It's called a proof
a proof
A counter example is a statement that shows conjecture is false.
A conjecture should be testable. You test it and if it fails the test, it is a false conjecture.
A counter-example.
pie tree
It's a counterexample.
hypothesis
Counter example
a way that shows clear sound reasoning
a way that shows clear sound reasoning
The Goldbach conjecture is probably one of the best known. The conjecture is that every even number greater than 2 can be expressed as a sum of two primes. T. Oliveira e Silva has confirmed the conjecture for number up to 4*10^18 but, despite many years of effort, the conjecture has not been proved.