I ask this question because I want to try out some probability theories and I want to get as close as possible to randomness. What my instinct tells me is that we cannot fabricate any function that is perfectly random, because we are in the first place defining an algorithm for it to work on.

In that case, I am seeking mathematical proof why perfectly random functions cannot exist?

Thanks,
Abhinav

Try google like everyone else.

nothing in the universe, even a number that a human makes up can ever be purely random

I guess that's why we call them pseudo random functions. Oh boy, the more I think of this, the more my head is getting twisted.

Anyway, thanks, but I'm still looking for the mathematical proof, although I'm certain it exists, if someone finds it do let me know.

You can't prove something is a random sequence, but you can apply a number of tests to see how random it might be.

The Mersenne_twister seems to be the usual choice for anyone wanting good random data for statistical purposes.

If you want random data for crypto, your best bet is something based on machine entropy, such as /dev/random

That seems like very useful information, thank you.