I find it amusing that I could probably impress my family at the dinner table by using terminology from my mathematics classes. If I used words like logarithmic, multivariable calculus, hypersurfaces, tangent planes, and linear approximations, I could get them to think that what I’m doing is pretty advanced stuff that they wouldn’t even be able to wrap their heads around.
But that’s not the case. Many of these terms can be explained much more simply. Tangent planes have an easy geometric visualization that is easy to understand, and the linear approximation is essentially the tangent plane! Even those two terms sound complex but are really the same and not that difficult to understand.
Mathematics is good at defining concepts rigorously, but the terminology used in mathematics can make the discipline seem very confusing, even when it isn’t. In this sense, there’s a sort of “masking” going on. The terms can seem more difficult than the concepts themselves.
This is why it’s difficult to communicate mathematics with people outside of the discipline. A lot of the concepts can make sense, but the terminology is difficult if one does not have a solid background in mathematics. And since explaining a concept requires terminology, those outside of the discipline tend to find the whole thing just too complicated.
For some subjects within mathematics, it’s possible to sidestep this issue through the use of visuals. If the concept you’re trying to explain has any sort of geometric intuition, it’s usually enough to show them the geometric situation to gain an understanding of what is going on. Unfortunately, this isn’t possible with many subjects, such as linear algebra or anything involving more than three dimensions. At this point, the mathematics becomes the sole anchor point for a concept, and terminology is important.
Terminology in mathematics is usually precise, offering little wiggle room. However, the language that is used is often inaccessible to the casual observer outside of mathematics. This is a shame, since many mathematical ideas seem complicated from their names, yet are downright simple when explained. As such, there’s a potential to get more people interested in mathematics by breaking down these language barriers. Sure, it’s not necessarily rigorous, but the truth is that those outside of mathematics won’t really care about the more subtle points of a definition. Instead, simply introducing them to the subject is more beneficial in the long run.
Let’s try not to mask mathematics from the public with a veil of complex terminology. Instead, let’s try to move it away whenever someone asks a question concerning mathematics. Hopefully, we can then get many more people interested in mathematical concepts.