The claim that Christianity held science back for 1,000 years is so common among atheists that it deserves to be called a cliché. Though it is often repeated, it has absolutely no basis in fact, and can only be sustained by two key elements: Ignorance of history, and ignorance of theology.
Of course, many atheists will scoff at the idea that they need to be educated in theology to criticise Christianity, but in reality, it is just plain logic. Failure to understand a belief or argument you are criticising is called the straw man fallacy. Think of it like this: What would you think if Christians started criticising atheists for worshipping brass monkeys on their shelves? Most atheists do not even own brass monkeys, much less worship them, so this would obviously be a very stupid argument. Attacking Christianity without understanding its theology leads to equally stupid arguments.
Theologically speaking, it is impossible for Christianity to have held science back for any amount of time. Christianity is a very pro-science faith, as Scripture is absolutely riddled with high praise for both the human intellect, and for the study of the natural world.
When it comes to human reason, the Bible strongly encourages us not to be taken for fools. Indeed, there is a whole book (Proverbs) dedicated to teaching us to be wise in our lives. This book repeatedly describes fools as hating knowledge and speaking their own opinions, especially without understanding, whereas the wise are said to love knowledge, and even tells us that they will love correction (Proverbs 9:8).
Furthermore, Scripture sets God forward as the ultimate Creator. This is very important, for several reasons. The first is that a creation is very likely to reflect its Creator. Thus, when God tells us He is not the author of confusion (1 Corinthians 14:3), we can assume that His creation will conform to reason. Some might argue that, since the verse only speaks about the Church, it can only be applied to the Church. However, the verse is describing a personality trait of God, and using it as a reason for the passage's teaching. It gives us no reason to believe this trait is limited to the Church.
On top of this, Scripture is replete with indications that nature is, in a sense, a "second", though admittedly more vague, revelation of God. Psalm 19 opens with an excellent example: "The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard. Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun, Which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race. His going forth is from the end of the heaven, and his circuit unto the ends of it: and there is nothing hid from the heat thereof. The law of the Lord is perfect, converting the soul: the testimony of the Lord is sure, making wise the simple." (Psalm 19:1-7).
It seems unfathomable that God would tell us the heavens declare His glory, and the skies declare His handiwork, if He did not intend us to look to them. Obviously, day to day does not literally speak to us, nor does night after night teach us, but we do have to remember the Psalms are poetic. The Psalmist is personifying day and night as a multilingual teacher, but whereas a literal teacher is limited in time and space, day and night are omnipresent, and everyone can learn from them.
And that literally does mean everyone, as in the book of Romans, we learn that although special revelation is absolutely vital to knowing God, general revelation is sufficient to lead us to Him. He tells us "For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness; Because that which may be known of God is manifest in them; for God hath shewed it unto them. For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:" (Romans 1:18-20). In other words, the creation we observe, ultimately, helps even the unbeliever to get to know God. Therefore, we who seek to know God ought to be diligent in observing the creation.
This is not only a logical conclusion, but also an indirect command. For one thing, learning about God's creation helps us to fulfill His command to fill and subdue it (Genesis 1:27-28). But furthermore, we are commanded in multiple places to both avoid and oppose deception. In 1 Thessalonians 5:21, we are told "Prove all things; hold fast that which is good." (More modern translations say "test" all things). In 2 Timothy 2:15, we are told "Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth." In 2 Corinthians 10:3-5, we are told "For though we walk in the flesh, we do not war after the flesh: (For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds;) Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ;"
All of the above makes it very very difficult for a consistent Christian to oppose science. This would explain why science is effectively a Christian invention. Now of course, science has always existed to some degree. It would be impossible for the human race to survive without some degree of scientific knowledge. We need to know how to distinguish between edible and poisonous food, lest we ingest something that kills us. We need to know how to find or construct shelter, lest we die from exposure. We need to be aware of how to reproduce, and of course how to raise the otherwise defenceless children that result from this. Every day, without even thinking about it, you use some form of science. For our ancestors, living in a far more dangerous world, science was much more important.
But most people don't need a historian to tell them that our forerunners were not as scientifically advanced as we are. That's not to say our ancestors were somehow more primitive than us. Our success in science is built, in large part, on the success of our forerunners. As Sir. Isaac Newton once said, "If I have seen further it is by standing on the shoulders of Giants." In the same way, if we see further regarding gravity, for example, it is because we stand on the shoulders of giants like Isaac Newton, a notoriously devout Christian.
It might seem strange, especially to the atheist, that I state Newton's faith. Is it really relevant? Does it particularly matter that Newton was a Christian? On its own, no. Although it can't be denied that Newton's primary motivation in his life, including his scientific inquiry, was motivated by his faith, on its own this would be a very weak argument. After all, many scientists today are very devout atheists. Evolutionists, even.
But the significance of Newton's faith is that he was not alone in holding, or being guided by it. Rather, much to the chagrin of many atheistic historians, the entire philosophy of science springs from the Christian faith. Whereas science was effectively dead on arrival in other cultures, the Christian West raised it like a tree from an acorn.
The myth that Christianity supposedly held science back for so long is helped, in large part, by the existence of the so-called "Dark Ages" (~450 A.D. - 1000 A.D). I say so-called because, contrary to the popular understanding, the Dark Ages were actually so named due to the perception that, compared to the prior days of the Roman Empire, and the later period of the Renaissance, there had been a significant decline in culture, learning, and especially stability. This is actually greatly exaggerated. Although there was certainly instability, including a lot of wars (as if any time in human history has been perfectly peaceful anyway), both cultural and intellectual advancements are often overlooked.
Aside from the obvious fact Christianity failed to hinder science during the Middle Ages (~450 A.D. - ~ 1450 A.D), there is a scant amount of evidence that they even tried. As Michael Newton Keas notes in his book Unbelievable: 7 myths about the history and future of science and religion, "...there is no record of priests or theologians refusing to look through a telescope. In fact, when Cardinal Bellarmine asked about Galileo’s telescopic discoveries, the Jesuit astronomers at the Roman College confirmed their accuracy" (emphasis original). Likewise, in God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science, James Hannam notes "During the Middle Ages, the Catholic Church actively supported a great deal of science, which it also kept control of when speculation could impinge on theology. Furthermore and contrary to popular belief, the Church never supported the idea that the earth was flat, never banned human dissection, never banned zero and certainly never burnt anyone at the stake for scientific ideas."
It is a complete myth that Christianity hindered science. In reality, the opposite is the case. Just as the Catholic Church was initially supportive of science, it is no accident that the Scientific Revolution, typically acknowledged as beginning with Copernicus in 1543 A.D., coincided with the Reformation, marked by Martin Luther's publication of his 95 theses in 1517 A.D.
As effective as the Catholic Church were regarding science, they did have one critical flaw, which they maintain to this day. That is, the heavy emphasis on "authoritative", man-made tradition. Rather than studying Scripture according to its words, Catholics were not allowed to interpret Scripture in a manner contrary to Catholic tradition. In the latter half of the middle ages, this attitude became so extreme, the Catholic Church even banned the Bible from the laity. Sadly, this attitude was applied to science (though not in the way atheists often think).
The Reformation sought to overturn this disgraceful practice of widespread eisegesis, and of course it succeeded. Christians, thanks in large part to more widespread access to the Bible in their own language, finally began reading that Bible according to what it said, without imposing tradition on it. Science, as we know it, was born when Christians started applying the same method to nature.
Science, in and of itself, is neither Theistic, nor atheistic. Of course, scientists are a different kettle of fish. A scientist may be a Christian, an atheist, or any wide range of other religious worldviews. Nevertheless, it is indisputable that science, from a historical perspective, is Christianity's goldmine. Christians showed the world where to dig, and dig they did. Every nugget of truth brought back to the surface is owed to the God who buried it in the first place, waiting for us to find.
Indeed, not only is science a Christian invention from a historical point of view, but it is also founded and grounded in assumptions that can only be found in the Christian faith. Other religions, in one way or another, cast doubt on either the reliability of the world, or the reliability of the human intellect. If we lived under the rule of whimsical gods, how could we predict the world any better than we predict a grumpy toddler? If our world was ruled by an almighty deceiver, how could we trust even our lying eyes? If our minds are the product of chance, they weren't designed for thinking, so how could we trust them to think any more than we can expect to get an accurate map of London by spilling milk on the ground? Only the God of the Bible provides a stable foundation for scientific inquiry. With Him at the helm, we have:
Reason to believe we live in a rational, predictable world.
Reason to believe in our ability, at least as a collective, to study it.
Permission, and arguably a direct command to do so.
A fixed set of ethics preventing us from doing evil things, such as torture, or murder, in the process.
Men who figured out all of the above and guided humanity into an era of reason.
With all of the above, the claim that Christianity held science back for any amount of time seems ludicrous. And that's because it is. As Evolutionary anthropologist Loren Eilsley notes, "It is surely one of the curious paradoxes of history that science, which professionally has little to do with faith, owes its origins to an act of faith that the universe can be rationally interpreted, and that science today is sustained by that assumption."
So did Christianity hold science back? Not even by one year. Rather, any competent historian will tell you it propelled science forward at full speed, and any competent theologian will tell you it's shocking how long that process took to begin. Saying Christianity hinders science is like saying the ocean stops fish from swimming. Nevertheless, science is a blessing from Christianity, not the point of it. Rather, the point of Christianity, as indeed it is with science, is to enter a strong relationship with our God.
The problem we have is that each and every one of us has actually broken that relationship. God, being Holy, is very much incompatible with sinners. When we do evil in His sight, as all of us do, we store up His eternal wrath for ourselves. Yet, because He is a loving God, He takes no pleasure in dealing out even the most just of punishments. Therefore, before the world even began, He set His plan of salvation in motion. This plan culminated in the death and resurrection of His Son, Jesus. All who sincerely confess Him as Lord, and believe He rose from the dead, will be saved.