Science satisfies the sense of curiosity built in all of us; and scientists often possess a healthy dose of curiosity. Still, that is not a sufficient reason to do science. Curiosity may motivate us to begin an investigation or may direct us in an area that interests us, but it hardly explains why we sometimes wrestle with problems for years.  

Some of us may do it for fame and glory, some for riches, some out of sheer stubbornness, or just as a plain old job. But, deep down, most of us do science because it is exciting. This excitement often includes a sense of exploration and discovery. But, the ultimate reward comes at the end of the task. That feeling of achievement, of rightness when we know we have the correct explanation is hard to describe, but it is what happens to any human being when he masters, understands, discovers. It is that "aha" that sense of glory that for a moment, however fleeting, we have been privileged to see a small part of the universe that was hidden to us before now. Small wonder that some 2200 years ago, when Archimedes suddenly understood the principles of buoyancy when taking a bath, he jumped up and ran naked through the streets of Syracuse (Sicily, that is) yelling "Eureka! Eureka!" (I've got it! I've got it!"). 

The definition of science already embodies the results: science creates a body of explanations and descriptions. To be more specific, the products of science are descriptions, models, ideas, theories. These models are NOT reality, not nature itself. They are man-made. This concept that the models are not real, leads to another central characteristic of science, namely that it is self-correcting. Suppose, as happens all the time, that a scientist becomes aware of a new phenomenon not accounted for by present theory, or a phenomenon that violates present theory. Because theories are man-made and nature is real, we must assume that the discrepancy is the result of a problem with the model. Therefore the efforts of scientists will be directed towards expanding or changing the model in such a way as to include or explain the new phenomenon rather than to dismiss it as anomalous. Consequently, with time, scientific models become more general, more sophisticated and match reality (nature) more closely. 

Often, as a scientific discipline matures and becomes more sophisticated, its explanations will be written in the language of science, mathematics. Because math has its roots in tenets and postulates rather than in nature, it itself, is not a science, but a language.  

We use it because it provides certain advantages. It is concise; a few symbols can cover a multitude of relationships. It is universal; mathematics is understood all around the world; it is quantitative and precise; it allows exact numerical solutions. It is cheap; it is cheaper to mathematically model the structure of matter than to build a supercollider. It is safe; better to model a fusion reaction than to set one off in the lab. Because of these advantages, scientific concepts and explanations are often couched in mathematics.