phukraut

Just a quick note: just because what there is to know is infinite in scope, that doesn't necessarily mean we will keep on discovering. Take mandal's example of the integers. Yes, the set of integers is infinite in size, but we can completely describe them with that set. A curve is similar in the sense that we can think of it as being composed of an infinite number of points, yet we can completely describe (and understand it) with an equation.

Of course, that doesn't mean all things can work like this. There may be things that are infinite in scope AND cannot be completely described: a random sequence for example.

Also, a sufficiently complicated problem may be solvable but not in the lifetime of the universe, say. This is sort of on the same lines as mo42's response.