"In mathematics, a true random number generator it's impossible, because any formula defines a process that, however complex, is not random."
I'm going to point out that this question and its answer here suffer from a lack of any clear description of what constitutes a "random number generator" in mathematics, since "random number generator is not a technical term. But also, it has no obvious technical meaning.
The answer presented in this quote suggests that the random number generator is supposed to be defined by a formula. But what kinds of formulas count as formulas? This is left unstated, even though it would be possible to try to answer the question only if this is specified.
That addresses how to define what kinds of generators might or might not ever be random.
But also: What does random mean here? What is the criterion that a generator must satisfy in order to be classified as random? This, too, is not so easy to define. Suppose in the simplest case our random number generator started outputting a string of 0's and 1's, and the ideal case is the mythical fair coin flipped repeatedly in an unending sequence of (1/2,1/2) Bernoulli trials. Roughly speaking, the best definitions of a "random" sequence seem to require that for every natural number K, every string of 0's and 1's of length K occurs with the expected frequency 1/2^K.
The trouble is that to know this frequency, a) it is necessary to know an entire countable sequence of outputs, and b) for any finite initial string of outputs, that string can be ignored and the countable sequence will be just as random (or not) as it was with the finite initial string.
So for instance if for n = 1, 2, 3, ... we let the nth output of the generator be
F(n) = 0 if p(n+1) = 1 (modulo 4),
F(n) = 1 if p(n+1) = -1 (modulo 4)
(where p(n) denotes the nth prime number)
then this would probably satisfy my definition above.
But that "generator" is entirely deterministic.