Value of Science and Meaning of Proof

We live in times people question the value of science.
Is science good for us or bad for us?
Can people simply refuse to accept or refuse to apply parts of science?

If we compare the living conditions of people in the past and in the future we see that people in the future living with better conditions.
Isn't that right? If so, then progress of science is responsible for the improvement or not?
If science is responsible then practical value of science is obvious.

If we want to refuse science, is it because thinking science has no practical value?
Or are we thinking too much science is bad?
Or are we thinking some parts of science may not be correct?

Of course establishing any part of science is correct or not depends on the proof for it.
In mathematics a logically valid proof is absolute.
There is no way to argue against it (assuming a valid counter-argument).
In physics it seems there is no way for absolute proof.
There are two great theories of physics (relativity and quantum)
and there are countless experiments and observations for both showing them to be true.
But the situation looks like trying to prove Riemann Hypothesis by checking integers one by one.
One can never complete the proof that way because there are infinite cases to check.
Newton mechanics looked pretty good that way but later turned out to be ultimately wrong.
Is that mean we can disregard relativity and quantum theories?
Obviously not, unless we have a better theory to replace them.

What about proof in other branches of science?
How certain a proof in chemistry, biology, psychology, sociology?
Which proofs we can refuse or argue against in science?