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If you were a Martian trying to figure out how to get along on earth, you might think that the most useful thing would be to understand human beings. You'd be wrong. It is almost impossible to understand people; it's easier to model them mathematically.
What is mathematics?
Mathematics is a toolbox for thinking; an indispensable guide to the art of intellectual discovery. We should value it not only for its ability to bring about reason, and also for its practical power to transform big problems into small ones.
The ultimate goal of mathematics—to discover truths—is not the same as the ultimate goal of technology, which is to build things. But mathematics can accomplish technological goals too, by providing a way to make any giant task manageable.
Much more than just a conceptual framework or a conveniently rigorous way of codifying what we observe in the world, mathematicians take the fundamental properties of our universe and combine them in such a way that we can solve problems we couldn't solve any other way.
Math is the language of the universe.
It is the language of the earth.
The language of life, of business, of government, of the arts.
It is the language of economics.
The language of computers.
The language of measurement, of accounting, of statistics.
It is the language of science.
The language of engineering.
And most of all, the language of understanding.
What is understanding?
Understanding is not just memorizing. It is knowing the things that are true, or the essence of things, or the connection of things.
Understanding is to knowledge as seeing is to vision.
Understanding is an experience. It's an expansion of what you can imagine. Understanding is an appreciation of how things fit together.
If you understand a movie, it's because you see the connections between its parts—the significance of each scene in terms of what preceded it and what follows.
If you understand a book, it's because you see the connections between its sentences—where each one fits into the sequence of sentences before it and after, and how each sentence relates to those around it.
If you understand a person, it's because you see the connections between her actions—how each fits into her character and into what she did before and after.
In a sense, understanding is knowing the essence of something. You can know a lot about a thing without knowing why it is the way it is. For example, a language arts teacher may know a lot about how a car engine works, but unless he understands why it's an engine, he doesn't really understand it.
Understanding comes from seeing connections. If you have two ideas and you can't see how one follows from the other, this suggests there's no real understanding there.
Math is a tool to solve complex problems
Some students avoid math as much as possible because they think it’s hard and they think it’s not useful. However, math is a tool to solve complex problems, and it’s a tool that’s useful in a lot of different ways.
You can do math for more reasons than just getting good grades during your school days. You can use math to create beautiful works of art, boost a business, and improve your personal finances.
You can use math in analysis of student attendance, proficiency, and safety. In short, there are a lot of things you can do with math.
If you’re lucky enough to get into calculus or one of the many other math-based subjects that aren’t too uncommon to see in schools, then you’ll be amazed at how powerful math can be. Math helps businesses and entrepreneurs do things better. It helps investors invest in businesses and make more money. It helps people analyze deals and make better decisions.
Math is also extremely important for consumers to help make buying decisions, keep track of products or services, and make lifestyle adjustments. The list goes on.
A special kind of language
Mathematics is a language. But it's a special kind of language, one that's more precise and more powerful than ordinary language. The power of mathematical language comes from the precision with which you can express ideas.
Thinking of the world in mathematical terms isn't just a matter of mastering technical skills. It is more like learning a new way to look at the familiar.
Once you know how to do it, you have an easier time of solving problems that stumped you before.
Many people think of math as a set of rules or procedures to follow to get the right answer, but mathematics is also about thinking, reasoning, and problem-solving.
