Proving a hypothesis often requires the development of new and powerful techniques and maybe even new branches of mathematics.
However disproving such a hypothesis could result from a single counterexample.
Are there any existing non-trivial mathematical hypotheses that cannot, even in principle, be disproved by counterexample?
Note
By existing, I mean that have been published or discussed in reputable mathematical journals.
By non-trivial, I mean hypotheses that are not explicitly designed for the purpose of not being susceptible to counterexample.
Working in ZFC,
The Continuum Hypothesis is a famous example.
That there is no set with Cardinality greater than the naturals, and less than the Reals.