I'm compulsively watching WW2 week by week on Youtube and I'm struck by how little I actually know about the conflict.
From a purely military perspective, this war seems to have been fought and won on a technological knife's edge, with all sides struggling to adapt to the newest developments.
Which brings me to my question. How come Nazi Germany - which was in the vanguard of military technology - did not invest in aircraft carriers, even after the Japanese proved it was the superior platform on the sea?
Well, to a certain extent they did. Graf Zeppelin was laid down in December 1936 and launched in December 1938, but she was never completed. However, there are a variety of reasons why an aircraft carrier wouldn't have really been useful for the Kriegsmarine in WW2, many of which are discussed here by both /u/kieslowskifan and /u/The_Chieftain_WG. There were strong institutional issues within the the wider Wehrmacht that caused severe issues for the constitution of the carrier's air wing. Ignoring those, there's the question of what it would actually do. During the 1930s when the Graf Zeppelin was designed and laid down, the general consensus was that aircraft carriers were a useful adjunct to the fleet, providing air cover, reconnaissance, and harassment of the enemy's battleline. Most of the Kriegsmarine's operations would be within the range of land based aircraft, and thus there would really be no need for a carrier. Were she to break out into the Atlantic, she'd've met a similar fate to that of Bismarck, as she would be isolated, alone, and likely surrounded and defeated by more numerous superior hostile forces, especially as the Germans would've lacked the extensive pre-war carrier experience of the Royal Navy, US Navy, and Imperial Japanese Navy.
Moreover, while carriers had indeed demonstrated that they were the dominant players in war at sea, the Battle of Midway was not fought until June 1942, by which point the surviving German heavy surface units had already been withdrawn to Norway. Any operations in this theatre would've been well in range of land based air cover from Norway. By this point, it was likely far too late for the Germans to invest more heavily in carriers.
The Germans had started work on an aircraft carrier, the Graf Zeppelin, in the late 1930s. However, technical problems, interservice rivalries and the diversion of resources to other projects delayed her construction; while she was launched, she was never completed. /u/kieslowskifan has written a more full description of the issues she faced here.