Is Random class thread safe?
It is thread safe in the sense it will still generate random numbers when used by multiple threads.
The Sun/Oracle JVM implementation uses synchronized and AtomicLong as seed to improve consistency across threads. But it doesn't appear to be guarenteed across all platforms in the documentation.
I wouldn't write your program to require such a guarantee, especially as you cannot determine the order in which nextInt() will be called.
It is thread safe, although it wasn't always.
See http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=6362070 for more details.
Acording to the Java 6 documentation, Math.random() guarantees it's safe for use by multiple threads. But the Random class does not. I would assume then you'll have to synchronize that yourself.
EDIT:
According to the accepted answer, though, the documentation seems to have changed since Java 7 and the Random class seems to offer that guarantee too.