Religion and science are not opposed. Claiming otherwise comes, at the very least, as not well informed.
Sorry to nitpick, but science isn't verifiable, it's falsifiable. Also, there are religious people who'd agree with your characterisation of faith and there are others who wouldn't.
If you want it in an academic sense, then you could say that authentic biblical faith is always on the basis of the historical method.
For example, see Luke writing to Theopilus:
"Inasmuch as many have undertaken to compile a narrative of the things that have been accomplished among us, just as those who from the beginning were eyewitnesses and ministers of the word have delivered them to us, it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, that you may have certainty concerning the things you have been taught."
And see Paul writing to the early Corinthian church:
"And if Christ has not been raised, then our preaching is in vain and your faith is in vain."
"Faith is the assurance of things hoped for, the conviction of things not seen" (Catechism of the Catholic Church.)
Which is exactly what science is not.
And if all your faith and your preaching depends on the actual historicity of an impossible event, to which you seek no further explanation than something equivalent to "it's magic" (and no further interpretation but "then it means we're right"!), then of course this attitude is very far from being compatible with science.
And if it is original to Hebrews 11, then what does the phrase "assurance of things hoped for" mean in context if it does not have the same sense as 1 Corinthians 15 or Luke 1?
When you speak of "an impossible event", what do you mean exactly?
And when you say "impossible", then according to what logic?
Are you saying that it is impossible for God (should he exist) to raise the dead?
Are you saying that it is impossible for the dead to be raised because you presuppose that God does not exist?
Or are you saying that it is impossible in the sense that we have very few occurrences of such an event and therefore it must be impossible?
Well, they believe it because somebody told them to. Then, if you're asking why that formulation and not another one, then yes, it comes from Hebrews 11. But even if that passage justified the Catholic one, wouldn't that just shift the question: if they believe so and so because it comes from Hebrews 11, then why do they believe in Hebrews 11?
I mean "impossible" in natural terms, according to the believers themselves. If it were possible, but just a rare occurrence, then it wouldn't justify building a whole faith system on it, don't you agree? For a Christian the resurrection must have happened despite being impossible: the impossibility it's exactly where it derives its value from. The impossibility is cherished, treasured.
Contrast now with a scientific attitude. It has happened? Therefore it's possible and (until further understanding) it doesn't prove anything except its own possibility. And understanding means discovering the mechanical, reproducible and predictable nature of the process. Any aspect that is not mechanical, reproducible and predictable will have to be ignored by the scientific inquiry. Even if it contains the right answer.
That is not the definition of scientific inquiry, or you would be ruling out most of the sciences.
As for Hebrews 11, that chapter does in fact give examples of authentic biblical faith, as opposed to "blind faith". In other words, people (everyone from patriarchs and prophets to prostitutes) acting on the basis of what God said and did in history (often their own recent past). As a chapter by itself, Hebrews 11 is enough to show that faith is always on the basis of the historical method, not on the basis of wishful thinking. And Hebrews is not the only book in the Bible. The Bible has much to say that defines authentic faith.
To come back to the resurrection, if I understand you correctly, then you are saying that the fact of the resurrection proves its possibility (incredulous as it is) and nothing more. In other words, God himself would still have to speak to give meaning to the event of the resurrection? That is the Bible's claim. You can examine it should you choose to, on the basis of the historical method according to disciplines such as textual criticism etc. which are not opposed to scientific inquiry.
And this is all at least part of the reason why some people who took the Bible seriously, started taking the world around them seriously. That at least, is the history for founding fathers of science such as Johannes Kepler (a protégé of Melanchthon, himself a protégé of Luther).
What is your name? I am sure you would want to take science seriously. I wonder if you have ever taken the Bible as seriously, like people like Luther did? With a fresh pair of spectacles?
Of course debates can go on forever, but I think that religion and science are indeed opposed, it just happens that some individuals can do excellent science while keeping religion safely confined to a corner of their brains (and the other way round, maybe).
Religion is about faith, science is- well, not. Religion starts with believing in something without adequate proof (by definition, or it would be science). Science looks for the proof of everything. Religion searches for unexplainable things, to be used as a proof of an immutable knowledge; science searches for unxplainable things to prove that the existing knowledge is wrong, and by modifying it, make them more explainable.
Galileo studied at the University of Pisa, which was created by Papal edict. He wanted to enter the priesthood when he was young.
In medieval times the Islamic world used to be quite keen on science and progress as well. It's only in modern times that Islam has become increasingly conservative and backwards (as in Salafism, which quite literally as about wanting society to be like it was in the day when Muhammad still lived) again.
Without the church, there would have been far less research (mostly happened within the church, mostly by order of the Vatican), we would have wiped out the scientific knowledge several times in history (mostly, but not exclusively during revolutions, when monasteries saved entire libraries containing scientific knowledge), and scientists have been explicitly wiped out as a matter of state policy several times, when again the church saved large numbers of them.
And that's ignoring that, even today, a university that doesn't originate within the catholic church, or is even still part of it (like my alma mater) is still not very common. Even today, at least organizationally, very significant amounts of scientific research still happen within the catholic church (as in the boss of the boss of the boss of the boss of the scientist is the pope). Today.
Honorable mentions go to several ecclesiastical orders, most famously the Jesuit priests.
Sadly, Christianity is the exception here. While, yes, most religions had their priests do some form of scientific research, most religions wiped out the scientific knowledge they amassed, rather than protecting and safeguarding it, famously the burning of the great library of Alexandria by one of the main sources of islam, caliph Omar (who for instance is the source of sharia, as in the law system called sharia) [1]
In my opinion this happens because in most religions there is no separation of church and state, like Christianity first had because of it's fights with the Roman Empire. This meant that the church could continue when the empire split, fell or otherwise had issues (and could remain popular when the state failed, as states inevitably seem to do), that the Catholic church had a constant and functional international organization from AD 200-300 onwards or so, and it remained functional and separate from states until ... well it's still going, isn't it ? And even today, neither faithful nor atheists would say that the catholic church is the state, anywhere except perhaps Vatican city (and even there, it's mostly the Italian and Swiss state). In most religions, when a revolution happened, the revolution was as much against the religion as it was against the state, meaning the priests were the first to get their heads chopped off and books burned. This is not to say that Christian priests escaped that fate every time, but often they did.
[1] https://en.wikipedia.org/wiki/Destruction_of_the_Library_of_...
You would have to prove that such curious people didn't gravitate towards the church instead of other place because _they were already_ financing such research, meaning, that the research wouldn't have happened in another place/group if the church didn't exist.
The best place to do science is one which takes nothing for granted, in which people is free to doubt event their own existence if their ratinalizations lead them to believe so; that's pretty much the opposite of religion and the church, where there is a bunch of dubious "facts" that cannot be doubt, such as "There is a God, God is smart, There was Jesus, He made some miracles".
The other thing is that each single scientist that the Church killed may have discovered something even bigger had they not been killed, perhaps setting back science for decades or even centuries; and an even worse outcome was fear, because they inserted fear from then on in all researches of the same subject, for example I wouldn't have dare to say the earth gravitates around the sun the years after Galileo was killed; so you would have to "calculate" if what they did for science was bigger than what they did against it.
There were and are plenty of places beyond the reach of the church, and whilst I wouldn't go so far to say research didn't happen at all there, there was far, far less. The more fundamental the research, the less of it happened. There was a distinct tendency for research to be military related outside of the church.
Even so the main problem with research outside of the church wasn't so much whether it happened or not, but only very few cultures managed to keep the knowledge over time, never mind kept teaching the knowledge over time (not a single atheist culture did so successfully, despite many attempts, the Greek philosophers' culture got lucky because it was embraced by the church, and even among the original philosophers most were not atheists). You could say that only Christian/western civilization, and to a much lesser but nonzero extent Islamic culture (although that was mainly preserved in Christian monasteries as well). When science is not preserved, it cannot be built up, which means it never gets to be really advanced.
What makes these religions special is their resiliency (atheism has been shown by history to be seriously lacking in resiliency), combined with the freedom that existed within them. Firstly, science doesn't happen if it's not tolerated. Secondly, a culture that doesn't stay alive cannot build up scientific knowledge over time. Either will prevent significant scientific development. Scientific research doesn't help anyone if it's destroyed every time a harvest fails, which was the more common case, and such an environment means the knowledge doesn't stay alive, and can't be built upon. Christianity did not just not destroy Greek and Roman philosophy and science, but embraced, preserved and taught it, adding on to it over the centuries until eventually it accelerated. Islam, while it never tolerated muslim scientists to any great extent, had the dhimma system, where they let large groups of non-muslims contribute to society through trade, and this left mostly non-muslim groups that practiced science alive, some important ones as slaves to a court somewhere, who managed to get the knowledge back into the west where the church preserved it. But importantly: science in islamic lands died out. The communities teaching science to their kids dwindled to nothing. All traces of it, and certainly the teaching of it, disappeared from all islamic lands.
Keep in mind that Christians certainly destroyed all scientific knowledge in parts of the world on a regular basis (every century or so). What kept Christian science alive is that the church, and in particular monks, would re-divide the knowledge back into the areas where it got destroyed. The most famous example of this work is the painstaking copying of entire libraries by hand, and sending them to other monasteries.
I think given history there's an extremely solid case there would be no modern science without the church, or at the very least, it'd have taken millenia more to get there.
What scientists get taught in school is only a very tiny part of the equation that got us to modern science, and frankly, doesn't appear to be a very important part.
You have heard that it was said, "You shall love your neighbor and hate your enemy." But I say to you, Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven. For he makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust. For if you love those who love you, what reward do you have? Do not even the tax collectors do the same? And if you greet only your brothers, what more are you doing than others?