The connection to the remote
host can be automated, but the process is a little tricky. You
may be able to write a shell script for your local system and
name it math. This would allow you to simply type
you wanted to run Mathematica. The script could create a new
shell for you, invoke rlogin, connect to the remote machine, and
start up Mathematica. However, several steps in this procedure
might fail, depending on the security measures in place on your
network. Another problem is that you might need to specify a
password to log in to the remote system; you may be tempted to
put this password in your script, but this is a security leak and
is discouraged at most locations.
The definitions of X clients and servers provide a more concise definition of an X terminal: an X terminal is a device that implements the X server software. Often the server software is stored in ROM, along with common fonts and other data, and it runs the window manager and other server software. However, it does not normally run any client applications. It passes keystrokes, mouse clicks, and other events to the client software for processing, and then responds to client requests to move or redraw windows or update the contents of windows.
The definition of servers and clients may seem confusing at first. You may prefer to think of yourself as a client, and think of the machine that implements a shared software package like Mathematica as the server. However, this is the opposite of the X Window terminology, which calls Mathematica the client. Just remember that X clients and servers are defined from the application programmer's perspective. A client is an application that needs a window, and a server is a process running on a workstation that will draw the window for the client.