity to his own way leads to the inevitable tragic denouement.

But the book is not fiction, rather a biography, and the inevitability is there only in hindsight. Srinvasa Ramanujan (accent on the second syllable) was born in 1887 with a mathematical gift–he attributed it to his family’s goddess Namagiri. Inspired by a totally undistinguished book (one much like a synopsis of GRE questions), his talent took off. At the time, his part of India was a portion of the British Raj, and education was meant to produce clerks and minor functionaries. He did not do well in school, flunking out of several, because he wanted only to do his mathematics. He worked in a series of petty jobs, moving from patron to patron. He wrote to British mathematicians, sending them samples of his work. George Hardy responded. He contrived to bring Ramanujan to England (Ramanujan at first would not go because of religious proscriptions), and Ramanujan arrived in 1913. From 1913 to 1918, though the war years, the two worked together. Ramanujan’s mathematical talent was singular, an intuition based on years of solitary exploration. Even today, his insights contain mysteries for researchers. He was made a fellow of the Royal Society and other prestigious societies, thanks in large part to Hardy’s insistence (among other things, there was racial animosity). In 1918, he returned to India, after some years of treatment in England for tuberculosis. He returned in intellectual triumph, but religious dishonor, for having left the country. After some personally and medically unpleasant months, he died in 1920.

These outlines of Ramanujan’s story are well-known in the mathematical and scientific communities. In India, he is a national figure. His country issued a stamp in his honor in 1962. His life has been the subject of western television documentaries. Hardy himself has written about Ramanujan, saying his “association with him was the one romantic incident in my life.” Robert Kanigel, an award-winning scientific journalist at Johns Hopkins, has revisited Ramanujan’s life, both geographically and intellectually. He travelled to India and England and interviewed everybody he could, especially including people who had known Ramanujan and people who have made Ramanujan’s mathematics their vocations. Kanigel has written a distinguished and thorough biography. It is not a technical scientific biography; there is a bare minimum of mathematics. Rather it is a social biography, putting Ramanujan and Hardy in their cultures, exploring the life of this beguiling man whose intellect could not remain in the India of the time, but whose being could not belong to western science, and who became an icon to both.

Kanigel presents new perspectives on Ramanujan’s life. For example, Hardy, who probably didn’t know Ramanujan the person very well, believed him not to be religious, and this has come to be the accepted wisdom. Kanigel makes a convincing case, that, on the contrary, Ramanujan was fanatically devout. His life turned on his religion as much as it turned on his mathematics and indeed he may not have dissociated the two. Consider the following from the book:

All his life, for festivals, or devotions, or just to pass the time, with his family or by himself, Ramanujan came to the temple. He’d grown up virtually in its shadow. Stepping out of his little house, he had but to turn his head to see, at the head of the street, close enough that he could make out the larger figures, the great gopuram. Indeed, the very street on which he lived bore the temple’s name… Here, to the sheltered columned coolness, Ramanujan would come. Here, away from the family, protected from the high hot sun outside, he would sometimes fall asleep in the middle of the day, his notebook, with its pages of mathematical scrawl, tucked beneath his arm, the stone slabs of the floor around him blanketed with equations inscribed in chalk.

Kanigel discusses Ramanujan’s need for recognition in terms of fellowships and honors. He gives considerable detail about Ramanujan’s family life in India (he had none in England), in particular the role of his mother. Kanigel also presents a new perspective on Ramanujan’s death. He discusses the modern medical theory that vitamin D deficiency reduces a body’s resistance to tuberculosis, and asserts that Ramanujan, a strict vegetarian in war-rationed England, would have had such a deficiency. Indeed then, as the romantic movie script would have it, the cultural dissonance did lead to the final tragedy.

Library shelves contain many biographies of people in literature and the arts, but proportionally few of scientific figures. This is a comment more on biographers than biographees. It is my impression that there is now a cadre of scientifically literate, talented writers who are opening up the worlds of science and scientific personalities to the general public. Both science and the public will benefit


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1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111


9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888







Brilliant, isn’t it?
And finally, take a look at this symmetry:


1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=123456789 87654321




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