Jeremy Côté


The above word is one that I think a lot about as a physicist. That’s because there are two ways in which the word is used around me, with one being very detrimental to students.

The first is the mathematical use of “trivial”. This is often tied closely to something being true or a solution by definition. For example, if you are working with a matrix equation of the form Ax = 0 (where A is a matrix and x is a vector), one such solution is x = 0. That would be called the trivial solution. However, there are potentially other solutions where x ≠ 0. Those solutions would be called non-trivial.

I have no problem with this use. It’s simple and precise. The other definition is where I start having problems.

Really, it’s not even a definition. Instead, “trivial” becomes a catch-all term for describing things that are obvious and easy. You will often hear this when physicists talk about a proof being trivial, or the required steps to derive an equation being trivial. They aren’t using the precise, mathematical definition. Instead, they are using the looser concept of trivial.

Why is this bad?

It has to do with the fact that using the word “trivial” in this way induces a value judgement on whatever you’re talking about. When you say something is trivial, you’re saying that it should be clear to everyone who is looking at it.

This might be true in some contexts, but I would argue that it’s much rarer than you would think. For example, if a teacher uses the word “trivial” in class, I start to get worried. That’s because students are almost never at the same level. Therefore, while some might agree with the teacher that these steps are easy, another student might find them baffling at first. This is the nature of education. Not everything is straightforward at the beginning. Using this word ignores the fact that even students within the same class are at different levels.

Imagine how you would feel if a teacher said something was obvious, most people around you nodded in agreement, and you just couldn’t make sense of the argument. Actually, scratch that. If you have ever been in school, there’s a good chance you have experienced this firsthand. I know I have, and it’s not a fun feeling.

Nobody wants to feel slow or stupid, but using this kind of language accomplishes exactly that. For basically no gain, people who use this word elevate the chance that they make others feel unintelligent. Is it really worth doing so?

This is why I’ve basically banned this word from my vocabulary. It has its place in technical conversations, but I don’t feel like it’s a burden to go from “the trivial solution” to “the zero solution” (for the matrix equation example). The benefit, on the other hand, is clear: You don’t make people feel stupid. I think that’s a worth goal.

Fostering an inclusive physics community (particularly for students, who will form the future of this community) is hugely important to me. With this small step, we can help people feel more comfortable being beginners.

Remember, things that are obvious are rarely so at first. As soon as you acknowledge, the word “trivial” starts to feel like a relic that needs to be replaced.