I took courses in mathematics all through grammar and secondary school, and even a few at the college level, all without ever really asking myself this simple question – what is math?
My handy shortened edition of the Oxford English Dictionary offers this definition: “a group of related sciences that use a specialized notation to study number, quantity, shape, space, and their interrelated relationships.”
I always love how fancy dictionaries can use so many words to define a concept without ever really defining it in a satisfactory way.
What is arithmetic?
It’s plus signs, minus signs, integers, proofs, charts, and long division – the stuff of nightmares for those of us taught by mean-spirited nuns with hair trigger rulers.
At the same time, math can be beauty – think of riddles, logic, word problems, circuits, programming, robotics, and cosmology, mathematics as the language of science fiction, fantasy, and our very dreams.
In this post, I try to answer this broad and complex question in as direct and meaningful a way as I can. Regardless of any initial panic at the mention of the word, wrapping your head around mathematics as a whole and defining it as simply as you can is a worthy exercise.
The Etymology of “Mathematics”
It’s a trigger word for many, calling to mind hours spent sweating over page after page of repeated exercises, equations, and calculations. Other folks see math as something like a spiritual practice, or at least a creative one. These are people who can, as mathematics professor Jeffrey J. Wanko puts it, “… feel math, rather than do math.”
I like the sound of that.
Where does the word “mathematics” come from?
We get our English word “math” from the Greek máthēma, meaning literally “the thing a person learns.” At its invention, the word that instills fear in grade school kids the world over had nothing at all to do with numbers. The ancient Greeks used the word as a stand-in for the word “study” used as a noun. In fact, to this day modern Greeks use a similar word to refer to any school lesson, regardless of whether or not it involves calculation.
So, when did the word come to refer specifically to the study of numbers?
The best etymology sources I can find can only say “… sometime in the 18th century.”
Before then, English users of the word were referring to what we might call astrology, a study of the positions of the planets, one of the world’s first global scientific pursuits. The change to a number-specific meaning appears to have happened gradually and casually, with no inciting incident.
It stands to reason that, as modern science supplanted astrology, the word scholars used to refer to complex study areas would shift as well.
And in an interesting twist, modern astronomy (a far more reason-based approach to the universe) is a mathematics-heavy field.
A Brief History of Math
Mathematics doesn’t have a tidy history, being a foundational aspect of society that came about at least in part by an accident of nature – the fact that we have fingers and toes.
Math has been a part of recorded history as long as history has been recorded. We know that primitive cultures who failed to create a written language had means of keeping track of numerals, sometimes using sophisticated systems of knotted ropes or other handheld gadgets.
As cultures develop wants and needs, mathematics flows in. Knotted ropes are great if all you need to do is count pelts or a small number of people – calculating the positions of stars and planets and predicting weather require more sophisticated mathematical languages.
All of the world’s great ancient civilizations (those of India, China, Egypt, Mesopotamia, and the Americas) played a part in creating, codifying, popularizing, and spreading the concepts that we today call mathematics.
Math is a global language, requiring only knowledge of an agreed-upon set of symbols and systems. As such, it is its own lingua franca, a communication method available to you no matter where you were raised.
We have the ancient Sumerians (in present-day southern Iraq) to thank for our various counting systems.
Mathematicians in the Arab world also developed basic arithmetic.
Sumer mathematics made its way around the Babylonian kingdom by 300 BCE, around the time that the Mayan people in Central America were using math to create complex calendar and dating systems that led them to be the world’s first large-scale astronomers.
Our modern concept of zero comes straight from India, an area of the world that also gave us the confusingly named Arabic numerals.
The Perils (& Pleasures) of Math Class
We have math class to blame for our trepidation about numbers. Most of us come into contact with traditional mathematics and numeracy in a school setting. That means our perceptions of the numerical arts come from the ways we were taught, the ways we learned, and the ways we succeeded or failed. I’m convinced that a person’s reaction to this subject depends heavily on the way they were brought up in the language of math.
Thankfully, we have math teachers who work above and beyond their calling as educators to spark a real interest in the nitty-gritty of the field, inspiring students with capital-M Mathematics, avoiding the painful pitfalls that made math-phobes out of most of us.
Take a look at what mathematics teacher Julie Reulbach is doing at her blog I Speak Math. Her lesson “Math-magic for Solving Multi-Step Equations” is a great example of the kind of math instruction middle-schoolers need to take numeracy out of the realm of boilerplate calculations and memorization and reveal it as the philosophical way of thinking it really is.
The gamification of education is as evident in math instruction as in any other field.
Want to create a generation of people who aren’t entirely sure what mathematics is but are 100% sure that they loathe it?
Force people to memorize charts and proofs without real-world practice, pigeonhole or ignore students who struggle with the basics, and use your status as math-wizard to gatekeep the topic at every opportunity.
Math in Everyday Life
Demystifying a subject means taking the fear away and replacing it with knowledge. I thought of a number of ways regular folks like you and me use this particular numerical philosophy every day of our lives, usually without realizing it. Perhaps showing people the ways that math influences their day-to-day will help the general public unlearn their math-phobia.
If you eat three meals a day like I do, you’re a mathematician. Even something simple like heating a microwave meal requires basic numeracy, while adjusting recipes on the fly based on serving size or figuring out how much ground beef to buy for a family dinner can require basic algebra skills.
Drivers are constantly working out geometric patterns and inferring motion and other factors related to safely getting around their city. Planning a road trip? Use those mathematics classes to figure out where you’ll need to stop, how far you can go before your next pit stop, and the better buy on car snacks.
An understanding of geometry and trigonometry isn’t required to play sandlot baseball, but it’s often been said that kids playing games in the street understand more about these mathematics subsets at a corporeal level than academics studying the subjects for years.
I dare you to figure out what to tip on a dinner date without doing some mathematics. The same goes for counting out change for your purchase and counting the change you get back to make sure you aren’t being shorted.
Want to calculate body fat? Need to know how long to run to get your proper cardiovascular exercise? What about planning a jogging, running, or biking route? All of these are driven by math.
When we try to say what math is and isn’t, it is important to make a distinction between mathematics and numeracy.
Generally, math is the underlying philosophy, while “numeracy” is math in action.
Or, as blogger and career math consultant Janice Novakowski puts it, “Mathematics is the discipline, the body of knowledge, content and processes/competencies. Numeracy is using mathematics to interpret and understand issues or solve contextual problems.”
It seems to me that most people are referring to both mathematics and numeracy when they use the word “math” to casually refer to the actions of adding, subtracting, and calculating. For the purpose of trying to come up with a specific definition for the word, I think we should assume that the average person isn’t ready to distinguish between these two things.
So why is it so hard to define, anyway?
The term “steep learning curve” applies.
Higher math is obtuse and requires a huge background in jargon. What starts out as a simple thing we can all do – we even have fingers and toes to help us along the way – quickly gets specialized into something for which we can’t easily produce a definition.
I’m content to sum it up thusly – mathematics is the work we do when we calculate, much the way music is what we make when we sing or play musical instruments.
Math is a language that we can learn without specific instruction, in the case of basic counting and figuring. But to really engage with the world around us, we need to study the ways numbers interact on a deeper level.
Answering the question “What is math?” means rethinking what we mean when we use the m-word.
I like the way Dr. Tai-Danae Bradley of Google X sums things up: “Mathematics is a language – a language of ideas, concepts, and notions. And just like some ideas are best communicated in a particular language, other ideas are best communicated in math.”