I'm speaking on this in a week's time - here's a first draft for your interaction.
So how do you answer this question? I could I suppose wheel out some clever Christians to show that clever people believe in Jesus. But there are plenty of stoopid Christians in the world. Instead I'm going to interact with Richard Dawkins. He's the professor for public understanding of science, but he's also rather interested in this question about faith and intellect. It's the subject of his recent bestseller, The God Delusion, and all quote from him are from that book.
Firstly, Dawkins says (p51) "It is the nature of faith that one is capable of holding a belief without adequate reason to do so". He asserts that faith is anti-intellectual because it isn't based on evidence. So the question is, does this describe Christianity. In John 20v31, an eyewitness of Jesus' life writes to say that he has gathered a stockpile of evidence. That evidence is for us to consider so that we may believe Jesus to be the Son of God. He doesn't expect blind believe, but writes so we would believe with adequate reason. You need to consider that evidence for yourself and see if it stacks up - and we can talk about that if you like. But, for now, we must conclude that Christianity is not anti-intellectual because it is a worldview based on evidence.
Secondly, Dawkins (p283) "My belief in evolution is not fundamentalism, and it is not faith, because I know what it would take to change my mind, and I would gladly do so if the necessary evidence were forthcoming". He asserts his own position but in the process demonstrates that he considers Christians to be fundamentalists. Anti-intellectual because nothing could change their minds. So let us ask, is there anything that could refute Christianity. In 1 Corinthians 15, in the Bible, we're told that if Jesus did not rise from the dead - resurrection - then Christians are pitiful fools. That is to say, the whole thing falls apart if the resurrection did not happen. It should be abandoned in such circumstance. Therefore, Christianity is not anti-intellectual fundamentalism because like Richard Dawkins we know what it would take to change our minds, and would recant if required.
Titanic director, James Cameron, recently claimed to have found Jesus' tomb - complete with his body and that of his family. If this is authentic then he has found the 'necessary evidence'. You ought to check his evidence, weigh it against the evidence for Jesus resurrection and see which carries best fits what happened.
Thirdly, let us observe that far from being anti-intellectual Christianity is more than just intellectual. Anyone of any IQ is welcomed by Jesus. Class, culture and mental competence are not barriers to belief in him. The good news about Jesus is remarkably simple to understand - a child could manage it. Yet, it is deep and rigorous enough to occupy a lifetimes study. Further, Jesus calls people to follow him completely. Do not leave your brain at the door. Nor your heart, body, emotions or desires.
But if there is evidence and we have a criteria for refuting Christianity, and it's open to all... why isn't everyone queuing up to become a Christian?
Dawkins again, this time quoting Martin Luther with relish (p190). "Reason is the greatest enemy of faith, it never comes to the aid of spiritual things but frequently struggles against the divine word, treating with contempt all that emanates from God" Dawkins plays dirty here because he imposes his own definition of reason (something he wont let happen when it suits him - for example with Einstein earlier in his book). We have already said that Christianity fits criteria for being reasonable. The mind is not to be bypassed. But the quote is accurate. We should observe that Martin Luther was a theologian, a lawyer, a scholar, a linguist as well as being a brewer. He was no intellectual lightweight. But, his quote is right...
We'll see how. Let's play Bruce Almighty (illustration borrowed from Mike Reeves). Suppose for 24 hours you are God. What would you do with your great power? More importantly, how would you want your creatures to relate to you? Inevitably we'd ask for devotion, obedience, good morals, performance. And The Bible calls this "the wisdom of the world" (1 Corinthians 1v21). It's the way that human wisdom dictates what God is like. I almost don't dare put these words in their context. It might cause a riot. But, we can't avoid the evidence. This comes at the start of the letter that includes the famous poem about love that we read at weddings. Paul writes that the wisdom of this world cannot know God. If we try to come up with what God is like we only ever get cheap fakes, imitations, false gods, idols... Christianity is having none of it. All human attempts to reach God will fail. Human intellect will fail.
Rather, the only way is through what he goes on to call "my foolish message" namely that the only way we can know God is through "Christ Crucified". God on a cross, dying to bring us to him. No one invents God like that - Me Almighty wouldn't die for creatures who hated me. Not going to happen. But this is Christianity. It isn't clever or sophisticated. It doesn't pander to our desire to show off our intellect. In fact it is designed to thwart our intellectual pride and superiority complexes. It leaves us foundering without the knowledge of God unless we are prepared to trust in God on a Roman Cross to save us. That is to say boldly that our confidence to come and know God comes from the shameful criminal death of Jesus of Nazareth. No one looks clever when they say that.
Endorsing Richard Dawkins book, Derren Brown says... "In hope that those secure and intelligent enough to see the value of questionity their beliefs will be big and strong enough to read this book". And Jesus says - yes engage your brain. But ultimately if you try to think yourself to God, to prove that you're "big and strong" enough you'll fail. Christians are people who come on their knees to "God on the Cross" with no boasts. They look stupid at times but there is no other way. In this "reason is the greatest enemy of faith" because it demolishes our self-confidence. It flushes it down the toilet. Dawkins, one last time (p50). "If he existed and chose to reveal it, God could clinch the argument unequivocally, in his favour". The cross of Jesus says he has - and that this is a matter of evidence to consider not irrational leaping in the dark but it does thwart our proud minds... it puts us on the spot and asks us to consider the evidence.