But if God is logical, logic would lead people to think more logically and believe in Him, but it seems to lead people to reject God.
With that alone, yes, logic should lead one to God. There are many (such as Anthony Flew) who have recognized this. The other thing we must keep in mind in this matter is the nature of man-kind(this includes the ladies).
Prior to regeneration;
2 Corinthians 5:17 Therefore, if anyone is in Christ, he is a new creation; the old has gone, the new has come!
Mans intellect is effected by sin. This is sometimes called the "Noetic Effects of Sin".
The Noetic Effects of Sin
Of course human reasoning in the present age is never completely free from the influence of sin. Therefor, we must now discuss the nature of unbelief, of disobedience to God's words, and how that unbelief affects knowledge and reasoning-- what theologians call the "noetic effects of sin."
Those who deny god do so, not because they lack evidence, but because their hearts are rebellious. In Romans 1:19-20, the apostle Paul says that
what may be known about God is plain to them, because God has made it plain to them. for since the creation of the world God's invisible qualities-- his eternal and divine nature--have been clearly seen, being understood from what has been made, so that men are without exscuse.
Paul even says that they "knew God" (v.21). God's revelation is clear, but fallen human beings "suppress the truth by their wickedness"(V.18). So the unbeliever's problem is first ethical, and only secondarily intellectual. His intellectual problems stem from his ethical unwillingness to acknowledge the evidence. Unbelief distorts human thought.
..... [continued on next page]
When someone recognizes the truth but seeks to repress it, the result is irrationality. In some cases, we call such repression, "wishful thinking." Sometimes there is psychological repression, in which a person relegates the truth to some subconscious level of the mind. Other times, the truth and error simply exxist side by side, interacting in odd ways, creating contradictions in thought and life. For example, the unbeliever may accept historical evidences for Wellington's defeat of Napoleon, while denying equally cogent evidences for the resurrection of Jesus. This sort of inconsistency does not come from a mere lack of intelligence. It has, rather a spiritual wroot. It comes from living in God's world with a mind created to acknowledge God, but with a disposition of resistance and rebellion against him.
(Five Views on Apologetics, John Frame, P 211-212.)
Another example of how atheism is both rational and irrational at the same time, and a good example at that is the matter of Morality.
Atheists will denounce all sorts of moral evils, and rightly so. Yet when questioned about what grounding it is evil, they can't offer anything rational. Rather it often turns into "It's objectively wrong because I subjectively say so". I could link you to a forum where I've pressed that matter, and a gentleman began to argue on such a level if you so desire.
The origins of the universe is another good example. The atheist in trying to maintain that there is no God, will respond by saying either the universe is eternal, or that which begins to exist doesn't require a cause. That things can come out of existance from nothing by nothing for no reason whatsoever.
Which essentially makes this picture unfortunately accurate:
People who smart in mathematics, true science, etc. seem to the be the ones who are more likely to reject God.
Well, first of all mathematics has little to do with "discovering" God. The one way that I could see where mathematics would be relevant is going to be a philosophical argument demonstrating the existance of God via laws of logic (and thus mathematical laws). Mathematics when applied to the universe would also cause us to recognize that it is finite (not eternal) and thus due to having begun to exist requires a cause outside of itself.
I would not say there is such a thing as "true science", there is a branch of Philosophy known as "Philosophy of Science". Most scientists don't like to admit it these days, but science is actually the product of philosophy. Another good example of the rationality and irrationality of atheism at the same time. The Christian has good grounds (god) for believing there are immutable laws of nature, while the atheist has no good grounds and rather must simply assume them.
In philosophy of science, I would be an Instrumentalist.
What does that mean?
There is a debate in philosophy of science called realism vs. anti-realism. Basically the question attempted to be answered is, "Can we formulate theories that are anywhere near actuality?" The realist says yes, the anti-realist says no. As an instrumentalist I say, "I don't know, I just want to know if it's going to be useful or not."
The current dominate scientific frame-work is that of Philosophical naturalism. That is why most scientists don't believe in God, it's not a scientific matter but rather is a philosophical assumption. That the only things which exist essentially are matter and energy. When one approaches science and has this assumption, then God to them is not an acceptable conclusion.
The Philosophical naturalism will claim that, "we don't know what caused the beginning of the universe, and we're going to keep looking." What is often un-stated is the fact that they don't want God to be a possible explaination. This is more-so true in philosophy.
The question of "Does God exist?" is primarily a philosophical question rather than a scientific one. Science tells us things, and can give us reasons to believe in God, no doubt.
I think DNA is a great example of that.
Ultimately though, science is the study of the natural world. So when you say, "I can't find God in the trees", then the reason for that is because you're committing a category error, as God is not a part of the natural world (unless you count the body of Christ).
Sure evolution, progressive education, and other humanistic-based ideas are illogical, but the Bible's view point on everything seems just as illogical as atheism's logic and reasoning.
Sure, there are plenty of things in any world-view that upon impression seem illogical, but the thing to do is to examine it beyond feelings. I think most Christians would admit that, parting of the red sea, burning bushes that don't turn to ask, the earth "Standing still", talking donkeys, virgin births, resurrections, and many more supernatural events on feeling alone "seem illogical". When we examine this further we find that that, is not the case at all. In fact, I would argue that it is logically neccesary for these things to have happened.
Everything always goes back to feeings (for atheists) or the Holy Spirit (for theists). What's the difference?
There is feeling involved, yes. No doubt about that at all. What we can see though through philosophy, science, history, etc, is the rationality of Christianity, and the irrationality of atheism. I will gladly stand on that point.
EDIT:
I know this post is full of spelling and grammar mistakes, and I apologize. I'm not going to fix them though(there's too many for 5 minutes of edit time), if something needs clarified due to an error, please point it out.