  Usually creative telescoping is used to derive recurrences for sums. In this
article we show that the non-existence of a creative telescoping solution, and
more generally, of a parameterized telescoping solution, proves algebraic
independence of certain types of sums. Combining this fact with
summation-theory shows transcendence of whole classes of sums. Moreover, this
result throws new light on the question why, e.g., Zeilberger's algorithm fails
to find a recurrence with minimal order.
