Breaking news: the order of operations that elementary schools teach students is not a fundamental law of nature but a convention to make our lives easier. Unfortunately, many students add PEMDAS (as the order of operations is commonly called in the US) to the list of mystical yet unquestionable truths to be memorized and feared. Everyone’s life might be a bit easier if we realized that mathematical expressions are written in a special mathematical language, and that like any language it has its own rules. The English language, for example, has spelling rules that dictate how to spell the word “bite” in the sense of eating and the word “byte” in the sense of data stored in a computer. If it wasn’t for those rules, there would be a great deal more confusion, and different people would read the same sentence in multiple ways. The same is true in mathematics. The notation and rules that we learn in school have developed over centuries to make reading and writing mathematical expressions an unambiguous activity. In the short video below, Henry Reich explores the conventions we use today and reminds us that thinking deeply about even the most basic ideas is more important than memorizing them. If you’re interested in the history of modern mathematical notation Ask Dr. Math has a bit more information.