String theory does not work with de-Sitter spaces, only with anti de-Sitter spaces. Science has proved we are living in a de-Sitter space. String theory cannot be true.
> Still, the work is expected to launch a new era in matching the mathematical > elegance of string theory to the actual world we live in."
yeah, sounds real promising. string theory all over. nice maths but who cares if it doesnt map to reality, its nice maths!
Remember resources are limited. We cannot fund everyone who wants it. Society needs to make choices, we are generally okay with a bit of "interesting but unlikely to produce anything important", but most of what we fund needs a return on investment.
You can only disprove.
The only way to prove a positive if there is a finite number of possibilities and you have disproven all but one. But even then, someone could conceivably come up with an alternate description that preserves the current understanding but makes additional predictions or is a simpler model making the same.
As Feyman said: "We can never know if we are right, we can only be certain if we are wrong".
For example:
Every continuous symmetry of action in a physical system with conservative forces has a corresponding conservation law. (Noether's Theorem)
There must be two antipodal points on Earth with exactly the same temperature and barometric pressure (as a result of the Borsuk-Ulam Theorem)
As far as I know these are absolutely proved positively because they are mathematical consequences of the properties of continuous functions etc. I'm not a scientist, but there are thousands of things like this where we are definitely absolutely certain we are right because of the possibility of a mathematical direct proof.
Likewise, we assume at an operational level that temperature and barometric pressure are continuous functions (as assumed in Borsuk-Ulam), but it's not something you can conclusively prove aobut reality.
There's an argument that you are still doing science if you construct a logical proof showing that "if the world is like X, then it will behave like Y". A lot of theoretical physics is like this, and people call that science. But I think there's truth to what OP is saying in that science does not conclusively positively prove things about reality.
But otherwise, there is nothing special about positive or negative statements. You can express any positive statement as the negation of a negative statement, so to the extent that science can "disprove negatives", it can equivalently "prove positives".