Beautiful equations


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An equation means nothing to me unless it expresses a thought of GodSrinivasa Ramanujan 

To Ramanujan equations meant everything, for him illumination of a equation is enough and most of the time he did not pursue in getting the vigorous proof needed for it. For him all equations were divine in nature.

In his letter to Hardy Ramanujan claimed that he had found a function which exactly represented the number of prime numbers along with his many of his self found equations but no formula had been supplied in  the letter, worst of all the letters contained no proofs of anything. The letter also contained the following equation saying that Ramanujan had proved it.

1 + 2 + 3 + 4 +   ….∞ = – 1/12

Initially Hardy was convinced that this is a curious kind of fraud but latter that evening he along with Littlewood cracked the equation and realized how Ramanujan had rediscovered of how to define the missing part if Riemann’s zeta landscape.

1 + 2 + 3 +… + n + … = 1 + 1/2-1 + 1/3-1 + 1/4-1 + 1/5-1 + …+ 1/n-1 + … = -1/12

Bertrand Russell summarizes the excitement of Hardy and Littlewood on discovery of Ramanujan in the following words.

In Hall I found Hardy and Littlewood in a state of Wild excitement, because they believe they have discovered a second Newton, a Hindu clerk in
Madras on ₤20 a year”

Also check Mathematical Beauty


14 Responses to “Beautiful equations”

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  6. 6 nikhil kumar November 25, 2007 at 12:10 pm

    can i get more information about ramanujan….

  7. 7 yeskarthi July 26, 2006 at 5:58 pm

    Thanks for the info Jim. Keep frequenting!

  8. 8 jimw July 26, 2006 at 5:00 pm

    Another book recommendation: “The man who loved only numbers” – about Erdos.

  9. 9 S.Karthikeyan July 10, 2006 at 2:57 pm

    I had erred in one of my previous comment.

    “In end of nineteenth century Hilbert announced the ten great unsolved problems in Mathematics”

    Actually Hilbert addressed 23 mathematical problems in his lecture. You can find the complete list and their status at Mathworld.

    And it you have the computing bandwidth you can subscribe to ZetaGrid and help to illuminate the problem. Meanwhile in ZetaGrid you are not going to prove anything it’s just plain verification.

    Hilbert’s List :
    ZetaGrild :

  10. 10 yeskarthi July 10, 2006 at 1:38 pm

    Quoting Gp :did i tell you I admire ur ability to explore…

    No you didn’t 🙂

    Gp. There can be only one Ramujam. He did undergo a lot problems in UK. You can read Robert Kanigel’s biography on Ramanujam. I will post few of the tidbits about hime in future.

  11. 11 gp July 7, 2006 at 9:00 pm

    did i tell you I admire ur ability to explore…

    Ramanujan the greatest natural mathematician India and the world has known…I wanted to get the book about him.

    He faced many problems in uk, I dont know its true or not…but he tried to commit suicide a few times. The world has no special place for geniuses…either ur in the front page with some scandal or the science pages somewhere deep inside the paper in a small column.

    I dont think anyone can be like Ramanujan anymore…the information flood is killing creativity.

  12. 12 Venkat July 7, 2006 at 12:17 pm

    Oh thats wonderful your going to write more on maths!

  13. 13 S.Karthikeyan July 7, 2006 at 11:12 am

    Venkat. Yes I have read the book “The Man Who Knew Infinity” by Robert Kanigel. The book is great Also I read book in Kannada on Ramujam I don’t remember author’s name though.

    Even I can’t comprehend the Riemann’s Mathematics but once you read articles and books on his work it’s easy to appreciate the work. I will write about Riemann in comming post.

    As a prelude let me tell you that why Riemann’s hypothesis is taken so seriously. In end of nineteenth century Hilbert announced the ten great unsolved problems in Mathematics. It’s over 100 years now still one of the problem that ws on the list is yet to be cracked and that is Reimann’s hypothese. More on this on my future post.

    Note : Even my maths skills is at graduate level only 🙂

  14. 14 Venkat July 7, 2006 at 6:26 am

    Very interesting again Karthik. Have you read “The Man who knew Infinity”? It is a book about Ramanujan. I have not learnt enough maths to comprehend all of what you have included, hopefully this year or next year we should be learning all this stuff!

    Just a question for you, in the Riemman hypothesis, why is it being taken so seriously, considering its almost luck that got him that equation, or am I very wrong?

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