"He found none of the hats."
Translation:Er hat keinen der Hüte gefunden.
The sentence given by DL speaks about a specific set of hats that have not been found (therefore the definite article in both English and German), your sentence translates as He did not find any hats.
Can someone explain what forces the dative case when this sentence is negative, but if this sentence was positive I believe it would be "Er hat die Hüte gefunden"? Thanks!
Unless I misunderstand what's going on in this sentence, there's nothing dative here. "Der Hüte" is genitive. It's not changing because of "none" (the "positive"/"negative" distinction you made), but rather because of "of". If, as was asked about elsewhere in this thread, the sentence was "He has found no hats" instead of "none of the hats", you'd use the accusative ("keine Hüte").