The implication of Godel’s theorems is that scientists are just as subject to faith as non-scientists. Indeed, the renowned atheist Bertrand Russel was so shaken up by this fact that he lamented “I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than anywhere...But after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.”
Again, in the ultimate sense, science requires FAITH. Therefore science and faith ARE NOT strictly incompatible.
In the end this increase in knowledge (and the knowledge that we can't prove all true theorems is an increase in knowledge) was achieved entirely by reason.
It may have disappointed Russell, but then he spent years of intense work trying to construct a complete formal system for basic math. So that makes some sense. It still doesn't imply anything about the universe as a whole.
Hope, maybe, dashed hope. They are disabused of all that going on 3/4 century.