5 ms·

The legacy of Srinivasa Ramanujan

238 points by rehack 15y ago

rehack 15y ago
"Ramanujan cultivated his love for mathematics singlehandedly and in total isolation" ... "At the age of 12, he borrowed from a friend a copy of Loney's book on Plane Trigonometry, published by Cambridge University Press in 1894"... "It is not a remarkable book, and Ramanujan's use of it to propel himself to the centre stage of 20th century mathematics, has made the book remarkable. It was largely used by students of Carr who were preparing for the entrance examination in mathematics at Cambridge University. Ramanujan used the book to master all of 18th and 19th century mathematics. He set about to demonstrate each of the assertions of the book, using only his slate to do the calculations. He would jot down the formula to be proved, and then erase it with his elbow, and then continue to jot down some more formulas. In this way, he worked through the entire book. People used to speak of his “bruised elbow.” Sadly, he took Carr's book as a model for mathematical writing and left behind his famous notebooks containing many formulas but practically no proofs."
- huhtenberg 15y ago
  I remember once going to see him [Ramanujan] when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways. Courtesy of G.H.Hardy
  - rehack 15y ago
    Indeed. http://en.wikipedia.org/wiki/1729_(number) http://en.wikipedia.org/wiki/1729_(number)
    - ricksta 15y ago
      Did he just figured that out on the spot when his ill or knew it from before?
      - top_commenter 15y ago
        I have a feeling that even he would not be able to tell you the answer to that question if he were alive!
      - abhaga 15y ago
        I think Kanigel's book talks about this. It seems he had worked through first few thousand numbers and knew all of them quite well. Thus instead of a spark of genius, this seems to be a fruit of years worth of hard work and an excellent memory.
        Someone 15y ago
        Few thousand? There are only 12 third powers below 1729: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728. Spotting that 729 + 1000 almost is equal to 1728 is not hard, either. Everybody who has computed that list will have noticed it. Translating that observation into a concise, interesting description is not hard, either, but it does require creativity. That, he had way more than most. I wonder what he would have said about the pair 3^5 and 7^3 (243 and 343)
        LearnYouALisp 15y ago
        The first few thousand integers, and knew their properties quite well; that seems to be what is meant.
      - josyula 15y ago
        He was a genius,Yet shy person ,Its said that he also gave properties of many other numbers which were not documented by anyone, But only Hardy knew them and would tell it to others.
signa11 15y ago
robert-kanigel's book, "the man who knew infinity" is an excellent chronicle into his life, and cambridge's culture during 20th century. it was hardy who created a rising scale of mathematical abilities as follows: g.h.hardy - 25 littlewood - 30 hilbert - 80 ramanujan - 100 hardy once described the formulas in ramanujan's first letters as "these must be true, if they are not, nobody would have the audacity to invent it."
- rehack 15y ago
  You might also like to read this interview of Kanigel on his book and how he researched on Ramanujan. http://www.thehindu.com/opinion/interview/article2747541.ece http://www.thehindu.com/opinion/interview/article2747541.ece PS: I was half inclined to share this interview (instead of the article, this is also quite interesting)
  - signa11 15y ago
    wow ! it definitely is pretty interesting. thanks for sharing.
mcl 15y ago
yeah thats right! vote up indians while the west is busy celebrating.
- rounak 15y ago
  greatness doesn't know a country
impendia 15y ago
Ramanujan's second letter to Hardy [1]: "Dear Sir, I am very much gratified on perusing your letter of the 8th February 1913. I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalls of divergent series. … I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + ... = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. ..." [1] http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4 http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4
jeswin 15y ago
Maybe it is just me, but overstating anyone's impact to this extent is disrespectful to that person. "....wealth of ideas that have transformed and reshaped 20th century mathematics" "His work has had a fundamental role in the development of 20th century mathematics" Maybe someone who has delved deeper into math can shine some light here.
- microarchitect 15y ago
  Not a mathematician, but some references I found after goolging a bit: [1] "The meaning of Ramanujam now and for the future", George E. Andrews. http://www.math.psu.edu/andrews/pdf/274.pdf http://www.math.psu.edu/andrews/pdf/274.pdf [2] "The Ramanujam Journal", http://www.springer.com/mathematics/numbers/journal/11139 http://www.springer.com/mathematics/numbers/journal/11139 Quote from the conclusion of [1]: In his Presidential address to the London Mathematical Society in 1936, G. N. Watson spoke movingly of his emotional response to Ramanujan's achievements. I close by quoting his last few paragraphs [54; p. 80]: "The study of Ramanujan's work and of the problems to which it gives rise inevitably recalls to mind Lame's remark that, when reading Hermite's papers on modular functions, \on a la chair de poule." I would express my own attitude with more prolixity by saying that such a formula as: <snipped formula> gives me a thrill which is indistinguishable from the thrill which I feel when I enter the Sagrestia Nuova of the Capelle Medicee and see before me the austere beauty of the four statues representing Day, Night, Evening, and Dawn which Michelangelo has set over the tombs of Guiliano de Medici and Lorenzo de Medici. Ramanujan's discovery of the mock theta functions makes it obvious that his skill and ingenuity did not desert him at the oncoming of his untimely end. As much as any of his earlier work, the mock theta functions are an achievement sucient to cause his name to be held in lasting remembrance" To me, it's interesting that a community where fairly easy to build web-applications are called transformative and disruptive also has two out of thirteen comments critical of Ramanujam's impact.
  - jeswin 15y ago
    Being critical of the article is not the same as being critical of Ramanujan's impact. So, there isn't a need to down vote. I am genuinely interested in knowing what Ramanujan did to "transform and reshape" 20th century mathematics.
medius 15y ago
Whenever I think about Ramanujan, I cannot help but wonder how many Ramanujans are out there that are just not visible and struggling with poverty.
rhizome 15y ago
I believe there are at least several previouslies for this guy.

238 points by rehack 15y ago

"Ramanujan cultivated his love for mathematics singlehandedly and in total isolation" ... "At the age of 12, he borrowed from a friend a copy of Loney's book on Plane Trigonometry, published by Cambridge University Press in 1894"... "It is not a remarkable book, and Ramanujan's use of it to propel himself to the centre stage of 20th century mathematics, has made the book remarkable. It was largely used by students of Carr who were preparing for the entrance examination in mathematics at Cambridge University. Ramanujan used the book to master all of 18th and 19th century mathematics. He set about to demonstrate each of the assertions of the book, using only his slate to do the calculations. He would jot down the formula to be proved, and then erase it with his elbow, and then continue to jot down some more formulas. In this way, he worked through the entire book. People used to speak of his “bruised elbow.” Sadly, he took Carr's book as a model for mathematical writing and left behind his famous notebooks containing many formulas but practically no proofs."

huhtenberg 15y ago
I remember once going to see him [Ramanujan] when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways. Courtesy of G.H.Hardy
- rehack 15y ago
  Indeed. http://en.wikipedia.org/wiki/1729_(number) http://en.wikipedia.org/wiki/1729_(number)
  - ricksta 15y ago
    Did he just figured that out on the spot when his ill or knew it from before?
    - top_commenter 15y ago
      I have a feeling that even he would not be able to tell you the answer to that question if he were alive!
    - abhaga 15y ago
      I think Kanigel's book talks about this. It seems he had worked through first few thousand numbers and knew all of them quite well. Thus instead of a spark of genius, this seems to be a fruit of years worth of hard work and an excellent memory.
      - Someone 15y ago
        Few thousand? There are only 12 third powers below 1729: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728. Spotting that 729 + 1000 almost is equal to 1728 is not hard, either. Everybody who has computed that list will have noticed it. Translating that observation into a concise, interesting description is not hard, either, but it does require creativity. That, he had way more than most. I wonder what he would have said about the pair 3^5 and 7^3 (243 and 343)
        LearnYouALisp 15y ago
        The first few thousand integers, and knew their properties quite well; that seems to be what is meant.
    - josyula 15y ago
      He was a genius,Yet shy person ,Its said that he also gave properties of many other numbers which were not documented by anyone, But only Hardy knew them and would tell it to others.

signa11 15y ago

robert-kanigel's book, "the man who knew infinity" is an excellent chronicle into his life, and cambridge's culture during 20th century. it was hardy who created a rising scale of mathematical abilities as follows: g.h.hardy - 25 littlewood - 30 hilbert - 80 ramanujan - 100 hardy once described the formulas in ramanujan's first letters as "these must be true, if they are not, nobody would have the audacity to invent it."

rehack 15y ago
You might also like to read this interview of Kanigel on his book and how he researched on Ramanujan. http://www.thehindu.com/opinion/interview/article2747541.ece http://www.thehindu.com/opinion/interview/article2747541.ece PS: I was half inclined to share this interview (instead of the article, this is also quite interesting)
- signa11 15y ago
  wow ! it definitely is pretty interesting. thanks for sharing.

mcl 15y ago

yeah thats right! vote up indians while the west is busy celebrating.

rounak 15y ago
greatness doesn't know a country

impendia 15y ago

Ramanujan's second letter to Hardy [1]: "Dear Sir, I am very much gratified on perusing your letter of the 8th February 1913. I was expecting a reply from you similar to the one which a Mathematics Professor at London wrote asking me to study carefully Bromwich's Infinite Series and not fall into the pitfalls of divergent series. … I told him that the sum of an infinite number of terms of the series: 1 + 2 + 3 + 4 + ... = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. ..." [1] http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4 http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4

jeswin 15y ago

Maybe it is just me, but overstating anyone's impact to this extent is disrespectful to that person. "....wealth of ideas that have transformed and reshaped 20th century mathematics" "His work has had a fundamental role in the development of 20th century mathematics" Maybe someone who has delved deeper into math can shine some light here.

microarchitect 15y ago
Not a mathematician, but some references I found after goolging a bit: [1] "The meaning of Ramanujam now and for the future", George E. Andrews. http://www.math.psu.edu/andrews/pdf/274.pdf http://www.math.psu.edu/andrews/pdf/274.pdf [2] "The Ramanujam Journal", http://www.springer.com/mathematics/numbers/journal/11139 http://www.springer.com/mathematics/numbers/journal/11139 Quote from the conclusion of [1]: In his Presidential address to the London Mathematical Society in 1936, G. N. Watson spoke movingly of his emotional response to Ramanujan's achievements. I close by quoting his last few paragraphs [54; p. 80]: "The study of Ramanujan's work and of the problems to which it gives rise inevitably recalls to mind Lame's remark that, when reading Hermite's papers on modular functions, \on a la chair de poule." I would express my own attitude with more prolixity by saying that such a formula as: <snipped formula> gives me a thrill which is indistinguishable from the thrill which I feel when I enter the Sagrestia Nuova of the Capelle Medicee and see before me the austere beauty of the four statues representing Day, Night, Evening, and Dawn which Michelangelo has set over the tombs of Guiliano de Medici and Lorenzo de Medici. Ramanujan's discovery of the mock theta functions makes it obvious that his skill and ingenuity did not desert him at the oncoming of his untimely end. As much as any of his earlier work, the mock theta functions are an achievement sucient to cause his name to be held in lasting remembrance" To me, it's interesting that a community where fairly easy to build web-applications are called transformative and disruptive also has two out of thirteen comments critical of Ramanujam's impact.
- jeswin 15y ago
  Being critical of the article is not the same as being critical of Ramanujan's impact. So, there isn't a need to down vote. I am genuinely interested in knowing what Ramanujan did to "transform and reshape" 20th century mathematics.

medius 15y ago

Whenever I think about Ramanujan, I cannot help but wonder how many Ramanujans are out there that are just not visible and struggling with poverty.

rhizome 15y ago

I believe there are at least several previouslies for this guy.