According to Gödel's incompleteness theorem, no matter how many statements you prove, you will always have a set of statements not proved. Does this imply that some time in the future, scientific development will come to a halt due to our inability to discover/invent anything new?
No. In mathematics we prove conjectures, theorems, etc. In science we do not prove a hypothesis. We run experiments to either support or refute the hypothesis, but as time goes on and new evidence becomes available conclusions can swing direction. Proof is an exercise pursued by mathematicians.