Ah, so mysql does not like being run as root, and of course you are logged in as root when you log in at the console.
Have you tried simply re-booting the galieo? It might get started automatically then.
If not, you can run mysqld as another user, try this:
./mysqld -u kernel
I'm not sure if that will work as I don;t have mysql on my Galileo to try it.
However if you start mysql from the command prompt, it will most likely get killed when you log out.
You should try re-booting Galileo and if that doesn't work you should try looking at why mysqld isn;t getting started at boot time.