What if Romans won Carrhae, Teutoburg, Adrianople?

[Nathan Ross]

No loss at Adrianople = no Theodisius. Would there still have been a "closing of the western mind" with dogmatic Nicene Christianity mandated from on high?

I suspect religious affairs wouldn't have changed that much in the longer term. Christianity had been well established for over 60 years by the time of Adrianople, and Julian's attempts to overturn things didn't have that much effect, it seems. Constantine himself (according to Timothy Barnes at least) was no slouch when it came to dogma - not quite the tolerant emperor he's often presented as being. With christianity being so adverse to traditional religions, and making such rapid headway, the sort of strictures laid down by Theodosius probably wouldn't have been long in coming anyway.

Would Rome have needed to allow federates to settle into semi-autonomous areas and fight under their own leaders? Would the Goths have had as much access to Roman tactics and arms?.

Rome was already settling 'federates' (laeti) in the west in the third century, and barbarian groups fought under their own leaders at Chrysopolis in 324 (Franks under Bonitus, Goths under the peculiarly-named Aliquaca). So this was nothing new. The Franks in the west were repeatedly defeated, yet still gained access to Roman tactics and arms, so I doubt the Goths would have been different in this respect.

So while a Roman victory at Adrianople would have given the status quo of the day a short reprieve, it wouldn't, I think, have changed that much historically. Even if the battle were won, the conditions for the defeat (massive barbarian influx, weak or divided Roman army and leadership) were still in place - it would only have taken the next great wave across the Danube for the same thing to have occurred.