Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability. But of course mathematics is all about proof, and for that reason I was wary of it for a very long time.
>Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability
not really. You can consider positive proof as an experiment confirming your theory and the negative proof and counter examples as an experiment falsifying your theory.
Fortunately this is not basing science on proof. It's just making it much easier to do proofs when that is what we choose to do