> The universe is infinite ...
Yet we can describe most of what we observe with a tiny set of equations. What's more meaningful to science is that the universe is not bound to our models and assumptions. Even the assumption that the universe is ordered and so will remain ordered is not guaranteed. It's just a convenient and historically effective assumption that appears to be justified as far back as we can look. No science, therefore, is a done science.
> ...the human mind is finite.
A whiteboard is finite. It is bound in spacetime and no matter how small the writing, there is an upper limit to the amount of information that can be displayed on it at any one time. No matter how quick the erasing, there is an upper limit amount of information that can be displayed within the lifetime of the board.
Despite this, it can have an uncountably infinite variety of information impressed upon it.