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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!

By
Jason Marshall, PhD
April 5, 2013
Episode #148

Page 2 of 3

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.”

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