Formatting of a trigonometric function:

Formatting of a hypergeometric function:

Partial derivative of an arbitrary function:

Euler's formula in traditional mathematical notation:

A triangle inequality:

When an input evaluates to TraditionalForm[expr], TraditionalForm does not appear in the output:

Out is assigned the value Sin[x], not TraditionalForm[Sin[x]]:

TraditionalForm is two-dimensional:

StandardForm is two-dimensional and unambiguous for input:

OutputForm uses only keyboard characters:

InputForm and FullForm provide one-dimensional formatting:

Use ToBoxes to see the underlying box structure:

Use ToExpression to convert the boxes to the original expression:

Add formatting via Format:

TraditionalForm is ambiguous, i.e. different expressions can display similarly:

The following box structure has similar display:

When interpreting the boxes, a particular interpretation is selected:

Wolfram Language–generated formatting includes data for unambiguous interpretation:

Even when an output omits TraditionalForm from the top level, it is not stripped from subexpressions:

The output does not have TraditionalForm in it:

However, the variable e does have TraditionalForm in it, which may affect subsequent evaluations:

The integral is not evaluated due to the intervening TraditionalForm:

Assign variables first and then apply TraditionalForm to the result to maintain computability: