IF (very big if) you could have access to all known variables (with an arbitrarily high precision) and enough compute power AND the system was deterministic, you could very well deduce it. Putting some quantum noise in the mix makes it so no matter how well you know the system and compute it, you can't predict its behavior beyond a certain hard limit.

I argue that part of the source of quantum noise is baked in already in the finer workings of the neurons. So a mathematian isn't condemended to be one just because the universe was in certain configuration a few millenia ago.