While it's relatively easy to argue for the importance of studying mathematics, it is unfortunate to have to. But, the fact remains that in some cases a majority of college students enter their freshman year needing some remedial mathematics courses. This clearly indicates that they are not getting a good math education in high school and probably also means they are not being shown the importance of learning math. This is more unfortunate as the job market continues to develop more and more jobs where math skills are in demand. Even in the information age, where information is usually taken to mean verbal or written communication, mathematics still ranks as an important skill set.
Everyday Use: The most obvious argument for studying math is the many everyday uses. Calculating percentages, balancing a checkbook, calculating area are just a few skills everyone needs virtually every day of their lives. Unfortunately, such applied math skills are sorely lacking even in students with good grades in high school math courses. The philosopher and mathematician Pythagoras recognized that numbers are an integral part of every life and that has never been more true than today.
Numeracy: One of the most important aspects of studying math is gaining what mathematician John Allen Paulos calls numeracy, defined as a general familiarity with numbers or having a good sense of numbers. This is quite different than being skilled in everyday uses of math though the two are connected. Being numerate involves such skills as estimation and a firm grasp of statistical principles and how to apply them. Being numerate also involves being able to see the connections between numbers and aspects of life not immediately obvious and not often taught in math classes. What does the population of a city tell you about how many ethnic restaurants there are or the chances of finding a good used bookstore?
Universality: In many areas of life people tend to be relativists in spite of the many problems with this view especially in the realm of ethics. But, the study of mathematics can be a good antidote to this relativism as it shows that there are certain universal principles which govern how the world works and how we can understand it which are independent of culture or opinion. There is no such thing as Chinese mathematics which differs from European mathematics. The same principles apply wherever you happen to live.
Foundations: Perhaps for reasons connected with the points made above about universal rules, Plato advised that before studying philosophy and ethics students in his Academy first master the principles of mathematics and geometry. Pythagoras believed that everything consisted of numbers and to the extent that we can quantify a wide range of phenomena both physical and social this is true. Mathematics is the foundation of physics, chemistry, and most other hard sciences. Through the use of statistics it can also be seen as an integral part of such soft sciences as sociology and economics. To fully understand the principles of these disciplines requires a good working knowledge of mathematics.
More than any other area in the curriculum, with the possible exception of history, how math is taught has led to the problem of mathematical illiteracy. Unless we begin teaching mathematics with an eye towards helping students master everyday use and gain numeracy as well as see the connections and foundations of math in other disciplines we will continue to struggle in a world more driven by math than ever. Ultimately, students will grow into adults who see first-hand the costs of this illiteracy in their shrinking income, investments, and savings. Perhaps those numbers will motivate the drive towards improved math literacy!
For book recommendations in math and many other subjects check out Learning Through Reading.