The topic of how religious people view the interplay between human reason and the mind of God is very important. The way in which the Catholic tradition understands this is one of those things that make me especially grateful to be Catholic. It helps us to steer clear of the two extremes that are rationalism (putting all the weight upon human reason) and fideism (putting all the weight upon what comes to us by faith).
Faith and Reason Together. The most enduring and robust strands of Catholic theology have long grasped a vision of the human person which realizes that the sort of knowledge that comes to us by faith (i.e. by a supernatural self-communication of God to man) should always be received in the context of a human mind fully alive in every way--whose natural powers of reason are always striving to fire on all cylinders.
Thus, we should have no fear or hesitation of simultaneously and vigorously engaging a most devout and pious faith together with the most rigorous and probing rational thought processes! The book of nature and the book of Sacred Scripture come from the same divine source. Our faith, necessarily, brings our minds beyond where our reason alone could go. But, in so doing faith never violates our reason; indeed, faith, in turn, gives our reason more nourishment to feed upon as it turns back to the book of nature enriched with the truths of faith.
Reason by Itself Knows Traces of God in the World. After briefly mentioning faith and reason together, I would now like to narrow my focus just to natural human reason, exploring how natural reason on its own, considered apart from faith, is still involved with God (and this is so regardless of whether a particular person is aware that God is real).
The natural operation of human reason itself has a connection with the knowledge God has of Himself within the Trinity.
If I understand this properly, according to St. Thomas Aquinas, God knows us (in the deepest, most thorough sense of the Creator knowing his creatures) within the same act of knowledge that is His own knowledge of Himself. In other words, as His creatures, God's knowledge of us is contained inside His own self-Knowledge. (Important note: this does not in any way mean that human creatures are a part of God's own nature, which would blur the clear distinction between God and His creation; it has more to do with the fact that God's knowledge of His creation does not add anything new to the knowledge He had of Himself before creation)
Now, what about human nature and our own ability to reason aside from faith? The idea (still using St. Thomas) of 'Image' is very important here. We are "images" of God (Gen 1:26). More specifically, we are images of The Image--who is Jesus Christ, the Son, the Word, the one Perfect Image of the Father. Now this Perfect Image which is God the Son is also the Truth and the Word--the Word which is the Father's perfect self knowledge, "spoken" to Himself.
What impact does this have upon our own natural reason? Because we are in our very nature images of this one Perfect Image of the Father, we, in our own human acts of knowing the created world, share (participate) in the very self-understanding of God within Himself. To gain authentic knowledge--to grow in wisdom and understanding of the world and of ourselves--is, by the very activity of our minds, to come more deeply into contact with the interior "thought" of God Himself. (Note: the new knowledge of God we gain by the gift of faith, opened to us at Baptism, is another thing beyond this and is not attainable by our reason alone; I am trying now to remain on the natural plane that all mankind shares regardless of faith.)
This train of thought leads us to see (though dimly) that knowledge and love--in God--are united. To know is to love and to love is to know, at least from the divine perspective. In the beatific vision knowledge and love will be one in the awesome splendor of each individual person's direct encounter with the Triune God. (The role of grace in our earthly life and how the infused virtues transform and elevate natural reason with a new capacity is another important aspect of all this which I won't try to go into here.)
I find this mysterious interplay between the mind of God and the minds of men fascinating. Without losing sight of the clear demarcation between God and man, creature and creator, it means that exercising the human mind upon the created realm is already to possess an awesome dignity--the dignity of being an image of God in the very operation of our minds as we learn and grow in our understanding of reality. For indeed, even as we know things independently as unique, free, self-possessed thinkers, ultimately it is also the case that we know all that we know in Him (in whom and through whom all things were made; Jn 1:1-5)! How's this for anthropological awesomeness!