Math - What is it?
Beginning early on in the first grade math becomes part of our daily routine, and in America nearly 3,000 hours of our lives are spent studying this subject even before heading off to college. So after hitting the textbooks for such a large amount of time, you would expect we'd come away with a solid definition of what the term means. Right? That's what I thought too. But it's interesting - whenever I start meeting with a new math student and I ask them, "so, what does math mean?" almost always they'll respond with either a blank stare or a facial expression hinting I'm a total nerd for asking. I won't deny the nerd part, but it seems those countless hours studying math aren't exactly giving us helpful hints as to what it means.
In school we're usually given some sort of a working definition of the subjects we study. For example, biology is the study of living organisms. Chemistry is the study of the elements and properties of matter. Physics - the study of forces and motion. And history is, well, the study of history. But math, that's a little more difficult to pin a definition on.
And if you're one of those scratching your head at what the definition may be, don't worry. You're not alone. A few years ago I overheard a professor of mathematics at Harvard tell his class that, even after studying math for 30 years, he had yet to find a good definition of it.
After reflecting on what the professor said, I too realized the same about myself. I had never come across a good definition of math, nor had I ever been taught one or figured it out on my own.
Of course, doing a little research on dictionary.com or Websters dictionary yields various definitions. But I'm of the opinion that the truth is almost always simple. And every definition of math I've found online or in a hard cover dictionary has been rather drawn out or overly complicated.
So while I may not have the best Webster's approved definition of math, for those out there who may be curious about a simple way of explaining it, this is the best I have so far:
Math is a system of symbols we've developed to describe the world around us. It is the logic, the concepts, quantities and relationships that already exist in the universe, converted into a symbolic language. In one word - math is an abbreviation.
Think about it. Every mathematical symbol, number and arithmetic operation is short for some real life concept. A plus (+) sign means you add what comes after it to what comes before it. A minus (-) sign means you subtract what comes after it from what comes before it. The number (2) is an abbreviation for the real life concept of a quantity of two. The number (36) is an abbreviation for the real life quantity of thirty six. The equals ( = ) sign means two things are equivalent. And so on and so forth. We've just simplified everything down to symbols so we can write things that are fairly lengthy in a much shorter manner.
So, even though you can hold two of something, you cannot physically hold the number "2," because numbers and every other mathematical symbol are just abbreviations. They're not physically real.
Furthermore, math can be broadly separated into two parts: concrete and abstract. The concrete part deals with hard numbers like 1, 2, 45, 91, etc; the abstract part deals with variables and relationships. And the two are often mixed. For example, the equation 2x + 3y = 4z has both a concrete part (the hard numbers of 2, 3, and 4, which also represent real life quantities) and an abstract part (the variables x, y, and z, which represent some unknown factors). And the equation as a whole is also representative of a larger relationship between x, y, and z.
This explanation is by no means exhaustive, but I hope it helps those of you who were scratching your heads like I was a few years ago.