Applied mathematician here; my solution is putting them on the same slide as the material. I use formats such as [Someone '99], [Lin WW, '00] (initials are almost mandatory for some common surnames), [Doe et al, book '04], [P and SomeoneElse, preprint '12] (my name is always abbreviated to an initial, which is a common convention). I find it a good compromise between clarity and shortness: I don't need to include a full sentence, but only the names in brackets.
You can use a different color or font to differentiate them visually from the text --- preferably something light but readable, a color that does not attract much attention.
I use them sparingly nevertheless --- overall I have typically less than 10 such citations in a 15-20 slide talk.
This makes immediately clear whether I think that a theorem is new/mine or not. Its original authors could be in the audience, so I think it's important to acknowledge them properly.
If your slides are already so cramped that these citations won't fit, then you have a much bigger problem. :)