I think that prompt should let you move directly to the download page (I've encountered it for some other third-party software), but if not you can download the Java SE Runtime Environment for OS X from http://www.oracle.com/technetwork/java/javase/downloads/jre7-downloads-1880261.html.

But yes, Mathematica is compatible with OS X 10.10. I'm using it right now.

I think that prompt should let you move directly to the download page (I've encountered it for some other third-party software), but if not you can download the Java SE Runtime Environment for OS X from [EDITED thanks to szabolcs]: http://support.apple.com/kb/DL1572

But yes, Mathematica is compatible with OS X 10.10. I'm using it right now.