There are various testing techniques used by the Quality Assurance and Penetration Testing professions known as blind testing. Essentially it is where you can’t see something to prove it exists, so you test it by feel, or by testing for an absence of something. For example there are database injection attacks that utilise time. You ask questions you know to be true, followed by ones that you know to be false. With each you measure the time taken for the question to be answered. If there is a measurable difference between the right and wrong ones then you can blind test something based on the time taken to answer your questions even if the response is a return of the prompt with no answer.
How often have you been asked to prove that something is not true? Someone states their argument as if it is gospel, providing no evidence whatsoever to back it up, and then demands that you prove them wrong. You have to do all the work (assuming that you disagree and wish to prove them wrong). In some cases it is impossible to prove, such as the statement that there is some higher being. How do you prove/disprove it?
There is also the practice of proving something with a negative. If all alternative options cannot be true then the assumption is that you have proven that the statement or thing being tested is true.