It’s honestly quite difficult to think about mathematics at this point in our lives and try to ignore the existence of algebra. We’ve come to understand the significance of algebra in representing patterns, interpolating and extrapolating information, and logically illustrating the core information of problems in a universal and concise manner. However, when trying to explain the same mathematical concepts to students that haven’t experienced algebra, we employ the use of imagery and clearer explanations to relay the same ideas. In the same effect, I think that pre-algebraic mathematics would have relied more heavily on the use of effective depictions. When thinking of most everyday mathematics, such as algebra, the Shakespearean quote, “A rose by any other name would smell as sweet”, often comes to mind. That’s simply because basic algebra is a fairly intuitive concept that we use often in many scenarios, and often don’t realize that what we’re applying is math!
From an outsider perspective, I would like to agree that math is just about generalizations and abstractions; but then, isn’t everything? There are so many different classifications of mathematics that get swept under that umbrella. I like to think of math as a toolbox- picture your standard hammer/nails, screwdriver/bits/screws, crescent, saw, and tape measure. Those are your tools that really come in handy on a variety of projects. However, that doesn’t mean that you will always use each of them on every project, and it certainly doesn’t mean that those are all the tools you’ll ever need. So, no, math is not all about generalizations and abstractions.
Algebra undoubtedly is a systematic and concise way of translating long word problems down to a simpler form that allows for easier manipulation and pattern recognition, and it saves a lot of time from creating comprehensive diagrams to get the same points across. I'm not actually sure how I would even begin to state the Mean Value Theorem or the Pythagorean Theorem explicitly and rigidly without algebra. In fact, algebra is fundamental to so many mathematical proofs that we study in our post-secondary 'Introduction to Mathematical Proof' classes. We've come to be quite dependent on algebra, for good reason. But, we seem to forget that there are methods that pre-date algebra and use different perspectives to approach the same problem. Before 0 was invented, humans still had a concept of ‘nothing’; and, before x was our basic variable, humans still had a general understanding of ‘unknown’. It certainly would be considerably difficult to have number theory, geometry, calculus, graph theory, etc. and not have algebra, but I don’t think it would be impossible- the Mayans somehow made accurate astronomical predictions and they didn’t have the same tools or connections everyone else did, right?
Good work, Asiya! And we'll hear lots more about Maya mathematics and astronomy in the next few weeks.
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