Some teachers will tell you that you are going to use math in a wide range of professions. They find examples of "applications." Some are of obvious usefulness, but many seem contrived. "When all is said and done, who really cares when train A will meet train B? How likely am I to remember how to do this once I've taken the final?" After years of taking math courses and using math ideas in many different jobs, I have never had to solve a "radical equation" except when teaching it. When are you going to use it? You're not. I doubt most people will ever use math outside of a math class. So, why teach it?
I lift weights. One exercise is called the military press. One sits straight up, holds the weights on the shoulders, then lifts them straight up above the head. Never once has a boss come up to me and said "For the next week, I want you to lift these weights above your head!" Why lift weights? Lifting weights makes my body stronger. A strong body is useful in countless ways every day. Sure, I can point to specific examples -- strong shoulders make it possible for me to write notes on a chalkboard for hours a day -- but naming a few examples might be misleading. I use my shoulders thousands of times each day in ways too numerous to count. I use my shoulders at work, at home, while playing, all of the time. It doesn't matter what I do for a living, everything I do with my body is easier because I have a strong body.
Math is the study of patterns. What is a number? It's a pattern. "Three" is the quality that is the same whether we are talking about three apples, three oranges, three fingers or three countries. Learning about quantity patterns is called arithmetic. Learning about shapes, another kind of pattern, is called geometry. There are lots of other kinds of patterns. People who study patterns are called mathematicians.
Have you ever noticed a person you don't know that you have seen before? Have you ever noticed something happen again and again? Have you ever timed your driving between traffic lights so you will get there just as the light turns green? You are noticing patterns, i.e. doing math. There is something wonderful about the world that makes it complicated enough to be interesting but repetitive enough that we can notice patterns.
Learning math is learning to recognize and take advantage of patterns. Patterns surround us, so knowing how to take advantage of patterns gives us power. Why learn math? Everything you do with your mind will be easier because you have a strong mind.
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