Things not seen - Ether 12:6

And now, I, Moroni, would speak somewhat concerning these things; I would show unto the world that faith is things which are hoped for and not seen; wherefore, dispute not because ye see not, for ye receive no witness until after the trial of your faith.

I have spoken before about the difference between faith and belief: Belief is more of a cognitive function, the result of being convinced from evidence or logical reasons. The world of science works on the principles of evidence and proofs. These proofs are typically based on observations and proposed models of how to represent and rationalize them. In short, beliefs are based on knowledge and experience rationalized by reasoning, regardless of whether the evidence or the reasoning is flawed or not.

Faith on the other hand, is not based on logic or reason. Though belief is an essential precursor to faith, faith itself goes beyond logic and is not a function of the head, but of the heart. Faith is not based on a belief system or scientific or mathematical models ~ such models are a representation of reality, attempting to mimic the real thing, but they fall short.

A short example is Newton's laws of Physics versus the theory of relativity. Newton's laws were able to describe the motion of an object in the presence of the forces of gravity very well. However, there were a few extreme circumstances in which Newton's model did not reflect reality. Scientists were at a loss to explain why for a very long time, until Einstein introduced the theory of relativity, which solved the problems seen in the extreme cases until quantum physics were taken into account. Scientists are still trying to produce a theory which will take into account the macro and the quantum level.

The point of this example is that while Newton's laws were very very good, they were still a model that "approximated" reality. Einstein's theories improved upon them, but even his model was shown to be inadequate.

Remember what Alma said:

Faith is not to have a perfect knowledge of things; therefore if ye have faith ye hope for things which are not seen, which are true.

Faith, unlike belief, works on true principles and promises spoken by the Spirit, not models, approximations or representations.

Jacob emphasizes this point:

...the Spirit speaketh the truth and lieth not. Wherefore, it speaketh of things as they really are, and of things as they really will be; wherefore, these things are manifested unto us plainly, for the salvation of our souls.

The Lord Himself defined knowledge thus:

... truth is knowledge of things as they are, and as they were, and as they are to come; And whatsoever is more or less than this is the spirit of that wicked one who was a liar from the beginning.

 Faith is belief in the truth, not some "model" - this is a major difference between faith and belief. While there are many theories out there which attempt to describe phenomenon that we observe in the natural world, such as the theory of evolution, or the big bang theory; even though they are well thought out and do a good job of describing things, because they are the inventions of men, we cannot assume that they are perfect nor stake our salvation on them.

I will not put my trust in the arm of flesh; for I know that cursed is he that putteth his trust in the arm of flesh. Yea, cursed is he that putteth his trust in man or maketh flesh his arm.

Having said this, we cannot condemn scientific research, honest inquiry or theory-making. I believe that the enthusiasm that goes along with secular learning is righteous and essential to our being. It is when we assume that there are no flaws in man's theories and replace God with them that we are in trouble. There is no man alive that knows enough through traditional secular learning to definitively say anything about the existence or attributes of God. On the other hand, we are commanded to take secular learning seriously:

... teach one another words of wisdom; yea, seek ye out of the best books words of wisdom, seek learning even by study and also by faith;

To wrap up, Faith is not to be had by engaging in secular study, meditation or "deep  and solemn thoughts". It is a gift based on the promises and whisperings of the Spirit. Secular study is essential to our salvation, and we should be excited about it, but we should not let it overcome, describe or even influence our faith. We are expected to do our best to understand the mysteries of God via all forms of study, but we should not expect to find Him in a textbook, or in a mathematical or scientific model. He is to be found by exercising faith, even when His promptings may seem to contradict popular secular knowledge.

For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.