^{I started a comment on Peter's answer (who happens to be well placed to appreciate the context of your question) but then I found out that I had too many ideas of my own and decided it appropriate to share them here.}

I'd say that there is a lot of overlapping between both definitions (the mathematical and the scientific one).

Note for instance that in mathematics a theory, in the first sense (a self consistent set of axioms, definitions and theorems), can be studied long before it is actually applied usefully in some scientific area.

Examples abound of these cases (e.g. imaginary numbers in 16c. Italy long before electromagnetism or quantum mechanics were discovered). This is arguably the rule rather than the exception.

So that the purely mathematical sense of the word theory is not that far from the scientific acceptation of "hypotheses making predictions waiting to be proven/disproved".

Which leads to the conclusion that a theory cannot wait to be proven to deserve the rank of theory. One might even argue that it stays a theory as long as it is not disproved (after that is is just an abandoned theory ;-).

If scientists were to put theories forward only when they'd have the technical abilities to prove them, we'd be way backwards. Newton would have had to wait for telescopes to be powerful enough to spot planet Neptune and Einstein for atomic clocks to be invented.

^{I started a comment on Peter's answer (who happens to be well placed to appreciate the context of your question) but then I found out that I had too many ideas of my own and decided it appropriate to share them here.}

I'd say that there is a lot of overlapping between both definitions (the mathematical and the scientific one).

Note for instance that in mathematics a theory, in the first sense (a self consistent set of axioms, definitions and theorems), can be studied long before it is actually applied usefully in some scientific area.

Examples abound of these cases (e.g. imaginary numbers in 16c. Italy long before electromagnetism or quantum mechanics were discovered). This is arguably the rule rather than the exception.

So that the purely mathematical sense of the word theory is not that far from the scientific acceptation of "hypotheses making predictions waiting to be proven/disproved".

Which leads to the conclusion that a theory cannot wait to be proven to deserve the rank of theory. One might even argue that it stays a theory as long as it is not disproved (after that is is just an abandoned theory ;-).

If scientists were to put theories forward only when they'd have the technical abilities to prove them, we'd be way backwards. Newton would have had to wait for telescopes to be powerful enough to spot planet Neptune and Einstein for atomic clocks to be invented.