Why do we use the word undiscovered? As far as I know, un– and dis– have the same negative meaning; why don't we just say "covered"?
Because “discovered” has over time developed its a meaning independent of its roots, and is not the converse of “covered” in modern usage. (That would be “uncovered.”) We therefore use a more complex word—undiscovered—to express this concept.
Because English language can express more florid concepts than mathematics. I am sure we could design a more logical language based on signed (positive/negative) concepts and I think it may have been tried before (1984 doublethink).
If I say I am tracted - by your logic that means I am focused rather than distracted. But if my point is not so much that I am focused but more that my focus has not been disturbed and I make no comment about whether I am focused or not - I could say I am undistracted.
I'm no etymology expert, but this is an interesting question. Might it be because covered suggests an intention to keep something secret, thus creating the need for an alternative word that means "something we just haven't found yet but that isn't an intentional secret"?
Un- and dis- don't have the same meaning. For example uninterested means not interested while disinterested means not biased. Dis- has a different effect on covered from un-. If something is uncovered it could mean that it has never been covered or hidden. If something is discovered it means that it has changed state from being covered to being uncovered. It would also usually be that whatever it is has been covered by ignorance - once something is known, the veil of ignorance has been lifted and the thing has been discovered. That's why you'd say undiscovered instead of hidden.
In general, negative prefixes do not cancel each other like free-standing negative words do (in standard English). "Uncover" means "to remove the cover from something." "Un-uncover" (insofar as it is a word at all) means "to put the cover back on something from which the cover had been previously removed." The simple word "cover" lacks the sense of putting back.