Is it possible to create random numbers using (time-dependent) functions or functionals?

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I saw a tv program asking for the name of a mathematician. The answer was von Neumann. It was said that he tried to create random numbers, but these numbers showed periodic behavior. After a while, the same row of numbers came back again and again.
Now if you use mathematics only, is it possible to create random numbers? Is it possible to create a function that has as its values random numbers? Functions that depend on time or maybe functional? Or will they cease to be a function or a functional if that could be done?