Beautiful equations

Ramanujan 

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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

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16 Responses to “Beautiful equations”


  1. 1 tech adviser September 1, 2017 at 7:33 am

    Please write more. I found your page on my Reddit feed. Nice page.


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