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It was often speculated, back in the day, that there might be some land somewhere out there in the arctic ice: it shows up in Jules Verne, for instance. So, let's assume some sort of Hawaii-like crustal hot spot under the Artic ice, and handwave the probable butterflies. When Peary (or Cook: http://en.wikipedia.org/wiki/Robert_Peary#Controversy ) reaches the Pole, there are a couple islands, one with an active volcano, poking up a mile or so above the icecap (let's make the actual Pole between the two islands, so the poor guy doesn't have to climb up a glacial mountain to plant the flag).
So, besides making a good spot for the Fortress of Solitude, what changes due to the existence of these isles? Does someone try to claim them? Do Nazis occupy them? Do they become a contested spot during the cold war? (Shortens that cross-polar cap bomber flight if you can build an airbase).