How Input and Output Work
| Input | convert from a textual form to an expression |
| Processing | do computations on the expression |
| Output | convert the resulting expression to textual form |
Steps in the operation of Mathematica.
When you type something like 
what Mathematica at first sees is just the string of characters 
, 
, 
. But with the usual way that Mathematica is set up, it immediately knows to convert this string of characters into the expression Power[x, 2].
Then, after whatever processing is possible has been done, Mathematica takes the expression Power[x, 2] and converts it into some kind of textual representation for output.
Mathematica reads the string of characters
,
,
and converts it to the expression
Power[x, 2].
| Out[1]= |  |
This shows the expression in Fortran form.
Out[2]//FortranForm= |
| |  |
| Out[3]= |  |
It is important to understand that in a typical Mathematica session In[n] and Out[n] record only the underlying expressions that are processed, not the textual representations that happen to be used for their input or output.
If you explicitly request a particular kind of output, say by using TraditionalForm[expr], then what you get will be labeled with Out[n]//TraditionalForm. This indicates that what you are seeing is expr//TraditionalForm, even though the value of Out[n] itself is just expr.
Mathematica also allows you to specify globally that you want output to be displayed in a particular form. And if you do this, then the form will no longer be indicated explicitly in the label for each line. But it is still the case that In[n] and Out[n] will record only underlying expressions, not the textual representations used for their input and output.
This sets
to be an expression with
FortranForm explicitly wrapped around it.
Out[4]//FortranForm= |
| |  |
The result on the previous line is just the expression.
| Out[5]= |  |
Out[6]//FortranForm= |
| |  |
| Out[7]= |  |
