On 2/17/2013 10:56 AM, Bruno Marchal wrote:
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)
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
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.
Why is it surprising? We have finite brains that can only know so
much and have languages that can only represent a finite number of
possibilities. So why are we acting surprised that we 'discover'
relations in mathematics and from that surprise make claims of
"independence" for the math? I find this to be a tacit prejudice of our
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