On 2/17/2013 7:56 AM, Bruno Marchal wrote:

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On 13 Feb 2013, at 04:29, socra...@bezeqint.net wrote:

After proving Euler's identity during a lecture, Benjamin Peirce,
a noted American 19th-century philosopher, mathematician,
and professor at Harvard University, stated that
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, but we have proved it,
and therefore we know it must be the truth."
#
Stanford University mathematics professor Keith Devlin said,
"Like a Shakespearean sonnet that captures the very essence
of love, or a painting that brings out the beauty of the human
form that is far more than just skin deep, Euler's Equation reaches
down into the very depths of existence."
http://en.wikipedia.org/wiki/Euler's_identity
=====..
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, . . . . .’
. . . but . . .
‘ Euler's Equation reaches down into the very depths of existence."
===..

Yes. Euler identity is wonderful.

`It amazes me also that it makes the square of any complex number into a (non normalized)
``gaussian:
`(e^ix)^2 = e^(-x^2)

?? (e^ix)^2 = e^(2ix)
Brent

`I love also Euler even deeper identity relating the square of the integers and the prime
``numbers:
`

`Sum from n = 1 to infinity of 1/n^s = Product on all primes p of (1/(1- 1/p^s). This led
``Riemann to the deeper of all open problem in math
`(Riemann hypothesis).

`Ramanujan found quite amazing number relations. Some are so deep that they link
``gravitation, quantum computing, prime numbers, string theory and the arithmetic of the
``integers, all given a key role to the number 24.
`
Jacobi found amazing relations too, involving 24.

`Math is full of surprising relations. That's a reason, I think, to believe in their
``objectivity or 3p-independence.
`
Bruno

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