Since Newton and Leibniz both came up with calculus (I believe modern calculus is more Leibniz than Newton) is it not more accurate to describe them as 'discovering' calculus rather than 'inventing' it?
We have a theory that we know is not 100% right but continue to use it because we can't find a better 'measuring tape'. As we find different instances of where the ducks appear NOT to quack, and sometimes don't even walk like ducks, (the theory appears not to work) we formulate hypothesis about the existence of 'dark X,Y and Z' that distort what we are seeing. In effect modern science argues that 'ducks are ALWAYS ducks. However they do NOT always appear to walk and quack like ducks because of the unknown properties of unicorns/darks (who we can't find)'.
My basic problem with this is the methodology: At what point can one say "Perhaps we are just 'barking up the wrong tree'?". We can go on forever inventing more unicorns/darks/'known unknowns' to keep our origional theory eternaly consistent; ducks are always going to be ducks - even when they appear to be sharks. If indeed a duck appears to be a shark we should see this as a proof that there's a unicorn nearby!
Modern science and it's theories you say need 'data' to get a 'proof'. In what might be called 'classical physics' - or perhaps better called 'idealised science' - this is supposed to be the case. In 'dark energy' for example by the very definition no data is forthcoming yet this is 'adopted'; the data suggests only that the duck isn't quacking; it's meowing. The fact that the duck appears to be meowing leads us to believe that there is a 'dark energy' (or unicorn in my terms). Logical?
The problem is not with the 'data' (except that of course the data only provides a probability and never a proof) but in the interpretation of the data. Where something 'inconvenient' appears to be happening (ducks appearing not to quack etc) we hypothesise a cause for this (dark X or unicorns) rather than saying "perhaps it's NOT a duck after all!". With a methodology of this nature we can never have a 'proof' in the classical sense. It is as if they had turned 'classical science' on it's head; when the theory appears not apply this does NOT negate the theory but proves the existence of something we didn't know about before.
There is much else I could say on this matter but I am not sure it's relevant to this forums agenda.