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 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.

Dear Bruno,

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 own importance.



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