What Is Algebra?
What is algebra? What does it have to do with variables? And where did it come from? Keep on reading to learn the secret to understanding algebra!
People often think that “algebra” sounds like a big and scary thing, but I think that’s mostly just because they don’t understand what it actually is. Which is a real shame because algebra is incredibly useful in the real world. Plus, it turns out that the big ideas behind it all are actually fairly straight-forward. So today we’re going to combat this universal fear and misunderstanding of an otherwise beautiful subject by diving in and answering the big question: What is algebra?
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The Problem with Algebra
The problem with algebra is that it isn’t a simple tangible object…like a spoon. If it was, it’d be easy to explain. After all, few people who manage to eat lunch with a spoon will have trouble explaining how it works afterwards. But, unfortunately, that’s just not what algebra is. So, what is it then? Well, instead of being a thing like a spoon, algebra is more analogous to being something like a style or a method of using a spoon…
I’m thinking of a sensible two-fingered (plus a thumb) grip versus a crazy five-fingered silverware stranglehold. Sure, both styles will get the job done, but one technique is definitely more elegant and efficient than the other.
The same is true with “style” in math. One type of method—sometimes algebraic—is usually most appropriate for solving a particular type of problem. But styles are much harder to recognize, point at, and label than things—which is why recognizing and labeling algebra can be tricky. So then what’s the best way to think of algebra?
What Is Algebra?
My answer is that you should think of algebra as arithmetic…with variables. Honestly, once you understand what this means, you understand algebra. Sure, in truth there’s actually more to it than this, but for now “arithmetic with variables” is a perfectly good way for you to think about algebra. And the good news is that you’re almost certainly proficient at doing arithmetic already. Which means that you just need to focus on getting comfortable with the one caveat in that description—the “with variables” part.
Why Is Algebra Named “Algebra?”
Before we talk about those variables, have you ever wondered where the word “algebra” comes from? Although many of its ideas are probably much older, the word “algebra” dates back to the publication of an Arabic math book in the year 825 AD by a man named Al-Khwarizmi. What does that have to do with algebra? Well, the first word in the book’s title is “al-jebr” which, after a thousand years or so, became “algebra.”
Who is this person we have to thank for the name of today’s topic? Well, Al-Khwarizmi was a Persian mathematician whose writings revolutionized math in the Western world. In the 12th century, translations of his works found their way to Europe and introduced the West to the Hindu-Arabic numeral system that we use today, the number zero, and algebra. Sadly, most people have never heard of him! But now that we’ve taken care of that, let’s get back to answering today’s big question: What is algebra?
Variables and Symbols
So far we’ve learned that algebra is arithmetic with variables. Which leads us to the next big question: What are variables? The answer is that variables are symbols without predetermined values.
Symbols…predetermined values…huh? I know this all might be a bit confusing, so let’s take a minute and make sense of it. First, let’s talk about the different kinds of symbols in math. You’re already familiar with many of them. For example, “+” and “–” symbolize ways to combine numbers, “>” and “<” symbolize ways to compare numbers, and numerals such as “1,” “2,” and “3” are symbols that represent the concept of quantity. Of particular importance for us today is the fact that—unlike variables—these numerals are symbols that have predetermined values.
As a quick aside, most people don’t differentiate between the concepts of numbers like 1, 2, and 3 and the symbols used to describe them. But the ideas of 1 and 2 definitely have lives and meanings far beyond the way we write the numerals “1” and “2.” For example, the number 2 has an abstract property of “two-ness” associated with it. It doesn’t have to mean 2 people, 2 pigs, or 2 anythings. It can just mean “two-ness.”
What Is Algebra? — Redux
Now let’s now start putting all of these ideas together. We’ve learned that algebra is arithmetic with variables, that variables are symbols without predetermined values, and that numerals are symbols with predetermined values. What does it all mean? Let’s work backward through the list to unravel the meaning one thing at a time.
First, starting at the end, numerals are just symbols with pre-determined fixed values. In other words, the idea of “two-ness” or “three-ness” is encapsulated by the numerals “2” and “3.” With that in mind, it’s not such a big leap to understand what a variable is: Just like numerals, variables are symbols that represent numbers…except that the numbers they represent aren’t yet specified. Honestly, that’s really the only difference between something like the numeral 5 and the variable x.
Moving backwards up to the first item on the list, we’ve now arrived at the point where we know and understand all of the pieces required to “get” algebra. Here’s the gist:
Algebra is exactly like good old arithmetic…except that instead of just doing arithmetic with numbers, we’re also going to do it with these new things called variables…which are just symbols that represent the as-yet-unknown values of some numbers.
I know this is kind of a mouthful, but once it’s put this way I hope it’s clear that algebra really isn’t so scary after all.
Wrap Up
Okay, that’s all the math we have time for today. If you want to learn more about algebra, please check out my book The Math Dude’s Quick and Dirty Guide to Algebra.
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Until next time, this is Jason Marshall with . Thanks for reading, math fans!
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About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.
