I believe I know why mathematicians and scientists do what we do. Of course, some may say that they just "need a job" or "it's what they're good at" or, for some, "it brings practical benefits to society." But it is apparent enough, and often freely admitted, that a good deal of research that is going on has unlikely prospects of ever resulting in any tangible benefits to society.
   Many mathematicians are aware that their field of study is as much of an "art" as a "science." Even for those of us on the more applied side of mathematics, do we not praise an "elegant" proof and only with great reluctance accept a "brute force method" for showing our desired results? Have we not heard fellow mathematicians describe the "beautiful symmetries" of a diagram, or the "fascinating intricacies" that a simple equation can unfold? Let me just point out something, in case you hadn't noticed it before. "Elegance" and "beauty" are the vocabulary of an artist, and mathematicians belong to an artistic community, whether we were aware of it or not.
   But many outside of the community of mathematicians will want to know what is it that we see in equations and numbers and graphs which makes them so interesting. And most mathematicians will probably be at a loss for words beyond, "I don't know, it just seems interesting to me." But I think I know the answer, or at least a big piece of it. I think I know what keeps us pressing in for more and more mathematical discoveries (and likewise for many other sciences).
   The answer is captured in that moment when you have a page full of multi-line equations that have been derived on several previous pages, with various sideways scribblings in the margins,... and then suddenly things begin to cancel out "nicely", and your anxious expectations begin to rise up,... and after some things have been canceled out and other simplifications made you realize that some of the remaining terms can be gathered together, and you become even more hopeful,... and once those terms are gathered together they "just happen" to precisely match a form that can be discarded or drastically reduced by one of the assumptions behind the problem,... all this finally leading up to an amazingly "nice and compact" form that is easily understood and yields "rich insights" by exposing a new view of its relationship to the original problem, and indeed, to other problems.
   But think about it. What is happening within you in that experience? Why is your HEART racing right along at the same speed as your mind? If mathematics is a purely "intellectual" exercise in abstract facts, why should it be so ENJOYABLE to learn how one theorem encompasses three or four or five previously known, and seemingly unrelated, results? I expect that probably none of us see such a new unifying theory and merely say, "OK, I'll add that fact to my brain", but rather we experience, at least for a moment, a sense of AWE. Why else should professional mathematicians, writing in professional, peer-reviewed literature, describe their findings as "extremely satisfying"? Satisfying? Excuse me, did we mathematicians hear ourselves use the word "satisfying"? Why should one pure, abstract fact, be more "satisfying" than another? And why does such language pass through professional journals and publications, if not for the fact that it is a universal experience among us?
   I'll tell you why we speak this way. Because, at least on one level of your consciousness, you know that there is order in this universe. You know that the most profound of physical realities being described by the simplest of equations (such as E=mc^2) is not a mere "coincidence." That is the core of the quest for the "elegant" proof. You instinctively believe that any truly, truly significant and breakthrough mathematical fact should have a "nice", "intuitive", and relatively "simple" underpinning. Did academia explicitly TRAIN you to think that way? Certainly not, but you still do, at least on one level. Just as all your fellow mathematicians do.
   The reason that we find it "exciting" when a "nasty", complicated equation starts "falling into place", and yielding its simplifying secrets, is the same reason that it is "exciting" to come across stones arranged in a fire pit when you are lost on a deserted island. In that very moment you know, "I'm not alone." The difference is that, when it is a mathematical or scientific discovery about the orderly nature and workings of this universe, the trail of intelligent design which you have caught sight of is not due to the workings of any fellow man, but to the God and Creator of this universe, who unfailingly leaves behind His fingerprints in all he does.
   And so it is, fellow mathematicians, that every time you read or discover a new mathematical fact and say in both your heart and your mind, "Hmm, this is interesting", what you are really saying is, "Yes, there is a God, and I can see the evidence of His intelligent and orderly design of this universe." And in that moment of awe, your heart and mind are trying, though in an imperfect manner, to do the one thing they were meant to do whenever they look upon the glorious reflections of a glorious God in His works of creation, and that is, worship.
   And so I urge you, first of all gently. You have tasted but a small glimpse of the eternal power and divine nature of this Almighty God through your investigations of the countless patterns and regularity that make up the physical and abstract rules and relationships on which this universe runs. You have tasted but a small glimpse of His work and found it pleasant. How much more, then, to know the Author and Designer Himself! And to find the fulfillment that is only known in Him! As the Bible says, "Taste and see that the Lord is good." You have tasted the appetizers, move on to the feast.
   And second, again I urge you, but this time more firmly. (Though I don't want to, but out of concern I must.) Every second that you devote to exploring recognizable and logical patterns in the ordering of this universe, you are testifying against yourself that you KNOW this universe is made and governed by an intelligent designer. When you stand before God in the Judgment, how will you explain having spent your entire life exploring multitude evidences of His design and yet ignoring Him? These beautiful mathematical connections, these pleasures of seeing as you never saw before, to what will you attribute them then? If you call the fingerprints of the Creator's design "your own inventions" or "patterns of mere chance", He will not be pleased. Fear God, then, and repent of the evil of ignoring Him. God is patient, but do not take his patience for granted. When the greatest mathematicians of all times stand before God, He will not be at all impressed with their "clever discoveries", since everything man has found are all trivialities in His sight. So fear God, and if you are currently ignoring Him, change direction and return to Him. The very, very good news is that Jesus Christ suffered and died to take the punishment that we deserve for the sin of hating and ignoring God. Turn around and trust in Him and you will be forgiven. Believe in the good news, and let your mathematical inquiry (and entire life) take on a whole new meaning.